Ferrara, S; Morales, J F; Samtleben, H
2009-01-01
We apply the entropy formalism to the study of the near-horizon geometry of extremal black p-brane intersections in D>5 dimensional supergravities. The scalar flow towards the horizon is described in terms an effective potential given by the superposition of the kinetic energies of all the forms under which the brane is charged. At the horizon active scalars get fixed to the minima of the effective potential and the entropy function is given in terms of U-duality invariants built entirely out of the black p-brane charges. The resulting entropy function reproduces the central charges of the dual boundary CFT and gives rise to a Bekenstein-Hawking like area law. The results are illustrated in the case of black holes and black string intersections in D=6, 7, 8 supergravities where the effective potentials, attractor equations, moduli spaces and entropy/central charges are worked out in full detail.
Bellucci, S; Marrani, A
2008-01-01
We review recent results in the study of attractor horizon geometries (with non-vanishing Bekenstein-Hawking entropy) of dyonic extremal d=4 black holes in supergravity. We focus on N=2, d=4 ungauged supergravity coupled to a number n_{V} of Abelian vector multiplets, outlining the fundamentals of the special Kaehler geometry of the vector multiplets' scalar manifold (of complex dimension n_{V}), and studying the 1/2-BPS attractors, as well as the non-BPS (non-supersymmetric) ones with non-vanishing central charge. For symmetric special Kaehler geometries, we present the complete classification of the orbits in the symplectic representation of the classical U-duality group (spanned by the black hole charge configuration supporting the attractors), as well as of the moduli spaces of non-BPS attractors (spanned by the scalars which are not stabilized at the black hole event horizon). Finally, we report on an analogous classification for N>2-extended, d=4 ungauged supergravities, in which also the 1/N-BPS attrac...
Fermions, wigs, and attractors
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Gentile, L.G.C., E-mail: lgentile@pd.infn.it [DISIT, Università del Piemonte Orientale, via T. Michel, 11, Alessandria 15120 (Italy); Dipartimento di Fisica “Galileo Galilei”, Università di Padova, via Marzolo 8, 35131 Padova (Italy); INFN, Sezione di Padova, via Marzolo 8, 35131 Padova (Italy); Grassi, P.A., E-mail: pgrassi@mfn.unipmn.it [DISIT, Università del Piemonte Orientale, via T. Michel, 11, Alessandria 15120 (Italy); INFN, Gruppo Collegato di Alessandria, Sezione di Torino (Italy); Marrani, A., E-mail: alessio.marrani@fys.kuleuven.be [ITF KU Leuven, Celestijnenlaan 200D, 3001 Leuven (Belgium); Mezzalira, A., E-mail: andrea.mezzalira@ulb.ac.be [Physique Théorique et Mathématique Université Libre de Bruxelles, C.P. 231, 1050 Bruxelles (Belgium)
2014-05-01
We compute the modifications to the attractor mechanism due to fermionic corrections. In N=2,D=4 supergravity, at the fourth order, we find terms giving rise to new contributions to the horizon values of the scalar fields of the vector multiplets.
Attractors under discretisation
Han, Xiaoying
2017-01-01
This work focuses on the preservation of attractors and saddle points of ordinary differential equations under discretisation. In the 1980s, key results for autonomous ordinary differential equations were obtained – by Beyn for saddle points and by Kloeden & Lorenz for attractors. One-step numerical schemes with a constant step size were considered, so the resulting discrete time dynamical system was also autonomous. One of the aims of this book is to present new findings on the discretisation of dissipative nonautonomous dynamical systems that have been obtained in recent years, and in particular to examine the properties of nonautonomous omega limit sets and their approximations by numerical schemes – results that are also of importance for autonomous systems approximated by a numerical scheme with variable time steps, thus by a discrete time nonautonomous dynamical system.
De la Fuente, Ildefonso M; Cortes, Jesus M; Pelta, David A; Veguillas, Juan
2013-01-01
The experimental observations and numerical studies with dissipative metabolic networks have shown that cellular enzymatic activity self-organizes spontaneously leading to the emergence of a Systemic Metabolic Structure in the cell, characterized by a set of different enzymatic reactions always locked into active states (metabolic core) while the rest of the catalytic processes are only intermittently active. This global metabolic structure was verified for Escherichia coli, Helicobacter pylori and Saccharomyces cerevisiae, and it seems to be a common key feature to all cellular organisms. In concordance with these observations, the cell can be considered a complex metabolic network which mainly integrates a large ensemble of self-organized multienzymatic complexes interconnected by substrate fluxes and regulatory signals, where multiple autonomous oscillatory and quasi-stationary catalytic patterns simultaneously emerge. The network adjusts the internal metabolic activities to the external change by means of flux plasticity and structural plasticity. In order to research the systemic mechanisms involved in the regulation of the cellular enzymatic activity we have studied different catalytic activities of a dissipative metabolic network under different external stimuli. The emergent biochemical data have been analysed using statistical mechanic tools, studying some macroscopic properties such as the global information and the energy of the system. We have also obtained an equivalent Hopfield network using a Boltzmann machine. Our main result shows that the dissipative metabolic network can behave as an attractor metabolic network. We have found that the systemic enzymatic activities are governed by attractors with capacity to store functional metabolic patterns which can be correctly recovered from specific input stimuli. The network attractors regulate the catalytic patterns, modify the efficiency in the connection between the multienzymatic complexes, and stably
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Ildefonso M De la Fuente
Full Text Available BACKGROUND: The experimental observations and numerical studies with dissipative metabolic networks have shown that cellular enzymatic activity self-organizes spontaneously leading to the emergence of a Systemic Metabolic Structure in the cell, characterized by a set of different enzymatic reactions always locked into active states (metabolic core while the rest of the catalytic processes are only intermittently active. This global metabolic structure was verified for Escherichia coli, Helicobacter pylori and Saccharomyces cerevisiae, and it seems to be a common key feature to all cellular organisms. In concordance with these observations, the cell can be considered a complex metabolic network which mainly integrates a large ensemble of self-organized multienzymatic complexes interconnected by substrate fluxes and regulatory signals, where multiple autonomous oscillatory and quasi-stationary catalytic patterns simultaneously emerge. The network adjusts the internal metabolic activities to the external change by means of flux plasticity and structural plasticity. METHODOLOGY/PRINCIPAL FINDINGS: In order to research the systemic mechanisms involved in the regulation of the cellular enzymatic activity we have studied different catalytic activities of a dissipative metabolic network under different external stimuli. The emergent biochemical data have been analysed using statistical mechanic tools, studying some macroscopic properties such as the global information and the energy of the system. We have also obtained an equivalent Hopfield network using a Boltzmann machine. Our main result shows that the dissipative metabolic network can behave as an attractor metabolic network. CONCLUSIONS/SIGNIFICANCE: We have found that the systemic enzymatic activities are governed by attractors with capacity to store functional metabolic patterns which can be correctly recovered from specific input stimuli. The network attractors regulate the catalytic patterns
Ferrara, Sergio; Ferrara, Sergio; Kallosh, Renata
1996-01-01
We find a general principle which allows one to compute the area of the horizon of N=2 extremal black holes as an extremum of the central charge. One considers the ADM mass equal to the central charge as a function of electric and magnetic charges and moduli and extremizes this function in the moduli space (a minimum corresponds to a fixed point of attraction). The extremal value of the square of the central charge provides the area of the horizon, which depends only on electric and magnetic charges. The doubling of unbroken supersymmetry at the fixed point of attraction for N=2 black holes near the horizon is derived via conformal flatness of the Bertotti-Robinson-type geometry. These results provide an explicit model independent expression for the macroscopic Bekenstein-Hawking entropy of N=2 black holes which is manifestly duality invariant. The presence of hypermultiplets in the solution does not affect the area formula. Various examples of the general formula are displayed. We outline the attractor mecha...
Moduli Backreaction on Inflationary Attractors
Roest, Diederik; Werkman, Pelle
2016-01-01
We investigate the interplay between moduli dynamics and inflation, focusing on the KKLT-scenario and cosmological $\\alpha$-attractors. General couplings between these sectors can induce a significant backreaction and potentially destroy the inflationary regime; however, we demonstrate that this generically does not happen for $\\alpha$-attractors. Depending on the details of the superpotential, the volume modulus can either be stable during the entire inflationary trajectory, or become tachyonic at some point and act as a waterfall field, resulting in a sudden end of inflation. In the latter case there is a universal supersymmetric minimum where the scalars end up, preventing the decompactification scenario. The observational predictions conform to the universal value of attractors, fully compatible with the Planck data, with possibly a capped number of e-folds due to the interplay with moduli.
Cosmological attractors in massive gravity
Dubovsky, S; Tkachev, I I
2005-01-01
We study Lorentz-violating models of massive gravity which preserve rotations and are invariant under time-dependent shifts of the spatial coordinates. In the linear approximation the Newtonian potential in these models has an extra ``confining'' term proportional to the distance from the source. We argue that during cosmological expansion the Universe may be driven to an attractor point with larger symmetry which includes particular simultaneous dilatations of time and space coordinates. The confining term in the potential vanishes as one approaches the attractor. In the vicinity of the attractor the extra contribution is present in the Friedmann equation which, in a certain range of parameters, gives rise to the cosmic acceleration.
Attractors: architects of network organization?
Mpitsos, G J
2000-05-01
An attractor is defined here informally as a state of activity toward which a system settles. The settling or relaxation process dissipates the effects produced by external perturbations. In neural systems the relaxation process occurs temporally in the responses of each neuron and spatially across the network such that the activity settles into a subset of the available connections. Within limits, the set of neurons toward which the coordinated neural firing settles can be different from one time to another, and a given set of neurons can generate different types of attractor activity, depending on how the input environment activates the network. Findings such as these indicate that though information resides in the details of neuroanatomic structure, the expression of this information is in the dynamics of attractors. As such, attractors are sources of information that can be used not only in adaptive behavior, but also to effect the neural architecture that generates the attractor. The discussion here focuses on the latter possibility. A conjecture is offered to show that the relaxation dynamic of an attractor may 'guide' activity-dependent learning processes in such a way that synaptic strengths, firing thresholds, the physical connections between neurons, and the size of the network are automatically set in an optimal, interrelated fashion. This inter-relatedness among network parameters would not be expected from more classical, 'switchboard' approaches to neural integration. The ideas are discussed within the context of 'pulse-propagated networks' or equivalently as 'spike-activated networks' in which the specific order in time intervals between action potentials carries important information for cooperative activity to emerge among neurons in a network. Though the proposed ideas are forward-looking, being based on preliminary work in biological and artificial networks, they are testable in biological neural networks reconstructed from identified neurons in
Approximating hidden chaotic attractors via parameter switching
Danca, Marius-F.; Kuznetsov, Nikolay V.; Chen, Guanrong
2018-01-01
In this paper, the problem of approximating hidden chaotic attractors of a general class of nonlinear systems is investigated. The parameter switching (PS) algorithm is utilized, which switches the control parameter within a given set of values with the initial value problem numerically solved. The PS-generated attractor approximates the attractor obtained by averaging the control parameter with the switched values, which represents the hidden chaotic attractor. The hidden chaotic attractors of a generalized Lorenz system and the Rabinovich-Fabrikant system are simulated for illustration.
Ceresole, A; Gnecchi, A; Marrani, A
2009-01-01
We examine few simple extremal black hole configurations of N=8, d=4 supergravity. We first elucidate the relation between the BPS Reissner-Nordstrom black hole and the non-BPS Kaluza-Klein dyonic black hole. Their classical entropy, given by the Bekenstein-Hawking formula, can be reproduced via the attractor mechanism by suitable choices of symplectic frame. Then, we display the embedding of the axion-dilaton black hole into N=8 supergravity.
Cortical computations via transient attractors.
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Oliver L C Rourke
Full Text Available The ability of sensory networks to transiently store information on the scale of seconds can confer many advantages in processing time-varying stimuli. How a network could store information on such intermediate time scales, between typical neurophysiological time scales and those of long-term memory, is typically attributed to persistent neural activity. An alternative mechanism which might allow for such information storage is through temporary modifications to the neural connectivity which decay on the same second-long time scale as the underlying memories. Earlier work that has explored this method has done so by emphasizing one attractor from a limited, pre-defined set. Here, we describe an alternative, a Transient Attractor network, which can learn any pattern presented to it, store several simultaneously, and robustly recall them on demand using targeted probes in a manner reminiscent of Hopfield networks. We hypothesize that such functionality could be usefully embedded within sensory cortex, and allow for a flexibly-gated short-term memory, as well as conferring the ability of the network to perform automatic de-noising, and separation of input signals into distinct perceptual objects. We demonstrate that the stored information can be refreshed to extend storage time, is not sensitive to noise in the system, and can be turned on or off by simple neuromodulation. The diverse capabilities of transient attractors, as well as their resemblance to many features observed in sensory cortex, suggest the possibility that their actions might underlie neural processing in many sensory areas.
Generalized Attractor Points in Gauged Supergravity
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Kachru, Shamit; /Stanford U., Phys. Dept. /SLAC; Kallosh, Renata; /Stanford U., Phys. Dept.; Shmakova, Marina; /KIPAC, Menlo Park /SLAC /Stanford U., Phys. Dept.
2011-08-15
The attractor mechanism governs the near-horizon geometry of extremal black holes in ungauged 4D N=2 supergravity theories and in Calabi-Yau compactifications of string theory. In this paper, we study a natural generalization of this mechanism to solutions of arbitrary 4D N=2 gauged supergravities. We define generalized attractor points as solutions of an ansatz which reduces the Einstein, gauge field, and scalar equations of motion to algebraic equations. The simplest generalized attractor geometries are characterized by non-vanishing constant anholonomy coefficients in an orthonormal frame. Basic examples include Lifshitz and Schroedinger solutions, as well as AdS and dS vacua. There is a generalized attractor potential whose critical points are the attractor points, and its extremization explains the algebraic nature of the equations governing both supersymmetric and non-supersymmetric attractors.
Place Cells, Grid Cells, Attractors, and Remapping
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Kathryn J. Jeffery
2011-01-01
Full Text Available Place and grid cells are thought to use a mixture of external sensory information and internal attractor dynamics to organize their activity. Attractor dynamics may explain both why neurons react coherently following sufficiently large changes to the environment (discrete attractors and how firing patterns move smoothly from one representation to the next as an animal moves through space (continuous attractors. However, some features of place cell behavior, such as the sometimes independent responsiveness of place cells to environmental change (called “remapping”, seem hard to reconcile with attractor dynamics. This paper suggests that the explanation may be found in an anatomical separation of the two attractor systems coupled with a dynamic contextual modulation of the connection matrix between the two systems, with new learning being back-propagated into the matrix. Such a scheme could explain how place cells sometimes behave coherently and sometimes independently.
Topological classification of scattered IFS-attractors
Nowak, Magdalena
2012-01-01
We study countable compact spaces as potential attractors of iterated function systems. We give an example of a convergent sequence in the real line which is not an IFS-attractor and for each countable ordinal $\\delta$ we show that a countable compact space of height $\\delta+1$ can be embedded in the real line so that it becomes the attractor of an IFS. On the other hand, we show that a scattered compact metric space of limit height is never an IFS-attractor.
Global attractor alphabet of neural firing modes.
Baram, Yoram
2013-08-01
The elementary set, or alphabet, of neural firing modes is derived from the widely accepted conductance-based rectified firing-rate model. The firing dynamics of interacting neurons are shown to be governed by a multidimensional bilinear threshold discrete iteration map. The parameter-dependent global attractors of the map morph into 12 attractor types. Consistent with the dynamic modes observed in biological neuronal firing, the global attractor alphabet is highly visual and intuitive in the scalar, single-neuron case. As synapse permeability varies from high depression to high potentiation, the global attractor type varies from chaotic to multiplexed, oscillatory, fixed, and saturated. As membrane permeability decreases, the global attractor transforms from active to passive state. Under the same activation, learning and retrieval end at the same global attractor. The bilinear threshold structure of the multidimensional map associated with interacting neurons generalizes the global attractor alphabet of neuronal firing modes to multineuron systems. Selective positive or negative activation and neural interaction yield combinatorial revelation and concealment of stored neuronal global attractors.
Black Hole Attractors in Extended Supergravity
Ferrara, Sergio
2007-01-01
We review some aspects of the attractor mechanism for extremal black holes of (not necessarily supersymmetric) theories coupling Einstein gravity to scalars and Maxwell vector fields. Thence, we consider N=2 and N=8, d=4 supergravities, reporting some recent advances on the moduli spaces associated to BPS and non-BPS attractor solutions supported by charge orbits with non-compact stabilizers.
Attractors and basins of dynamical systems
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Attila Dénes
2011-03-01
Full Text Available There are several programs for studying dynamical systems, but none of them is very useful for investigating basins and attractors of higher dimensional systems. Our goal in this paper is to show a new algorithm for finding even chaotic attractors and their basins for these systems. We present an implementation and examples for the use of this program.
Linear response function for coupled hyperbolic attractors
Jiang, M
2004-01-01
We prove that when we take the thermodynamic limit in the context of coupled hyperbolic attractors, Ruelle's derivative formula of the SRB measure with respect to the underlying dynamical system remains true if one of the terms is interpreted appropriately.
Cusps enable line attractors for neural computation
Xiao, Zhuocheng; Zhang, Jiwei; Sornborger, Andrew T.; Tao, Louis
2017-11-01
Line attractors in neuronal networks have been suggested to be the basis of many brain functions, such as working memory, oculomotor control, head movement, locomotion, and sensory processing. In this paper, we make the connection between line attractors and pulse gating in feed-forward neuronal networks. In this context, because of their neutral stability along a one-dimensional manifold, line attractors are associated with a time-translational invariance that allows graded information to be propagated from one neuronal population to the next. To understand how pulse-gating manifests itself in a high-dimensional, nonlinear, feedforward integrate-and-fire network, we use a Fokker-Planck approach to analyze system dynamics. We make a connection between pulse-gated propagation in the Fokker-Planck and population-averaged mean-field (firing rate) models, and then identify an approximate line attractor in state space as the essential structure underlying graded information propagation. An analysis of the line attractor shows that it consists of three fixed points: a central saddle with an unstable manifold along the line and stable manifolds orthogonal to the line, which is surrounded on either side by stable fixed points. Along the manifold defined by the fixed points, slow dynamics give rise to a ghost. We show that this line attractor arises at a cusp catastrophe, where a fold bifurcation develops as a function of synaptic noise; and that the ghost dynamics near the fold of the cusp underly the robustness of the line attractor. Understanding the dynamical aspects of this cusp catastrophe allows us to show how line attractors can persist in biologically realistic neuronal networks and how the interplay of pulse gating, synaptic coupling, and neuronal stochasticity can be used to enable attracting one-dimensional manifolds and, thus, dynamically control the processing of graded information.
Prototypes of attractors in four dimensions
DEFF Research Database (Denmark)
Baier, G.; Thomsen, Jesper Skovhus
1993-01-01
We study an extension of Duffing's equation to three variables with external forcing. Starting from a phase-space preserving chaos, three prototypes of chaotic attractors with a dimension larger than 3 can be derived. We provide examples of hyperchaos and a ''bifractal'' in a four-dimensional how....... The second-order Poincare cross section of hyperchaotic how is qualitatively equivalent to the first-order cross section of Ueda's attractor with the same forcing....
Alternative Attractors of Shallow Lakes
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Marten Scheffer
2001-01-01
Full Text Available Ponds and shallow lakes can be very clear with abundant submerged plants, or very turbid due to a high concentration of phytoplankton and suspended sediment particles. These strongly contrasting ecosystem states have been found to represent alternative attractors with distinct stabilizing feedback mechanisms. In the turbid state, the development of submerged vegetation is prevented by low underwater light levels. The unprotected sediment frequently is resuspended by wave action and by fish searching for food causing a further decrease of transparency. Since there are no plants that could serve as refuges, zooplankton is grazed down by fish to densities insufficient to control algal blooms. In contrast, the clear state in eutrophic shallow lakes is dominated by aquatic macrophytes. The submerged macrophytes prevent sediment resuspension, take up nutrients from the water, and provide a refuge for zooplankton against fish predation. These processes buffer the impacts of increased nutrient loads until they become too high. Consequently, the response of shallow lakes to eutrophication tends to be catastrophic rather than smooth, and various lakes switch back and forth abruptly between a clear and a turbid state repeatedly without obvious external forcing. Importantly, a switch from a turbid to a stable clear state often can be invoked by means of biomanipulation in the form of a temporary reduction of the fish stock.
Noise-driven attractor switching device
Asakawa, Naoki; Hotta, Yasushi; Kanki, Teruo; Kawai, Tomoji; Tabata, Hitoshi
2009-02-01
Problems with artificial neural networks originate from their deterministic nature and inevitable prior learnings, resulting in inadequate adaptability against unpredictable, abrupt environmental change. Here we show that a stochastically excitable threshold unit can be utilized by these systems to partially overcome the environmental change. Using an excitable threshold system, attractors were created that represent quasiequilibrium states into which a system settles until disrupted by environmental change. Furthermore, noise-driven attractor stabilization and switching were embodied by inhibitory connections. Noise works as a power source to stabilize and switch attractors, and endows the system with hysteresis behavior that resembles that of stereopsis and binocular rivalry in the human visual cortex. A canonical model of the ring network with inhibitory connections composed of class 1 neurons also shows properties that are similar to the simple threshold system.
Black Hole Attractors and Pure Spinors
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Hsu, Jonathan P.; Maloney, Alexander; Tomasiello, Alessandro
2006-02-21
We construct black hole attractor solutions for a wide class of N = 2 compactifications. The analysis is carried out in ten dimensions and makes crucial use of pure spinor techniques. This formalism can accommodate non-Kaehler manifolds as well as compactifications with flux, in addition to the usual Calabi-Yau case. At the attractor point, the charges fix the moduli according to {Sigma}f{sub k} = Im(C{Phi}), where {Phi} is a pure spinor of odd (even) chirality in IIB (A). For IIB on a Calabi-Yau, {Phi} = {Omega} and the equation reduces to the usual one. Methods in generalized complex geometry can be used to study solutions to the attractor equation.
Erice Lectures on Black Holes and Attractors
Ferrara, Sergio; Marrani, A
2008-01-01
These lectures give an elementary introduction to the subject of four dimensional black holes (BHs) in supergravity and the Attractor Mechanism in the extremal case. Some thermodynamical properties are discussed and some relevant formulae for the critical points of the BH effective potential are given. The case of Maxwell-Einstein-axion-dilaton (super)gravity is discussed in detail. Analogies among BH entropy and multipartite entanglement of qubits in quantum information theory, as well moduli spaces of extremal BH attractors, are also discussed.
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Llibre, Jaume, E-mail: jllibre@mat.uab.cat [Universitat Autònoma de Barcelona, Departament de Matemàtiques (Spain); Valls, Claudia, E-mail: cvalls@math.ist.utl.pt [Universidade de Lisboa, Departamento de Matemática, Instituto Superior Técnico (Portugal)
2017-06-15
For a dynamical system described by a set of autonomous differential equations, an attractor can be either a point, or a periodic orbit, or even a strange attractor. Recently a new chaotic system with only one parameter has been presented where besides a point attractor and a chaotic attractor, it also has a coexisting attractor limit cycle which makes evident the complexity of such a system. We study using analytic tools the dynamics of such system. We describe its global dynamics near the infinity, and prove that it has no Darboux first integrals.
Sneutrino Inflation with $\\alpha$-attractors
Kallosh, Renata; Roest, Diederik; Wrase, Timm
2016-11-22
Sneutrino inflation employs the fermionic partners of the inflaton and stabilizer field as right-handed neutrinos to realize the seesaw mechanism for light neutrino masses. A crucial ingredient in existing constructions for sneutrino (multi-)natural inflation is an unbroken discrete shift symmetry. We demonstrate that a similar construction applies to $\\alpha$-attractor models. In this case the hyperbolic geometry protects the neutrino Yukawa couplings to the inflaton field, and the masses of leptons and Higgs fields, from blowing up when the inflaton is super-Planckian. We find that the predictions for $n_s$ and $r$ for $\\alpha$-attractor cosmological models, compatible with the current cosmological data, are preserved in the presence of the neutrino sector.
Gravitational waves in $\\alpha-$attractors
Kumar, K Sravan; Moniz, Paulo Vargas; Das, Suratna
2015-01-01
We study inflation in the $\\alpha-$attractor model under a non-slow-roll dynamics with an ansatz proposed by Gong \\& Sasaki \\cite{Gong:2015ypa} of assuming $N=N\\left(\\phi\\right)$. Under this approach, we construct a class of local shapes of inflaton potential that are different from the T-models. We find this type of inflationary scenario predicts an attractor at $n_{s}\\sim0.967$ and $r\\sim0.00055$. In our approach, the non-slow-roll inflaton dynamics are related to the $\\alpha-$parameter which is the curvature of K\\"ahler geometry in the SUGRA embedding of this model.
On some properties of the attractor equations
Energy Technology Data Exchange (ETDEWEB)
Bellucci, Stefano [INFN, Laboratori Nazionali di Frascati, Via Enrico Fermi 40, I-00044 Frascati (Italy)]. E-mail: stefano.bellucci@lnf.infn.it; Ferrara, Sergio [INFN, Laboratori Nazionali di Frascati, Via Enrico Fermi 40, I-00044 Frascati (Italy) and Physics Department, Theory Unit, CERN, CH-1211 Geneva 23 (Switzerland)]. E-mail: sergio.ferrara@cern.ch; Marrani, Alessio [INFN, Laboratori Nazionali di Frascati, Via Enrico Fermi 40, I-00044 Frascati (Italy) and Museo Storico della Fisica e Centro Studi e Ricerche ' Enrico Fermi' , Via Panisperna 89A, Compendio Viminale, I-00184 Rome (Italy)]. E-mail: marrani@lnf.infn.it
2006-04-06
We discuss the attractor equations of N=2, d=4 supergravity in an extremal black hole background with arbitrary electric and magnetic fluxes (charges) for field-strength two-forms. The effective one-dimensional Lagrangian in the radial (evolution) variable exhibits features of a spontaneously broken supergravity theory. Indeed, non-BPS attractor solutions correspond to the vanishing determinant of a (fermionic) gaugino mass matrix. The stability of these solutions is controlled by the data of the underlying special Kahler geometry of the vector multiplets' moduli space. Finally, after analyzing the 1-modulus case more in detail, we briefly comment on the choice of the Kahler gauge and its relevance for the recently discussed entropic functional.
Attractor dynamics in local neuronal networks
Directory of Open Access Journals (Sweden)
Jean-Philippe eThivierge
2014-03-01
Full Text Available Patterns of synaptic connectivity in various regions of the brain are characterized by the presence of synaptic motifs, defined as unidirectional and bidirectional synaptic contacts that follow a particular configuration and link together small groups of neurons. Recent computational work proposes that a relay network (two populations communicating via a third, relay population of neurons can generate precise patterns of neural synchronization. Here, we employ two distinct models of neuronal dynamics and show that simulated neural circuits designed in this way are caught in a global attractor of activity that prevents neurons from modulating their response on the basis of incoming stimuli. To circumvent the emergence of a fixed global attractor, we propose a mechanism of selective gain inhibition that promotes flexible responses to external stimuli. We suggest that local neuronal circuits may employ this mechanism to generate precise patterns of neural synchronization whose transient nature delimits the occurrence of a brief stimulus.
Supersymmetry of Bianchi attractors in gauged supergravity
Chakrabarty, Bidisha; Inbasekar, Karthik; Samanta, Rickmoy
2017-09-01
Bianchi attractors are near horizon geometries with homogeneous symmetries in spatial directions. We construct supersymmetric Bianchi attractors in N =2 ,d =4 , 5 gauged supergravity. In d =4 , we consider gauged supergravity coupled to vector and hypermultiplets. In d =5 , we consider gauged supergravity coupled to vector multiplets with a generic gauging of symmetries of the scalar manifold and the U (1 )R gauging of the R -symmetry. Analyzing the gaugino conditions, we show that when the fermionic shifts do not vanish, there are no supersymmetric Bianchi attractors. This is analogous to the known condition that for maximally supersymmetric solutions, all of the fermionic shifts must vanish. When the central charge satisfies an extremization condition, some of the fermionic shifts vanish and supersymmetry requires that the symmetries of the scalar manifold are not gauged. This allows supersymmetric Bianchi attractors sourced by massless gauge fields and a cosmological constant. In five dimensions in the Bianchi I class, we show that the anisotropic AdS3×R2 solution is 1 /2 BPS (Bogomol'nyi-Prasad-Sommerfield). We also construct a new class of 1 /2 BPS Bianchi III geometries labeled by the central charge. When the central charge takes a special value, the Bianchi III geometry reduces to the known AdS3×H2 solution. For the Bianchi V and VII classes, the radial spinor breaks all of supersymmetry. We briefly discuss the conditions for possible massive supersymmetric Bianchi solutions by generalizing the matter content to include tensor, hypermultiplets, and a generic gauging on the R -symmetry.
d=4 attractors, effective horizon radius, and fake supergravity
Ferrara, Sergio; Gnecchi, Alessandra; Marrani, Alessio
2008-09-01
We consider extremal black hole attractors [both Bogomol’nyi-Prasad-Sommerfield (BPS) and non-BPS] for N=3 and N=5 supergravity in d=4 space-time dimensions. Attractors for matter-coupled N=3 theory are similar to attractors in N=2 supergravity minimally coupled to Abelian vector multiplets. On the other hand, N=5 attractors are similar to attractors in N=4 pure supergravity, and in such theories only (1)/(N)-BPS nondegenerate solutions exist. All the above-mentioned theories have a simple interpretation in the first order (fake supergravity) formalism. Furthermore, such theories do not have a d=5 uplift. Finally we comment on the duality relations among the attractor solutions of N≥2 supergravities sharing the same full bosonic sector.
d=4 Attractors, Effective Horizon Radius and Fake Supergravity
Ferrara, Sergio; Marrani, A
2008-01-01
We consider extremal black hole attractors (both BPS and non-BPS) for N=3 and N=5 supergravity in d=4 space-time dimensions. Attractors for matter-coupled N=3 theory are similar to attractors in N=2 supergravity minimally coupled to Abelian vector multiplets. On the other hand, N=5 attractors are similar to attractors in N=4 pure supergravity, and in such theories only 1\\N-BPS non-degenerate solutions exist. All the above mentioned theories have a simple interpretation in the first order (fake supergravity) formalism. Furthermore, such theories do not have a d=5 uplift. Finally we comment on the ``duality'' relations among the attractor solutions of N\\geq2 supergravities sharing the same full bosonic sector.
A new five-term simple chaotic attractor
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Munmuangsaen, Buncha [Sirindhorn International Institute of Technology, Thammasat University, 131 M.5, Tivanont Road, Bangkadi, Muang, Pathum-Thani, 12000 (Thailand); Srisuchinwong, Banlue, E-mail: banlue@siit.tu.ac.t [Sirindhorn International Institute of Technology, Thammasat University, 131 M.5, Tivanont Road, Bangkadi, Muang, Pathum-Thani, 12000 (Thailand)
2009-10-26
A new chaotic attractor is presented with only five terms in three simple differential equations having fewer terms and simpler than those of existing seven-term or six-term chaotic attractors. Basic dynamical properties of the new attractor are demonstrated in terms of equilibria, Jacobian matrices, non-generalized Lorenz systems, Lyapunov exponents, a dissipative system, a chaotic waveform in time domain, a continuous frequency spectrum, Poincare maps, bifurcations and forming mechanisms of its compound structures.
Black-Hole Attractors in N=1 Supergravity
Andrianopoli, L; Ferrara, Sergio; Trigiante, M; Andrianopoli, Laura; Auria, Riccardo D'; Ferrara, Sergio; Trigiante, Mario
2007-01-01
We study the attractor mechanism for N=1 supergravity coupled to vector and chiral multiplets and compute the attractor equations of these theories. These equations may have solutions depending on the choice of the holomorphic symmetric matrix f_{\\Lambda\\Sigma} which appears in the kinetic lagrangian of the vector sector. Models with non trivial electric-magnetic duality group which have or have not attractor behavior are exhibited. For a particular class of models, based on an N=1 reduction of homogeneous special geometries, the attractor equations are related to the theory of pure spinors.
3rd School on Attractor Mechanism
SAM 2007; The Attractor Mechanism: Proceedings of the INFN-Laboratori Nazionali di Frascati School 2007
2010-01-01
This book is based upon lectures presented in June 2007 at the INFN-Laboratori Nazionali di Frascati School on Attractor Mechanism, directed by Stefano Bellucci. The symposium included such prestigious lecturers as S. Ferrara, M. Gunaydin, P. Levay, and T. Mohaupt. All lectures were given at a pedagogical, introductory level, which is reflected in the specific "flavor" of this volume. The book also benefits from extensive discussions about, and related reworking of, the various contributions. In addition, this volume contains contributions originating from short presentations of rece
Infinite-Scroll Attractor Generated by the Complex Pendulum Model
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Sachin Bhalekar
2013-01-01
Full Text Available We report the finding of the simple nonlinear autonomous system exhibiting infinite-scroll attractor. The system is generated from the pendulum equation with complex-valued function. The proposed system is having infinitely many saddle points of index two which are responsible for the infinite-scroll attractor.
Existence of global attractor for the Trojan Y Chromosome model
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Xiaopeng Zhao
2012-04-01
Full Text Available This paper is concerned with the long time behavior of solution for the equation derived by the Trojan Y Chromosome (TYC model with spatial spread. Based on the regularity estimates for the semigroups and the classical existence theorem of global attractors, we prove that this equations possesses a global attractor in $H^k(\\Omega^4$ $(k\\geq 0$ space.
Novel Principles and Methods for Computing with Attractors
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Horia-Nicolai Teodorescu
2001-08-01
Full Text Available We briefly analyze several issues related to the "computing with attractors" domain. We present a point of view on the topic and several new concepts, methods, and techniques for computing with attractors. We discuss applications where this method may prove useful. We answer several questions related to the usefulness of this computing paradigm.
Google matrix, dynamical attractors, and Ulam networks.
Shepelyansky, D L; Zhirov, O V
2010-03-01
We study the properties of the Google matrix generated by a coarse-grained Perron-Frobenius operator of the Chirikov typical map with dissipation. The finite-size matrix approximant of this operator is constructed by the Ulam method. This method applied to the simple dynamical model generates directed Ulam networks with approximate scale-free scaling and characteristics being in certain features similar to those of the world wide web with approximate scale-free degree distributions as well as two characteristics similar to the web: a power-law decay in PageRank that mirrors the decay of PageRank on the world wide web and a sensitivity to the value alpha in PageRank. The simple dynamical attractors play here the role of popular websites with a strong concentration of PageRank. A variation in the Google parameter alpha or other parameters of the dynamical map can drive the PageRank of the Google matrix to a delocalized phase with a strange attractor where the Google search becomes inefficient.
Extremal Black Hole and Flux Vacua Attractors
Bellucci, S; Kallosh, R; Marrani, A
2007-01-01
These lectures provide a pedagogical, introductory review of the so-called Attractor Mechanism (AM) at work in two different 4-dimensional frameworks: extremal black holes in N=2 supergravity and N=1 flux compactifications. In the first case, AM determines the stabilization of scalars at the black hole event horizon purely in terms of the electric and magnetic charges, whereas in the second context the AM is responsible for the stabilization of the universal axion-dilaton and of the (complex structure) moduli purely in terms of the RR and NSNS fluxes. Two equivalent approaches to AM, namely the so-called ``criticality conditions'' and ``New Attractor'' ones, are analyzed in detail in both frameworks, whose analogies and differences are discussed. Also a stringy analysis of both frameworks (relying on Hodge-decomposition techniques) is performed, respectively considering Type IIB compactified on $CY_{3}$ and its orientifolded version, associated with $\\frac{CY_{3}\\times T^{2}}{\\mathbb{Z}_{2}}$. Finally, recent...
Attractor mechanism as a distillation procedure
Lévay, Péter; Szalay, Szilárd
2010-07-01
In a recent paper it was shown that for double extremal static spherical symmetric BPS black hole solutions in the STU model the well-known process of moduli stabilization at the horizon can be recast in a form of a distillation procedure of a three-qubit entangled state of a Greenberger-Horne-Zeilinger type. By studying the full flow in moduli space in this paper we investigate this distillation procedure in more detail. We introduce a three-qubit state with amplitudes depending on the conserved charges, the warp factor, and the moduli. We show that for the recently discovered non-BPS solutions it is possible to see how the distillation procedure unfolds itself as we approach the horizon. For the non-BPS seed solutions at the asymptotically Minkowski region we are starting with a three-qubit state having seven nonequal nonvanishing amplitudes and finally at the horizon we get a Greenberger-Horne-Zeilinger state with merely four nonvanishing ones with equal magnitudes. The magnitude of the surviving nonvanishing amplitudes is proportional to the macroscopic black hole entropy. A systematic study of such attractor states shows that their properties reflect the structure of the fake superpotential. We also demonstrate that when starting with the very special values for the moduli corresponding to flat directions the uniform structure at the horizon deteriorates due to errors generalizing the usual bit flips acting on the qubits of the attractor states.
A Chaotic Attractor in Delayed Memristive System
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Lidan Wang
2012-01-01
Full Text Available Over the last three decades, theoretical design and circuitry implementation of various chaotic generators by simple electronic circuits have been a key subject of nonlinear science. In 2008, the successful development of memristor brings new activity for this research. Memristor is a new nanometre-scale passive circuit element, which possesses memory and nonlinear characteristics. This makes it have a unique charm to attract many researchers’ interests. In this paper, memristor, for the first time, is introduced in a delayed system to design a signal generator to produce chaotic behaviour. By replacing the nonlinear function with memristors in parallel, the memristor oscillator exhibits a chaotic attractor. The simulated results demonstrate that the performance is well predicted by the mathematical analysis and supports the viability of the design.
Multi-field conformal cosmological attractors
Kallosh, Renata; Linde, Andrei
2013-12-01
We describe a broad class of multi-field inflationary models with spontaneously broken conformal invariance. It generalizes the recently discovered class of cosmological attractors with a single inflaton field [1]. In the new multi-field theories, just as in the single-field models of [1], the moduli space has a boundary (Kähler cone) in terms of the original homogeneous conformal variables. Upon spontaneous breaking of the conformal invariance and switching to the Einstein frame, this boundary moves to infinity in terms of the canonically normalized inflaton field. This results in the exponential stretching and flattening of scalar potentials in the vicinity of the boundary of the moduli space, which makes even very steep potentials perfectly suitable for the slow-roll inflation. These theories, just like their single-field versions, typically lead to inflationary perturbations with ns = 1-2/N and r = 12/N2, where N is the number of e-foldings.
Strange Attractor in Immunology of Tumor Growth
Voitikova, M
1997-01-01
The time delayed cytotoxic T-lymphocyte response on the tumor growth has been developed on the basis of discrete approximation (2-dimensional map). The growth kinetic has been described by logistic law with growth rate being the bifurcation parameter. Increase in the growth rate results in instability of the tumor state and causes period-doubling bifurcations in the immune+tumor system. For larger values of tumor growth rate a strange attractor has been observed. The model proposed is able to describe the metastable-state production when time series data of the immune state and the number of tumor cells are irregular and unpredictable. This metastatic disease may be caused not by exterior (medical) factors, but interior density dependent ones.
An infinite 3-D quasiperiodic lattice of chaotic attractors
Li, Chunbiao; Sprott, Julien Clinton
2018-02-01
A new dynamical system based on Thomas' system is described with infinitely many strange attractors on a 3-D spatial lattice. The mechanism for this multistability is associated with the disturbed offset boosting of sinusoidal functions with different spatial periods. Therefore, the initial condition for offset boosting can trigger a bifurcation, and consequently infinitely many attractors emerge simultaneously. One parameter of the sinusoidal nonlinearity can increase the frequency of the second order derivative of the variables rather than the first order and therefore increase the Lyapunov exponents accordingly. We show examples where the lattice is periodic and where it is quasiperiodic, that latter of which has an infinite variety of attractor types.
No fermionic wigs for BPS attractors in 5 dimensions
Energy Technology Data Exchange (ETDEWEB)
Gentile, Lorenzo G.C., E-mail: lgentile@pd.infn.it [DISIT, Università del Piemonte Orientale, via T. Michel, 11, Alessandria I-15120 (Italy); Dipartimento di Fisica “Galileo Galilei”, Università di Padova, via Marzolo 8, I-35131 Padova (Italy); INFN, Sezione di Padova, via Marzolo 8, I-35131 Padova (Italy); Grassi, Pietro A., E-mail: pgrassi@mfn.unipmn.it [DISIT, Università del Piemonte Orientale, via T. Michel, 11, Alessandria I-15120 (Italy); INFN – Gruppo Collegato di Alessandria – Sezione di Torino (Italy); Marrani, Alessio, E-mail: alessio.marrani@fys.kuleuven.be [Instituut voor Theoretische Fysica, KU Leuven, Celestijnenlaan 200D, B-3001 Leuven (Belgium); Mezzalira, Andrea, E-mail: andrea.mezzalira@ulb.ac.be [Physique Théorique et Mathématique, Université Libre de Bruxelles, C.P. 231, B-1050 Bruxelles (Belgium); Sabra, Wafic A., E-mail: ws00@aub.edu.lb [Centre for Advanced Mathematical Sciences and Physics Department, American University of Beirut (Lebanon)
2014-07-30
We analyze the fermionic wigging of 1/2-BPS (electric) extremal black hole attractors in N=2, D=5 ungauged Maxwell–Einstein supergravity theories, by exploiting anti-Killing spinors supersymmetry transformations. Regardless of the specific data of the real special geometry of the manifold defining the scalars of the vector multiplets, and differently from the D=4 case, we find that there are no corrections for the near-horizon attractor value of the scalar fields; an analogous result also holds for 1/2-BPS (magnetic) extremal black string. Thus, the attractor mechanism receives no fermionic corrections in D=5 (at least in the BPS sector)
Attractor dynamics in the hippocampal representation of the local environment.
Wills, Tom J; Lever, Colin; Cacucci, Francesca; Burgess, Neil; O'Keefe, John
2005-05-06
Memories are thought to be attractor states of neuronal representations, with the hippocampus a likely substrate for context-dependent episodic memories. However, such states have not been directly observed. For example, the hippocampal place cell representation of location was previously found to respond continuously to changes in environmental shape alone. We report that exposure to novel square and circular environments made of different materials creates attractor representations for both shapes: Place cells abruptly and simultaneously switch between representations as environmental shape changes incrementally. This enables study of attractor dynamics in a cognitive representation and may correspond to the formation of distinct contexts in context-dependent memory.
Partially unstable attractors in networks of forced integrate-and-fire oscillators
Zou, Hai-Lin; Deng, Zi-Chen; Hu, Wei-Peng; Aihara, Kazuyuki; Lai, Ying-Cheng
2017-01-01
The asymptotic attractors of a nonlinear dynamical system play a key role in the long-term physically observable behaviors of the system. The study of attractors and the search for distinct types of attractor have been a central task in nonlinear dynamics. In smooth dynamical systems, an attractor is often enclosed completely in its basin of attraction with a finite distance from the basin boundary. Recent works have uncovered that, in neuronal networks, unstable attractors with a remote basi...
Hyperbolic Plykin attractor can exist in neuron models
DEFF Research Database (Denmark)
Belykh, V.; Belykh, I.; Mosekilde, Erik
2005-01-01
Strange hyperbolic attractors are hard to find in real physical systems. This paper provides the first example of a realistic system, a canonical three-dimensional (3D) model of bursting neurons, that is likely to have a strange hyperbolic attractor. Using a geometrical approach to the study...... of the neuron model, we derive a flow-defined Poincare map giving ail accurate account of the system's dynamics. In a parameter region where the neuron system undergoes bifurcations causing transitions between tonic spiking and bursting, this two-dimensional map becomes a map of a disk with several periodic...... holes. A particular case is the map of a disk with three holes, matching the Plykin example of a planar hyperbolic attractor. The corresponding attractor of the 3D neuron model appears to be hyperbolic (this property is not verified in the present paper) and arises as a result of a two-loop (secondary...
Attractors for stochastic strongly damped plate equations with additive noise
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Wenjun Ma
2013-04-01
Full Text Available We study the asymptotic behavior of stochastic plate equations with homogeneous Neumann boundary conditions. We show the existence of an attractor for the random dynamical system associated with the equation.
Algorithms for Finding Small Attractors in Boolean Networks
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Hayashida Morihiro
2007-01-01
Full Text Available A Boolean network is a model used to study the interactions between different genes in genetic regulatory networks. In this paper, we present several algorithms using gene ordering and feedback vertex sets to identify singleton attractors and small attractors in Boolean networks. We analyze the average case time complexities of some of the proposed algorithms. For instance, it is shown that the outdegree-based ordering algorithm for finding singleton attractors works in time for , which is much faster than the naive time algorithm, where is the number of genes and is the maximum indegree. We performed extensive computational experiments on these algorithms, which resulted in good agreement with theoretical results. In contrast, we give a simple and complete proof for showing that finding an attractor with the shortest period is NP-hard.
Black-Scholes theory for an underlying with multiple attractors
Herzberg, Frederik
2008-01-01
A valuation theory for derivatives on an underlying that is subject to multiple attractors is proposed, the economic justification being attraction-adjusted hedging. In non-critical regions -- outside the boundaries of the attractor regions -- a European option price can be viewed as a derivative on an underlying with a mean-reverting law, such as a commodity price, however with a different payoff function.
Strange nonchaotic attractors in quasiperiodically driven Izhikevich neuron models
Kim, Jae Seok; Kim, Youngtae
2012-02-01
Evidence for the existence of a strange nonchaotic attractor (SNA) in a two-frequency quasiperiodically driven Izhikevich neuron model is presented. In this study, we found that the SNA is formed by a Heagy-Hammel mechanism because the SNA arises as Poincare sections of a period-doubled torus attractor collides with its unstable parent. Analyses of the fractal dimension, autocorrelation function, power spectral density, power spectral distribution function and interspike interval distribution function also support the existence of the SNA.
Structure of attractors and estimates of their fractal dimension
Matheus Cheque Bortolan
2013-01-01
This work is dedicated to the study of the structure of attractors of dynamical systems with the objective of estimating their fractal dimension. First we study the case of exponential global attractors of some generalized gradient-like semigroups in a general Banach space, and estimate their fractal dimension in terms of themaximumof the dimension of the local unstablemanifolds of the isolated invariant sets, Lipschitz properties of the semigroup and rate of exponential attraction. We also g...
Quintessential inflation with α-attractors
Dimopoulos, Konstantinos; Owen, Charlotte
2017-06-01
A novel approach to quintessential inflation model building is studied, within the framework of α-attractors, motivated by supergravity theories. Inflationary observables are in excellent agreement with the latest CMB observations, while quintessence explains the dark energy observations without any fine-tuning. The model is kept intentionally minimal, avoiding the introduction of many degrees of freedom, couplings and mass scales. In stark contrast to ΛCDM, for natural values of the parameters, the model attains transient accelerated expansion, which avoids the future horizon problem, while it maintains the field displacement mildly sub-Planckian such that the flatness of the quintessential tail is not lifted by radiative corrections and violations of the equivalence principle (fifth force) are under control. In particular, the required value of the cosmological constant is near the eletroweak scale. Attention is paid to the reheating of the Universe, which avoids gravitino overproduction and respects nucleosynthesis constraints. Kination is treated in a model independent way. A spike in gravitational waves, due to kination, is found not to disturb nucleosynthesis as well.
Attractors and soak times in artisanal fi shing with traps
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Evandro Figueiredo Sebastiani
2009-12-01
Full Text Available Traps are used by artisanal fishers as fishing gear in places where other fishing modalities are impeded or limited. The advantage of this type of fishing modality is the possibility of keeping fish alive and in the case of capturing species of low commercial value or size below the permitted minimum this fishing gear allows the release of such specimens back to nature, resulting in a sustainability aspect to the use of this fishing gear. This study aims to evaluate the effects of different attractors and times of submersion on the efficiency of the traps used. Sardines, shrimps and trash fish were employed as attractors. To evaluate the soak time, two periods were tested: 24 and 96 hours. The sardines, used as the attractor, resulted in a production of 1,296.4 ± 397.4g, significantly superior (p <0.05 to other attractors. In relation to the soak time, the period of 24 hours resulted in an average production of 1,719.2 ± 866.0g, significantly (p <0.05 superior to the period of 96 hours. The results led to the conclusion that to optimize this capture by fishing gear, sardines should be used as the attractor, together with a soak time of 24 hours.
Robustness and information propagation in attractors of Random Boolean Networks.
Lloyd-Price, Jason; Gupta, Abhishekh; Ribeiro, Andre S
2012-01-01
Attractors represent the long-term behaviors of Random Boolean Networks. We study how the amount of information propagated between the nodes when on an attractor, as quantified by the average pairwise mutual information (I(A)), relates to the robustness of the attractor to perturbations (R(A)). We find that the dynamical regime of the network affects the relationship between I(A) and R(A). In the ordered and chaotic regimes, I(A) is anti-correlated with R(A), implying that attractors that are highly robust to perturbations have necessarily limited information propagation. Between order and chaos (for so-called "critical" networks) these quantities are uncorrelated. Finite size effects cause this behavior to be visible for a range of networks, from having a sensitivity of 1 to the point where I(A) is maximized. In this region, the two quantities are weakly correlated and attractors can be almost arbitrarily robust to perturbations without restricting the propagation of information in the network.
Upper Semicontinuity of Attractors for a Non-Newtonian Fluid under Small Random Perturbations
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Jianxin Luo
2014-01-01
Full Text Available This paper investigates the limiting behavior of attractors for a two-dimensional incompressible non-Newtonian fluid under small random perturbations. Under certain conditions, the upper semicontinuity of the attractors for diminishing perturbations is shown.
Separation of attractors in 1-modulus quantum corrected special geometry
Bellucci, S; Marrani, A; Shcherbakov, A
2008-01-01
We study the solutions to the N=2, d=4 Attractor Equations in a dyonic, extremal, static, spherically symmetric and asymptotically flat black hole background, in the simplest case of perturbative quantum corrected cubic Special Kahler geometry consistent with continuous axion-shift symmetry, namely in the 1-modulus Special Kahler geometry described (in a suitable special symplectic coordinate) by the holomorphic Kahler gauge-invariant prepotential F=t^3+i*lambda, with lambda real. By performing computations in the ``magnetic'' charge configuration, we find evidence for interesting phenomena (absent in the classical limit of vanishing lambda). Namely, for a certain range of the quantum parameter lambda we find a ``splitting'' of attractors, i.e. the existence of multiple solutions to the Attractor Equations for fixed supporting charge configuration. This corresponds to the existence of ``area codes'' in the radial evolution of the scalar t, determined by the various disconnected regions of the moduli space, wh...
Topological and metric properties of Henon-type strange attractors
Cvitanovic, Predrag; Gunaratne, Gemunu H.; Procaccia, Itamar
1988-08-01
A set of all periodic points of Henon-type mappings is used to develop a theory of the topological and metric properties of their attractors. The topology of a Henon-type attractor is conveniently represented by a two-dimensional symbol plane, with the allowed and disallowed orbits cleanly separated by the 'pruning front'. The pruning front is a function discontinuous on every binary rational number, but for maps with finite dissipation less than 1, it is well approximated by a few steps, or, in the symbolic dynamics language, by a finite grammar. Thus equipped with the complete list of allowed periodic points, the physical attractor is reconstructed by piecing together the linearized neighborhoods of all periodic points of cycle length n. This representation is used to compute the singularity spectrum f(alpha).
Classification of attractors for systems of identical coupled Kuramoto oscillators
Energy Technology Data Exchange (ETDEWEB)
Engelbrecht, Jan R. [Department of Physics, Boston College, Chestnut Hill, Massachusetts 02467 (United States); Mirollo, Renato [Department of Mathematics, Boston College, Chestnut Hill, Massachusetts 02467 (United States)
2014-03-15
We present a complete classification of attractors for networks of coupled identical Kuramoto oscillators. In such networks, each oscillator is driven by the same first-order trigonometric function, with coefficients given by symmetric functions of the entire oscillator ensemble. For N≠3 oscillators, there are four possible types of attractors: completely synchronized fixed points or limit cycles, and fixed points or limit cycles where all but one of the oscillators are synchronized. The case N = 3 is exceptional; systems of three identical Kuramoto oscillators can also posses attracting fixed points or limit cycles with all three oscillators out of sync, as well as chaotic attractors. Our results rely heavily on the invariance of the flow for such systems under the action of the three-dimensional group of Möbius transformations, which preserve the unit disc, and the analysis of the possible limiting configurations for this group action.
On the hydrodynamic attractor of Yang-Mills plasma
Spaliński, Michał
2018-01-01
There is mounting evidence suggesting that relativistic hydrodynamics becomes relevant for the physics of quark-gluon plasma as the result of nonhydrodynamic modes decaying to an attractor apparent even when the system is far from local equilibrium. Here we determine this attractor for Bjorken flow in N = 4 supersymmetric Yang-Mills theory (SYM) using Borel summation of the gradient expansion of the expectation value of the energy momentum tensor. By comparing the result to numerical simulations of the flow based on the AdS/CFT correspondence we show that it provides an accurate and unambiguous approximation of the hydrodynamic attractor in this system. This development has important implications for the formulation of effective theories of hydrodynamics.
Generating multi-scroll chaotic attractors by thresholding
Energy Technology Data Exchange (ETDEWEB)
Lue Jinhu [Institute of Systems Science, Academy of Mathematics and Systems Science, Chinese Academy of Sciences, Beijing 100080 (China)], E-mail: jhlu@iss.ac.cn; Murali, K. [Department of Physics, Anna University, Chennai 600 025 (India)], E-mail: kmurali@annauniv.edu; Sinha, Sudeshna [Institute of Mathematical Sciences, Taramani, Chennai 600 113 (India)], E-mail: sudeshna@imsc.res.in; Leung, Henry [Department of Electrical and Computer Engineering, University of Calgary, Calgary, T2N 1N4 (Canada); Aziz-Alaoui, M.A. [Applied Mathematics Laboratory, University of Le Havre, BP 540, 76058 Le Havre Cedex (France)
2008-04-28
This Letter proposes a novel thresholding approach for creating multi-scroll chaotic attractors. The general jerk circuit and Chua's circuit with sine nonlinearity are then used as two representative examples to show the working principle of this method. The controlled jerk circuit can generate various limit cycles and multi-scroll chaotic attractors by tuning the thresholds and the width of inner threshold plateau. The dynamic mechanism of threshold control is further explored by analyzing the system dynamical behaviors. In particular, this approach is effective and easy to be implemented since we only need to monitor the threshold variables or their functions and then reset them if they exceed the desired thresholds. Furthermore, two simple block circuit diagrams with threshold controllers are designed for the implementations of 1, 2, 3-scroll chaotic attractors. It indicates the potential engineering applications for various chaos-based information systems.
Generating multi-scroll chaotic attractors by thresholding
Lü, Jinhu; Murali, K.; Sinha, Sudeshna; Leung, Henry; Aziz-Alaoui, M. A.
2008-04-01
This Letter proposes a novel thresholding approach for creating multi-scroll chaotic attractors. The general jerk circuit and Chua's circuit with sine nonlinearity are then used as two representative examples to show the working principle of this method. The controlled jerk circuit can generate various limit cycles and multi-scroll chaotic attractors by tuning the thresholds and the width of inner threshold plateau. The dynamic mechanism of threshold control is further explored by analyzing the system dynamical behaviors. In particular, this approach is effective and easy to be implemented since we only need to monitor the threshold variables or their functions and then reset them if they exceed the desired thresholds. Furthermore, two simple block circuit diagrams with threshold controllers are designed for the implementations of 1, 2, 3-scroll chaotic attractors. It indicates the potential engineering applications for various chaos-based information systems.
Co-existing hidden attractors in a radio-physical oscillator system
DEFF Research Database (Denmark)
Kuznetsov, A. P.; Kuznetsov, S. P.; Mosekilde, Erik
2015-01-01
, this paper describes the formation of several different coexisting sets of hidden attractors, including the simultaneous presence of a pair of coinciding quasiperiodic attractors and of two mutually symmetric chaotic attractors. We follow the dynamics of the system as a function of the basic oscillator...
Attractor for a Viscous Coupled Camassa-Holm Equation
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Tian Lixin
2010-01-01
Full Text Available The global existence of solution to a viscous coupled Camassa-Holm equation with the periodic boundary condition is investigated. We obtain the compact and bounded absorbing set and the existence of the global attractor for the viscous coupled Camassa-Holm equation in by uniform prior estimate.
Approximating Attractors of Boolean Networks by Iterative CTL Model Checking.
Klarner, Hannes; Siebert, Heike
2015-01-01
This paper introduces the notion of approximating asynchronous attractors of Boolean networks by minimal trap spaces. We define three criteria for determining the quality of an approximation: "faithfulness" which requires that the oscillating variables of all attractors in a trap space correspond to their dimensions, "univocality" which requires that there is a unique attractor in each trap space, and "completeness" which requires that there are no attractors outside of a given set of trap spaces. Each is a reachability property for which we give equivalent model checking queries. Whereas faithfulness and univocality can be decided by model checking the corresponding subnetworks, the naive query for completeness must be evaluated on the full state space. Our main result is an alternative approach which is based on the iterative refinement of an initially poor approximation. The algorithm detects so-called autonomous sets in the interaction graph, variables that contain all their regulators, and considers their intersection and extension in order to perform model checking on the smallest possible state spaces. A benchmark, in which we apply the algorithm to 18 published Boolean networks, is given. In each case, the minimal trap spaces are faithful, univocal, and complete, which suggests that they are in general good approximations for the asymptotics of Boolean networks.
Exploring Strange Nonchaotic Attractors through Jacobian Elliptic Functions
Garcia-Hoz, A. Martinez; Chacon, R.
2011-01-01
We demonstrate the effectiveness of Jacobian elliptic functions (JEFs) for inquiring into the reshaping effect of quasiperiodic forces in nonlinear nonautonomous systems exhibiting strange nonchaotic attractors (SNAs). Specifically, we characterize analytically and numerically some reshaping-induced transitions starting from SNAs in the context of…
MAXIMUM-LIKELIHOOD-ESTIMATION OF THE ENTROPY OF AN ATTRACTOR
SCHOUTEN, JC; TAKENS, F; VANDENBLEEK, CM
In this paper, a maximum-likelihood estimate of the (Kolmogorov) entropy of an attractor is proposed that can be obtained directly from a time series. Also, the relative standard deviation of the entropy estimate is derived; it is dependent on the entropy and on the number of samples used in the
On the importance of the convergence to climate attractors
Drótos, Gábor; Bódai, Tamás; Tél, Tamás
2017-06-01
Ensemble approaches are becoming widely used in climate research. In contrast to weather forecast, however, in the climatic context one is interested in long-time properties, those arising on the scale of several decades. The well-known strong internal variability of the climate system implies the existence of a related dynamical attractor with chaotic properties. Under the condition of climate change this should be a snapshot attractor, naturally arising in an ensemble-based framework. Although ensemble averages can be evaluated at any instant of time, results obtained during the process of convergence of the ensemble towards the attractor are not relevant from the point of view of climate. In simulations, therefore, attention should be paid to whether the convergence to the attractor has taken place. We point out that this convergence is of exponential character, therefore, in a finite amount of time after initialization relevant results can be obtained. The role of the time scale separation due to the presence of the deep ocean is discussed from the point of view of ensemble simulations.
Attractor horizons in six-dimensional type IIB supergravity
Energy Technology Data Exchange (ETDEWEB)
Astefanesei, Dumitru, E-mail: dumitru.astefanesei@ucv.cl [Instituto de Fisica, Pontificia Universidad Catolica de Valparaiso, Casilla 4059, Valparaiso (Chile); Miskovic, Olivera, E-mail: olivera.miskovic@ucv.cl [Instituto de Fisica, Pontificia Universidad Catolica de Valparaiso, Casilla 4059, Valparaiso (Chile); Olea, Rodrigo, E-mail: rodrigo.olea@unab.cl [Universidad Andres Bello, Departamento de Ciencias Fisicas, Republica 220, Santiago (Chile)
2012-08-14
We consider near horizon geometries of extremal black holes in six-dimensional type IIB supergravity. In particular, we use the entropy function formalism to compute the charges and thermodynamic entropy of these solutions. We also comment on the role of attractor mechanism in understanding the entropy of the Hopf T-dual solutions in type IIA supergravity.
Multistability and hidden attractors in a relay system with hysteresis
DEFF Research Database (Denmark)
Zhusubaliyev, Zhanybai T.; Mosekilde, Erik; Rubanov, Vasily G.
2015-01-01
of the supply voltage. By investigating a four-dimensional model of the experimental relay system we finally show how a variety of hidden periodic, quasiperiodic and chaotic attractors arise, transform and disappear through different bifurcations. (C) 2015 Elsevier B.V. All rights reserved....
Competition between synaptic depression and facilitation in attractor neural networks.
Torres, J.J.; Cortes, J.M.; Marro, J.; Kappen, H.J.
2007-01-01
We study the effect of competition between short-term synaptic depression and facilitation on the dynamic properties of attractor neural networks, using Monte Carlo simulation and a mean-field analysis. Depending on the balance of depression, facilitation, and the underlying noise, the network
Recurrence quantification analysis in Liu's attractor
Energy Technology Data Exchange (ETDEWEB)
Balibrea, Francisco [Universidad de Murcia, Departamento de Matematicas, Campus de Espinardo, 30100 Murcia (Spain)], E-mail: balibrea@um.es; Caballero, M. Victoria [Universidad de Murcia, Departamento de Metodos Cuantitativos para la Economia, Campus de Espinardo, 30100 Murcia (Spain)], E-mail: mvictori@um.es; Molera, Lourdes [Universidad de Murcia, Departamento de Metodos Cuantitativos para la Economia, Campus de Espinardo, 30100 Murcia (Spain)
2008-05-15
Recurrence Quantification Analysis is used to detect transitions chaos to periodical states or chaos to chaos in a new dynamical system proposed by Liu et al. This system contains a control parameter in the second equation and was originally introduced to investigate the forming mechanism of the compound structure of the chaotic attractor which exists when the control parameter is zero.
Estimation of dynamic properties of attractors observed in hollow ...
Indian Academy of Sciences (India)
an infinite dimensional process, may corrupt the true data in phase space for very large value of DIM, resulting incorrect computation of λ1. Therefore, DIM should be kept as minimum as possible but higher than the minimum required one for correct computation. If the dimension of the attractor is not known beforehand, ...
Memory dynamics in attractor networks with saliency weights.
Tang, Huajin; Li, Haizhou; Yan, Rui
2010-07-01
Memory is a fundamental part of computational systems like the human brain. Theoretical models identify memories as attractors of neural network activity patterns based on the theory that attractor (recurrent) neural networks are able to capture some crucial characteristics of memory, such as encoding, storage, retrieval, and long-term and working memory. In such networks, long-term storage of the memory patterns is enabled by synaptic strengths that are adjusted according to some activity-dependent plasticity mechanisms (of which the most widely recognized is the Hebbian rule) such that the attractors of the network dynamics represent the stored memories. Most of previous studies on associative memory are focused on Hopfield-like binary networks, and the learned patterns are often assumed to be uncorrelated in a way that minimal interactions between memories are facilitated. In this letter, we restrict our attention to a more biological plausible attractor network model and study the neuronal representations of correlated patterns. We have examined the role of saliency weights in memory dynamics. Our results demonstrate that the retrieval process of the memorized patterns is characterized by the saliency distribution, which affects the landscape of the attractors. We have established the conditions that the network state converges to unique memory and multiple memories. The analytical result also holds for other cases for variable coding levels and nonbinary levels, indicating a general property emerging from correlated memories. Our results confirmed the advantage of computing with graded-response neurons over binary neurons (i.e., reducing of spurious states). It was also found that the nonuniform saliency distribution can contribute to disappearance of spurious states when they exit.
COSMOS-e{sup '}-soft Higgsotic attractors
Energy Technology Data Exchange (ETDEWEB)
Choudhury, Sayantan [Tata Institute of Fundamental Research, Department of Theoretical Physics, Mumbai (India)
2017-07-15
In this work, we have developed an elegant algorithm to study the cosmological consequences from a huge class of quantum field theories (i.e. superstring theory, supergravity, extra dimensional theory, modified gravity, etc.), which are equivalently described by soft attractors in the effective field theory framework. In this description we have restricted our analysis for two scalar fields - dilaton and Higgsotic fields minimally coupled with Einstein gravity, which can be generalized for any arbitrary number of scalar field contents with generalized non-canonical and non-minimal interactions. We have explicitly used R{sup 2} gravity, from which we have studied the attractor and non-attractor phases by exactly computing two point, three point and four point correlation functions from scalar fluctuations using the In-In (Schwinger-Keldysh) and the δN formalisms. We have also presented theoretical bounds on the amplitude, tilt and running of the primordial power spectrum, various shapes (equilateral, squeezed, folded kite or counter-collinear) of the amplitude as obtained from three and four point scalar functions, which are consistent with observed data. Also the results from two point tensor fluctuations and the field excursion formula are explicitly presented for the attractor and non-attractor phase. Further, reheating constraints, scale dependent behavior of the couplings and the dynamical solution for the dilaton and Higgsotic fields are also presented. New sets of consistency relations between two, three and four point observables are also presented, which shows significant deviation from canonical slow-roll models. Additionally, three possible theoretical proposals have presented to overcome the tachyonic instability at the time of late time acceleration. Finally, we have also provided the bulk interpretation from the three and four point scalar correlation functions for completeness. (orig.)
Inflationary α -attractor cosmology: A global dynamical systems perspective
Alho, Artur; Uggla, Claes
2017-04-01
We study flat Friedmann-Lemaître-Robertson-Walker α -attractor E- and T-models by introducing a dynamical systems framework that yields regularized unconstrained field equations on two-dimensional compact state spaces. This results in both illustrative figures and a complete description of the entire solution spaces of these models, including asymptotics. In particular, it is shown that observational viability, which requires a sufficient number of e -folds, is associated with a particular solution given by a one-dimensional center manifold of a past asymptotic de Sitter state, where the center manifold structure also explains why nearby solutions are attracted to this "inflationary attractor solution." A center manifold expansion yields a description of the inflationary regime with arbitrary analytic accuracy, where the slow-roll approximation asymptotically describes the tangency condition of the center manifold at the asymptotic de Sitter state.
Strong Attractors in Stochastic Adaptive Networks: Emergence and Characterization
Santos, Augusto Almeida; Krishnan, Ramayya; Moura, José M F
2016-01-01
We propose a family of models to study the evolution of ties in a network of interacting agents by reinforcement and penalization of their connections according to certain local laws of interaction. The family of stochastic dynamical systems, on the edges of a graph, exhibits \\emph{good} convergence properties, in particular, we prove a strong-stability result: a subset of binary matrices or graphs -- characterized by certain compatibility properties -- is a global almost sure attractor of the family of stochastic dynamical systems. To illustrate finer properties of the corresponding strong attractor, we present some simulation results that capture, e.g., the conspicuous phenomenon of emergence and downfall of leaders in social networks.
Stability and Multiscroll Attractors of Control Systems via the Abscissa
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Edgar-Cristian Díaz-González
2017-01-01
Full Text Available We present an approach to generate multiscroll attractors via destabilization of piecewise linear systems based on Hurwitz matrix in this paper. First we present some results about the abscissa of stability of characteristic polynomials from linear differential equations systems; that is, we consider Hurwitz polynomials. The starting point is the Gauss–Lucas theorem, we provide lower bounds for Hurwitz polynomials, and by successively decreasing the order of the derivative of the Hurwitz polynomial one obtains a sequence of lower bounds. The results are extended in a straightforward way to interval polynomials; then we apply the abscissa as a measure to destabilize Hurwitz polynomial for the generation of a family of multiscroll attractors based on a class of unstable dissipative systems (UDS of affine linear type.
Coupled flare attractors – a discrete prototype for economic modelling
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Georg C. Hartmann
1999-01-01
Full Text Available A chaotic environment can give rise to “flares” if an autocatalytic variable responds in a multiplicative, threshold-type fashion to the environmental forcing. An “economic unit” similarly depends in its growth behavior on the unpredictable (chaotic? buying habits of its customers, say. It turns out that coupled flare attractors are surprisingly robust in the sense that the resulting “economy” is largely independent of the extent of diffusive coupling used. Some simulations are presented.
Torus-doubling process via strange nonchaotic attractors
Mitsui, Takahito; Uenohara, Seiji; Morie, Takashi; Horio, Yoshihiko; Aihara, Kazuyuki
2012-05-01
Torus-doubling bifurcations typically occur only a finite number of times. It has been assumed that torus-doubling bifurcations in quasiperiodically forced systems are interrupted by the appearance of strange nonchaotic attractors (SNAs). In the present Letter, we study a quasiperiodically forced noninvertible map and report the occurrence of a torus-doubling process via SNAs. The mechanism of this process is numerically clarified. Furthermore, this process is experimentally demonstrated in a switched-capacitor integrated circuit.
High-dimensional chaotic and attractor systems a comprehensive introduction
Ivancevic, Vladimir G
2007-01-01
This is a graduate–level monographic textbook devoted to understanding, prediction and control of high–dimensional chaotic and attractor systems of real life. The objective of the book is to provide the serious reader with a serious scientific tool that will enable the actual performance of competitive research in high–dimensional chaotic and attractor dynamics. The book has nine Chapters. The first Chapter gives a textbook-like introduction into the low-dimensional attractors and chaos. This Chapter has an inspirational character, similar to other books on nonlinear dynamics and deterministic chaos. The second Chapter deals with Smale’s topological transformations of stretching, squeezing and folding (of the system’s phase–space), developed for the purpose of chaos theory. The third Chapter is devoted to Poincaré's 3-body problem and basic techniques of chaos control, mostly of Ott-Grebogi-Yorke type. The fourth Chapter is a review of both Landau’s and topological phase transition theory, as w...
Unstable periodic orbits and attractor of the barotropic ocean model
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E. Kazantsev
1998-01-01
Full Text Available A numerical method for detection of unstable periodic orbits on attractors of nonlinear models is proposed. The method requires similar techniques to data assimilation. This fact facilitates its implementation for geophysical models. This method was used to find numerically several low-period orbits for the barotropic ocean model in a square. Some numerical particularities of application of this method are discussed. Knowledge of periodic orbits of the model helps to explain some of these features like bimodality of probability density functions (PDF of principal parameters. These PDFs have been reconstructed as weighted averages of periodic orbits with weights proportional to the period of the orbit and inversely proportional to the sum of positive Lyapunov exponents. The fraction of time spent in the vicinity of each periodic orbit has been compared with its instability characteristics. The relationship between these values shows the 93% correlation. The attractor dimension of the model has also been approximated as a weighted average of local attractor dimensions in vicinities of periodic orbits.
Non-Equlibrium Driven Dynamics of Continuous Attractors in Place Cell Networks
Zhong, Weishun; Kim, Hyun Jin; Schwab, David; Murugan, Arvind
Attractors have found much use in neuroscience as a means of information processing and decision making. Examples include associative memory with point and continuous attractors, spatial navigation and planning using place cell networks, dynamic pattern recognition among others. The functional use of such attractors requires the action of spatially and temporally varying external driving signals and yet, most theoretical work on attractors has been in the limit of small or no drive. We take steps towards understanding the non-equilibrium driven dynamics of continuous attractors in place cell networks. We establish an `equivalence principle' that relates fluctuations under a time-dependent external force to equilibrium fluctuations in a `co-moving' frame with only static forces, much like in Newtonian physics. Consequently, we analytically derive a network's capacity to encode multiple attractors as a function of the driving signal size and rate of change.
Dynamics at infinity and a Hopf bifurcation arising in a quadratic system with coexisting attractors
Wang, Zhen; Moroz, Irene; Wei, Zhouchao; Ren, Haipeng
2018-01-01
Dynamics at infinity and a Hopf bifurcation for a Sprott E system with a very small perturbation constant are studied in this paper. By using Poincaré compactification of polynomial vector fields in R^3, the dynamics near infinity of the singularities is obtained. Furthermore, in accordance with the centre manifold theorem, the subcritical Hopf bifurcation is analysed and obtained. Numerical simulations demonstrate the correctness of the dynamical and bifurcation analyses. Moreover, by choosing appropriate parameters, this perturbed system can exhibit chaotic, quasiperiodic and periodic dynamics, as well as some coexisting attractors, such as a chaotic attractor coexisting with a periodic attractor for a>0, and a chaotic attractor coexisting with a quasiperiodic attractor for a=0. Coexisting attractors are not associated with an unstable equilibrium and thus often go undiscovered because they may occur in a small region of parameter space, with a small basin of attraction in the space of initial conditions.
On the Moduli Space of non-BPS Attractors for N=2 Symmetric Manifolds
Ferrara, Sergio
2007-01-01
We study the ``flat'' directions of non-BPS extremal black hole attractors for N=2, d=4 supergravities whose vector multiplets' scalar manifold is endowed with homogeneous symmetric special Kahler geometry. The non-BPS attractors with non-vanishing central charge have a moduli space described by real special geometry (and thus related to the d=5 parent theory), whereas the moduli spaces of non-BPS attractors with vanishing central charge are certain Kahler homogeneous symmetric manifolds. The moduli spaces of the non-BPS attractors of the corresponding N=2, d=5 theories are also indicated, and shown to be rank-1 homogeneous symmetric manifolds.
Intermittency induced by attractor-merging crisis in the Kuramoto-Sivashinsky equation.
Rempel, Erico L; Chian, Abraham C-L
2005-01-01
We characterize an attractor-merging crisis in a spatially extended system exemplified by the Kuramoto-Sivashinsky equation. The simultaneous collision of two coexisting chaotic attractors with an unstable periodic orbit and its associated stable manifold occurs in the high-dimensional phase space of the system, giving rise to a single merged chaotic attractor. The time series of the post-crisis regime displays intermittent behavior. The origin of this crisis-induced intermittency is elucidated in terms of alternate switching between two chaotic saddles embedded in the merged chaotic attractor.
An efficient algorithm for computing attractors of synchronous and asynchronous Boolean networks.
Zheng, Desheng; Yang, Guowu; Li, Xiaoyu; Wang, Zhicai; Liu, Feng; He, Lei
2013-01-01
Biological networks, such as genetic regulatory networks, often contain positive and negative feedback loops that settle down to dynamically stable patterns. Identifying these patterns, the so-called attractors, can provide important insights for biologists to understand the molecular mechanisms underlying many coordinated cellular processes such as cellular division, differentiation, and homeostasis. Both synchronous and asynchronous Boolean networks have been used to simulate genetic regulatory networks and identify their attractors. The common methods of computing attractors are that start with a randomly selected initial state and finish with exhaustive search of the state space of a network. However, the time complexity of these methods grows exponentially with respect to the number and length of attractors. Here, we build two algorithms to achieve the computation of attractors in synchronous and asynchronous Boolean networks. For the synchronous scenario, combing with iterative methods and reduced order binary decision diagrams (ROBDD), we propose an improved algorithm to compute attractors. For another algorithm, the attractors of synchronous Boolean networks are utilized in asynchronous Boolean translation functions to derive attractors of asynchronous scenario. The proposed algorithms are implemented in a procedure called geneFAtt. Compared to existing tools such as genYsis, geneFAtt is significantly [Formula: see text] faster in computing attractors for empirical experimental systems. The software package is available at https://sites.google.com/site/desheng619/download.
Hematopoietic differentiation: a coordinated dynamical process towards attractor stable states
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Rossi Simona
2010-06-01
Full Text Available Abstract Background The differentiation process, proceeding from stem cells towards the different committed cell types, can be considered as a trajectory towards an attractor of a dynamical process. This view, taking into consideration the transcriptome and miRNome dynamics considered as a whole, instead of looking at few 'master genes' driving the system, offers a novel perspective on this phenomenon. We investigated the 'differentiation trajectories' of the hematopoietic system considering a genome-wide scenario. Results We developed serum-free liquid suspension unilineage cultures of cord blood (CB CD34+ hematopoietic progenitor cells through erythroid (E, megakaryocytic (MK, granulocytic (G and monocytic (Mo pathways. These cultures recapitulate physiological hematopoiesis, allowing the analysis of almost pure unilineage precursors starting from initial differentiation of HPCs until terminal maturation. By analyzing the expression profile of protein coding genes and microRNAs in unilineage CB E, MK, G and Mo cultures, at sequential stages of differentiation and maturation, we observed a coordinated, fully interconnected and scalable character of cell population behaviour in both transcriptome and miRNome spaces reminiscent of an attractor-like dynamics. MiRNome and transcriptome space differed for a still not terminally committed behaviour of microRNAs. Conclusions Consistent with their roles, the transcriptome system can be considered as the state space of a cell population, while the continuously evolving miRNA space corresponds to the tuning system necessary to reach the attractor. The behaviour of miRNA machinery could be of great relevance not only for the promise of reversing the differentiated state but even for tumor biology.
Is attentional blink a byproduct of neocortical attractors?
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David N Silverstein
2011-05-01
Full Text Available This study proposes a computational model for attentional blink or blink of the mind, a phenomenon where a human subject misses perception of a later expected visual pattern as two expected visual patterns are presented less than 500 ms apart. A neocortical patch modeled as an attractor network is stimulated with a sequence of 14 patterns 100 ms apart, two of which are expected targets. Patterns that become active attractors are considered recognized. A neocortical patch is represented as a square matrix of hypercolumns, each containing a set of minicolumns with synaptic connections within and across both minicolumns and hypercolumns. Each minicolumn consists of locally connected layer 2/3 pyramidal cells with interacting basket cells and layer 4 pyramidal cells for input stimulation. All neurons are implemented using the Hodgkin-Huxley multi-compartmental cell formalism and include calcium dynamics, and they interact via saturating and depressing AMPA / NMDA and GABAA synapses. Stored patterns are encoded with global connectivity of minicolumns across hypercolumns and active patterns compete as the result of lateral inhibition in the network. Stored patterns were stimulated over time intervals to create attractor interference measurable with synthetic spike traces. This setup corresponds with item presentations in human visual attentional blink studies. Stored target patterns were depolarized while distractor patterns where hyperpolarized to represent expectation of items in working memory. Additionally, studies on the inhibitory effect of benzodiazopines on attentional blink in human subjects were compared with neocortical simulations where the GABAA receptor conductance and decay time were increased. Simulations showed increases in the attentional blink duration, agreeing with observations in human studies.
Exotic Attractors of the Nonequilibrium Rabi-Hubbard Model.
Schiró, M; Joshi, C; Bordyuh, M; Fazio, R; Keeling, J; Türeci, H E
2016-04-08
We explore the phase diagram of the dissipative Rabi-Hubbard model, as could be realized by a Raman-pumping scheme applied to a coupled cavity array. There exist various exotic attractors, including ferroelectric, antiferroelectric, and incommensurate fixed points, as well as regions of persistent oscillations. Many of these features can be understood analytically by truncating to the two lowest lying states of the Rabi model on each site. We also show that these features survive beyond mean field, using matrix product operator simulations.
Diffusion-Reorganized Aggregates: Attractors in Diffusion Processes?
Filoche, Marcel; Sapoval, Bernard
2000-12-01
A process based on particle evaporation, diffusion, and redeposition is applied iteratively to a two-dimensional object of arbitrary shape. The evolution spontaneously transforms the object morphology, converging to branched structures. Independently of initial geometry, the structures found after a long time present fractal geometry with a fractal dimension around 1.75. The final morphology, which constantly evolves in time, can be considered as the dynamic attractor of this evaporation-diffusion-redeposition operator. The ensemble of these fractal shapes can be considered to be the dynamical equilibrium geometry of a diffusion-controlled self-transformation process.
Inflationary α-attractors and F(R)-gravity
Kuiroukidis, A.
2017-09-01
We consider a generic class of the so-called inflationary α-attractor models and compute the cosmological observables in the Einstein and Jordan frames of the corresponding F(R)-gravity theory. We find that the two sets coincide (to within errors from the use of the slow-roll approximation) for moderate and large values of the number of e-foldings N, which is the novel result of this paper, generalizing previous results on the subject (see e.g. Ref. 24). We briefly comment on the possible generalizations of these results.
Multiple Coexisting Attractors and Hysteresis in the Generalized Ueda Oscillator
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Kehui Sun
2013-01-01
Full Text Available A periodically forced nonlinear oscillator called the generalized Ueda oscillator is proposed. The restoring force term of this equation consists of a nonlinear function sgn(x and an absolute function with a variant power. Dynamics is investigated by detailed numerical analysis as well as dynamic simulation, including the largest Lyapunov exponent, phase diagrams, and bifurcation diagrams. Multiple coexisting attractors and complex hysteresis phenomenon are observed. The results show that this system has rich dynamical behaviors, and it has a promising application in the fields of science and engineering.
Exploring strange nonchaotic attractors through Jacobian elliptic functions
Energy Technology Data Exchange (ETDEWEB)
GarcIa-Hoz, A Martinez [Departamento de Fisica Aplicada, Escuela Universitaria Politecnica, Universidad de Castilla La Mancha, E-13400 Almaden (Ciudad Real) (Spain); Chacon, R, E-mail: rchacon@unex.es [Departamento de Fisica Aplicada, Escuela de IngenierIas Industriales, Universidad de Extremadura, Apartado Postal 382, E-06006 Badajoz (Spain)
2011-11-15
We demonstrate the effectiveness of Jacobian elliptic functions (JEFs) for inquiring into the reshaping effect of quasiperiodic forces in nonlinear nonautonomous systems exhibiting strange nonchaotic attractors (SNAs). Specifically, we characterize analytically and numerically some reshaping-induced transitions starting from SNAs in the context of quasiperiodically forced systems. We found similar scenarios of SNAs from the analysis of two representative examples: a quasiperiodically forced damped pendulum and a two-dimensional map. This clearly well-suited and advantageous use of the JEFs, which in their own right lie at the heart of nonlinear physics, may encourage students at intermediate university levels to study them in depth.
Li, X Y; Yang, G W; Zheng, D S; Guo, W S; Hung, W N N
2015-04-28
Genetic regulatory networks are the key to understanding biochemical systems. One condition of the genetic regulatory network under different living environments can be modeled as a synchronous Boolean network. The attractors of these Boolean networks will help biologists to identify determinant and stable factors. Existing methods identify attractors based on a random initial state or the entire state simultaneously. They cannot identify the fixed length attractors directly. The complexity of including time increases exponentially with respect to the attractor number and length of attractors. This study used the bounded model checking to quickly locate fixed length attractors. Based on the SAT solver, we propose a new algorithm for efficiently computing the fixed length attractors, which is more suitable for large Boolean networks and numerous attractors' networks. After comparison using the tool BooleNet, empirical experiments involving biochemical systems demonstrated the feasibility and efficiency of our approach.
Sustainability as global attractor: the greening of the 2008 Beijing Olympics
Mol, A.P.J.
2010-01-01
If one interprets sustainability as an attractor, it means that across time and place notions and ideas of sustainability structure, order and pattern institutions and practices. One can effectively explore the idea that sustainability is turning into a global attractor through mega events. As high
Directory of Open Access Journals (Sweden)
Ping Zhou
2017-01-01
Full Text Available Based on the 3D autonomous continuous Lü chaotic system, a new 3D autonomous continuous chaotic system is proposed in this paper, and there are coexisting chaotic attractors in the 3D autonomous continuous chaotic system. Moreover, there are no overlaps between the coexisting chaotic attractors; that is, there are two isolated chaotic attractors (in this paper, named “positive attractor” and “negative attractor,” resp.. The “positive attractor” and “negative attractor” depend on the distance between the initial points (initial conditions and the unstable equilibrium points. Furthermore, by means of topological horseshoes theory and numerical computation, the topological horseshoes in this 3D autonomous continuous system is found, and the topological entropy is obtained. These results indicate that the chaotic attractor emerges in the new 3D autonomous continuous system.
Generation and control of multi-scroll chaotic attractors in fractional order systems
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Ahmad, Wajdi M. [Department of Electrical and Computer Engineering, University of Sharjah, P.O. Box 27272, Sharjah (United Arab Emirates)] e-mail: wajdi@sharjah.ac.ae
2005-08-01
The objective of this paper is twofold: on one hand we demonstrate the generation of multi-scroll attractors in fractional order chaotic systems. Then, we design state feedback controllers to eliminate chaos from the system trajectories. It is demonstrated that modifying the underlying nonlinearity of the fractional chaotic system results in the birth of multiple chaotic attractors, thus forming the so called multi-scroll attractors. The presence of chaotic behavior is evidenced by a positive largest Lyapunov exponent computed for the output time series. We investigate generation and control of multi-scroll attractors in two different models, both of which are fractional order and chaotic: an electronic oscillator, and a mechanical 'jerk' model. The current findings extend previously reported results on generation of n-scroll attractors from the domain of integer order to the domain of fractional order chaotic systems, and addresses the issue of controlling such chaotic behaviors. Our investigations are validated through numerical simulations.
Split Attractor Flow in N=2 Minimally Coupled Supergravity
Ferrara, Sergio; Orazi, Emanuele
2011-01-01
We classify the stability region, marginal stability walls (MS) and split attractor flows for two-center extremal black holes in four-dimensional N=2 supergravity minimally coupled to n vector multiplets. It is found that two-center (continuous) charge orbits, classified by four duality invariants, either support a stability region ending on a MS wall or on an anti-marginal stability (AMS) wall, but not both. Therefore, the scalar manifold never contains both walls. Moreover, the BPS mass of the black hole composite (in its stability region) never vanishes in the scalar manifold. For these reasons, the "bound state transformation walls" phenomenon does not necessarily occur in these theories. The entropy of the flow trees also satisfies an inequality which forbids "entropy enigma" decays in these models. Finally, the non-BPS case, due to the existence of a "fake" superpotential satisfying a triangle inequality, can be treated as well, and it can be shown to exhibit a split attractor flow dynamics which, at le...
Charge Orbits of Symmetric Special Geometries and Attractors
Bellucci, S; Günaydin, M; Marrani, A; Bellucci, Stefano; Ferrara, Sergio; Gunaydin, Murat; Marrani, Alessio
2006-01-01
We study the critical points of the black hole scalar potential $V_{BH}$ in N=2, d=4 supergravity coupled to $n_{V}$ vector multiplets, in an asymptotically flat extremal black hole background described by a 2(n_{V}+1)-dimensional dyonic charge vector and (complex) scalar fields which are coordinates of a special K\\"{a}hler manifold. For the case of homogeneous symmetric spaces, we find three general classes of regular attractor solutions with non-vanishing Bekenstein-Hawking entropy. They correspond to three (inequivalent) classes of orbits of the charge vector, which is in a 2(n_{V}+1)-dimensional representation $R_{V}$ of the U-duality group. Such orbits are non-degenerate, namely they have non-vanishing quartic invariant (for rank-3 spaces). Other than the 1/2-BPS one, there are two other distinct non-BPS classes of charge orbits, one of which has vanishing central charge. The three species of solutions to the N=2 extremal black hole attractor equations give rise to different mass spectra of the scalar fl...
Lai, Qiang; Zhao, Xiao-Wen; Rajagopal, Karthikeyan; Xu, Guanghui; Akgul, Akif; Guleryuz, Emre
2018-01-01
This paper considers the generation of multi-butterfly chaotic attractors from a generalised Sprott C system with multiple non-hyperbolic equilibria. The system is constructed by introducing an additional variable whose derivative has a switching function to the Sprott C system. It is numerically found that the system creates two-, three-, four-, five-butterfly attractors and any other multi-butterfly attractors. First, the dynamic analyses of multi-butterfly chaotic attractors are presented. Secondly, the field programmable gate array implementation, electronic circuit realisation and random number generator are done with the multi-butterfly chaotic attractors.
Attractor switching by neural control of chaotic neurodynamics.
Pasemann, F; Stollenwerk, N
1998-11-01
Chaotic attractors of discrete-time neural networks include infinitely many unstable periodic orbits, which can be stabilized by small parameter changes in a feedback control. Here we explore the control of unstable periodic orbits in a chaotic neural network with only two neurons. Analytically, a local control algorithm is derived on the basis of least squares minimization of the future deviations between actual system states and the desired orbit. This delayed control allows a consistent neural implementation, i.e. the same types of neurons are used for chaotic and controlling modules. The control signal is realized with one layer of neurons, allowing selective switching between different stabilized periodic orbits. For chaotic modules with noise, random switching between different periodic orbits is observed.
Terminal Attractor Optical Associative Memory for Pattern Recognition
Lin, Xin; Mori, Masahiko; Ohtsubo, Junji; Watanabe, Masanobu
2000-02-01
Optical associative memory with terminal attractor (TA) is proposed for pattern recognition. With numerical simulations, the optimal control parameter in the TA model associative memory is determined. The optimal control parameter is also used in an optical experiment. The capacity of TA model associative memory is also investigated based on the consistency between the stored pattern and the obtained equilibrium state in statistical thermodynamics. The results of numerical simulations indicate that the memory rate of the TA associative memory is greater than 0.35. We also compare TA model with the conventional Hopfield model, and show that the TA model can eliminate spurious states in the Hopfield model and increase recalling ability and memory capacity.
A new parameter in attractor single-field inflation
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Jinn-Ouk Gong
2015-07-01
Full Text Available We revisit the notion of slow-roll in the context of general single-field inflation. As a generalization of slow-roll dynamics, we consider an inflaton ϕ in an attractor phase where the time derivative of ϕ is determined by a function of ϕ, ϕ˙=ϕ˙(ϕ. In other words, we consider the case when the number of e-folds N counted backward in time from the end of inflation is solely a function of ϕ, N=N(ϕ. In this case, it is found that we need a new independent parameter to properly describe the dynamics of the inflaton field in general, in addition to the standard parameters conventionally denoted by ϵ, η, cs2 and s. Two illustrative examples are presented to discuss the non-slow-roll dynamics of the inflaton field consistent with observations.
Navigating cancer network attractors for tumor-specific therapy
DEFF Research Database (Denmark)
Creixell, Pau; Schoof, Erwin; Erler, Janine Terra
2012-01-01
Cells employ highly dynamic signaling networks to drive biological decision processes. Perturbations to these signaling networks may attract cells to new malignant signaling and phenotypic states, termed cancer network attractors, that result in cancer development. As different cancer cells reach...... these malignant states by accumulating different molecular alterations, uncovering these mechanisms represents a grand challenge in cancer biology. Addressing this challenge will require new systems-based strategies that capture the intrinsic properties of cancer signaling networks and provide deeper...... understanding of the processes by which genetic lesions perturb these networks and lead to disease phenotypes. Network biology will help circumvent fundamental obstacles in cancer treatment, such as drug resistance and metastasis, empowering personalized and tumor-specific cancer therapies....
Attractor for a Reaction-Diffusion System Modeling Cancer Network
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Xueyong Chen
2014-01-01
Full Text Available A reaction-diffusion cancer network regulated by microRNA is considered in this paper. We study the asymptotic behavior of solution and show the existence of global uniformly bounded solution to the system in a bounded domain Ω⊂Rn. Some estimates and asymptotic compactness of the solutions are proved. As a result, we establish the existence of the global attractor in L2(Ω×L2(Ω and prove that the solution converges to stable steady states. These results can help to understand the dynamical character of cancer network and propose a new insight to study the mechanism of cancer. In the end, the numerical simulation shows that the analytical results agree with numerical simulation.
How organisms do the right thing: The attractor hypothesis
Emlen, J.M.; Freeman, D.C.; Mills, A.; Graham, J.H.
1998-01-01
Neo-Darwinian theory is highly successful at explaining the emergence of adaptive traits over successive generations. However, there are reasons to doubt its efficacy in explaining the observed, impressively detailed adaptive responses of organisms to day-to-day changes in their surroundings. Also, the theory lacks a clear mechanism to account for both plasticity and canalization. In effect, there is a growing sentiment that the neo-Darwinian paradigm is incomplete, that something more than genetic structure, mutation, genetic drift, and the action of natural selection is required to explain organismal behavior. In this paper we extend the view of organisms as complex self-organizing entities by arguing that basic physical laws, coupled with the acquisitive nature of organisms, makes adaptation all but tautological. That is, much adaptation is an unavoidable emergent property of organisms' complexity and, to some a significant degree, occurs quite independently of genomic changes wrought by natural selection. For reasons that will become obvious, we refer to this assertion as the attractor hypothesis. The arguments also clarify the concept of "adaptation." Adaptation across generations, by natural selection, equates to the (game theoretic) maximization of fitness (the success with which one individual produces more individuals), while self-organizing based adaptation, within generations, equates to energetic efficiency and the matching of intake and biosynthesis to need. Finally, we discuss implications of the attractor hypothesis for a wide variety of genetical and physiological phenomena, including genetic architecture, directed mutation, genetic imprinting, paramutation, hormesis, plasticity, optimality theory, genotype-phenotype linkage and puncuated equilibrium, and present suggestions for tests of the hypothesis. ?? 1998 American Institute of Physics.
Generation of a New Three Dimension Autonomous Chaotic Attractor and its Four Wing Type
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F. Yu
2013-02-01
Full Text Available n this paper, a new three-dimension (3D autonomous chaotic system with a nonlinear term in the form of a hyperbolic sine (or cosine function is reported. Some interesting and complex attractors are obtained. Basic dynamical properties of the new chaotic system are demonstrated in terms of Lyapunov exponents, Poincare mapping, fractal dimension and continuous spectrum. Meanwhile, for further enhancing the complexity of the topological structure of the new chaotic attractors, the attractors are changed from two-wing to four-wing through making axis doubly polarized, theoretically analyzed and numerically simulated. The obtained results clearly show that the chaotic system deserves further detailed investigation.
Existence and continuity of global attractors for a degenerate semilinear parabolic equation
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Cung The Anh
2009-05-01
Full Text Available In this article, we study the existence and the upper semicontinuity with respect to the nonlinearity and the shape of the domain of global attractors for a semilinear degenerate parabolic equation involving the Grushin operator.
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Emenheiser, Jeffrey [Complexity Sciences Center, University of California, Davis, California 95616 (United States); Department of Physics, University of California, Davis, California 95616 (United States); Chapman, Airlie; Mesbahi, Mehran [William E. Boeing Department of Aeronautics and Astronautics, University of Washington, Seattle, Washington 98195 (United States); Pósfai, Márton [Complexity Sciences Center, University of California, Davis, California 95616 (United States); Department of Computer Science, University of California, Davis, California 95616 (United States); Crutchfield, James P. [Complexity Sciences Center, University of California, Davis, California 95616 (United States); Department of Physics, University of California, Davis, California 95616 (United States); Department of Computer Science, University of California, Davis, California 95616 (United States); Santa Fe Institute, Santa Fe, New Mexico 87501 (United States); D' Souza, Raissa M. [Complexity Sciences Center, University of California, Davis, California 95616 (United States); Department of Computer Science, University of California, Davis, California 95616 (United States); Santa Fe Institute, Santa Fe, New Mexico 87501 (United States); Department of Mechanical and Aerospace Engineering, University of California, Davis, California 95616 (United States)
2016-09-15
Following the long-lived qualitative-dynamics tradition of explaining behavior in complex systems via the architecture of their attractors and basins, we investigate the patterns of switching between distinct trajectories in a network of synchronized oscillators. Our system, consisting of nonlinear amplitude-phase oscillators arranged in a ring topology with reactive nearest-neighbor coupling, is simple and connects directly to experimental realizations. We seek to understand how the multiple stable synchronized states connect to each other in state space by applying Gaussian white noise to each of the oscillators' phases. To do this, we first analytically identify a set of locally stable limit cycles at any given coupling strength. For each of these attracting states, we analyze the effect of weak noise via the covariance matrix of deviations around those attractors. We then explore the noise-induced attractor switching behavior via numerical investigations. For a ring of three oscillators, we find that an attractor-switching event is always accompanied by the crossing of two adjacent oscillators' phases. For larger numbers of oscillators, we find that the distribution of times required to stochastically leave a given state falls off exponentially, and we build an attractor switching network out of the destination states as a coarse-grained description of the high-dimensional attractor-basin architecture.
Hunt, Fern Y.
1998-03-01
Asymptotically stable attractors supporting an invariant measure, for which the ergodic theorem holds almost everywhere with respect to Lebesgue measure, can be approximated by a space discretization procedure called Ulam's method. As an application of this result we propose the use of this method to approximate the `chaotic' attractors of flows in lower dimensions. A Monte Carlo implementation makes this feasible. The approximation method can be extended to attractors whose neighbourhoods contain positively invariant compact sets called blocks. Note that such attractors can fail to have open basins of attraction. When the attractor is uniquely ergodic, we also prove the weak convergence of the approximate measures constructed by the method and as an application, we show the weak convergence of Ulam's method for the logistic map at the Feigenbaum parameter value. More generally, using the work of Buescu and Stewart on transitive attractors of continuous maps, we prove weak convergence of the approximate measures and convergence of their supports to classes of Lyapounov stable attracting Cantor sets.
Structural alphabets derived from attractors in conformational space
2010-01-01
Background The hierarchical and partially redundant nature of protein structures justifies the definition of frequently occurring conformations of short fragments as 'states'. Collections of selected representatives for these states define Structural Alphabets, describing the most typical local conformations within protein structures. These alphabets form a bridge between the string-oriented methods of sequence analysis and the coordinate-oriented methods of protein structure analysis. Results A Structural Alphabet has been derived by clustering all four-residue fragments of a high-resolution subset of the protein data bank and extracting the high-density states as representative conformational states. Each fragment is uniquely defined by a set of three independent angles corresponding to its degrees of freedom, capturing in simple and intuitive terms the properties of the conformational space. The fragments of the Structural Alphabet are equivalent to the conformational attractors and therefore yield a most informative encoding of proteins. Proteins can be reconstructed within the experimental uncertainty in structure determination and ensembles of structures can be encoded with accuracy and robustness. Conclusions The density-based Structural Alphabet provides a novel tool to describe local conformations and it is specifically suitable for application in studies of protein dynamics. PMID:20170534
Structural alphabets derived from attractors in conformational space.
Pandini, Alessandro; Fornili, Arianna; Kleinjung, Jens
2010-02-20
The hierarchical and partially redundant nature of protein structures justifies the definition of frequently occurring conformations of short fragments as 'states'. Collections of selected representatives for these states define Structural Alphabets, describing the most typical local conformations within protein structures. These alphabets form a bridge between the string-oriented methods of sequence analysis and the coordinate-oriented methods of protein structure analysis. A Structural Alphabet has been derived by clustering all four-residue fragments of a high-resolution subset of the protein data bank and extracting the high-density states as representative conformational states. Each fragment is uniquely defined by a set of three independent angles corresponding to its degrees of freedom, capturing in simple and intuitive terms the properties of the conformational space. The fragments of the Structural Alphabet are equivalent to the conformational attractors and therefore yield a most informative encoding of proteins. Proteins can be reconstructed within the experimental uncertainty in structure determination and ensembles of structures can be encoded with accuracy and robustness. The density-based Structural Alphabet provides a novel tool to describe local conformations and it is specifically suitable for application in studies of protein dynamics.
Structural alphabets derived from attractors in conformational space
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Kleinjung Jens
2010-02-01
Full Text Available Abstract Background The hierarchical and partially redundant nature of protein structures justifies the definition of frequently occurring conformations of short fragments as 'states'. Collections of selected representatives for these states define Structural Alphabets, describing the most typical local conformations within protein structures. These alphabets form a bridge between the string-oriented methods of sequence analysis and the coordinate-oriented methods of protein structure analysis. Results A Structural Alphabet has been derived by clustering all four-residue fragments of a high-resolution subset of the protein data bank and extracting the high-density states as representative conformational states. Each fragment is uniquely defined by a set of three independent angles corresponding to its degrees of freedom, capturing in simple and intuitive terms the properties of the conformational space. The fragments of the Structural Alphabet are equivalent to the conformational attractors and therefore yield a most informative encoding of proteins. Proteins can be reconstructed within the experimental uncertainty in structure determination and ensembles of structures can be encoded with accuracy and robustness. Conclusions The density-based Structural Alphabet provides a novel tool to describe local conformations and it is specifically suitable for application in studies of protein dynamics.
The Radiative Kicked Oscillator A Stochastic Web or Chaotic Attractor ?
Ashkenazy, Yu
1999-01-01
A relativistic charged particle moving in a uniform magnetic field and kicked by an electric field is considered. Under the assumption of small magnetic field, an iterative map is developed. We consider both the case in which no radiation is assumed and the radiative case, using the Lorentz-Dirac equation to describe the motion. Comparison between the non-radiative case and the radiative case shows that in both cases one can observe a stochastic web structure for weak magnetic fields, and, although there are global differences in the result of the map, that both cases are qualitatively similar in their small scale behavior. We also develop an iterative map for strong magnetic fields. In that case the web structure no longer exists; it is replaced by a rich chaotic behavior. It is shown that the particle does not diffuse to infinite energy; it is limited by the boundaries of an attractor (the boundaries are generally much smaller than light velocity). Bifurcation occurs, converging rapidly to Feigenbaum's univ...
A Bayesian Attractor Model for Perceptual Decision Making.
Bitzer, Sebastian; Bruineberg, Jelle; Kiebel, Stefan J
2015-08-01
Even for simple perceptual decisions, the mechanisms that the brain employs are still under debate. Although current consensus states that the brain accumulates evidence extracted from noisy sensory information, open questions remain about how this simple model relates to other perceptual phenomena such as flexibility in decisions, decision-dependent modulation of sensory gain, or confidence about a decision. We propose a novel approach of how perceptual decisions are made by combining two influential formalisms into a new model. Specifically, we embed an attractor model of decision making into a probabilistic framework that models decision making as Bayesian inference. We show that the new model can explain decision making behaviour by fitting it to experimental data. In addition, the new model combines for the first time three important features: First, the model can update decisions in response to switches in the underlying stimulus. Second, the probabilistic formulation accounts for top-down effects that may explain recent experimental findings of decision-related gain modulation of sensory neurons. Finally, the model computes an explicit measure of confidence which we relate to recent experimental evidence for confidence computations in perceptual decision tasks.
Diffusion of intrinsic localized modes by attractor hopping
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Meister, Matthias [Dpto FIsica de la Materia Condensada, Facultad de Ciencias, Universidad de Zaragoza, 50009 Zaragoza (Spain); Instituto de Biocomputacion y FIsica de Sistemas Complejos, Universidad de Zaragoza, 50009 Zaragoza (Spain); Vazquez, Luis [Dpto Matematica Aplicada, Facultad de Informatica, Universidad Complutense de Madrid, 28040 Madrid (Spain); Centro de AstrobiologIa (CSIC-INTA), 28850 Torrejon de Ardoz (Spain)
2003-11-28
Propagating intrinsic localized modes exist in the damped-driven discrete sine-Gordon chain as attractors of the dynamics. The equations of motion of the system are augmented with Gaussian white noise in order to model the effects of temperature on the system. The noise induces random transitions between attracting configurations corresponding to opposite signs of the propagation velocity of the mode, which leads to a diffusive motion of the excitation. The Heun method is used to numerically generate the stochastic time-evolution of the configuration. We also present a theoretical model for the diffusion which contains two parameters, a transition probability {theta} and a delay time {tau}{sub A}. The mean value and the variance of the position of the intrinsic localized mode, obtained from simulations, can be fitted well with the predictions of our model, {theta} and {tau}{sub A} being used as parameters in the fit. After a transition period following the switching on of the noise, the variance shows a linear behaviour as a function of time and the mean value remains constant. An increase in the strength of the noise lowers the variance, leads to an increase in {theta}, a decrease in {tau}{sub A} and reduces the average distance a mode travels during the transition period.
Using a Projector to Control BZ Drops: Attractor Selection by Pattern Entrainment
Tompkins, Nathan; Gonzalez Ochoa, Hector; Epstein, Irving; Fraden, Seth
2011-03-01
An emulsion consisting of drops in the 100 μ m diameter range containing the Belousov-Zhabotinsky (BZ) oscillatory chemicals can interact via diffusive inhibition and can be thought of as coupled phase oscillators. For weak coupling, a 2-D hexagonal lattice of these drops naturally develop regions of attractor states of sequential oscillations with phase differences of plus/minus 2 π / 3 much like the 2D anti-ferromagnetic Heisenberg spin model. An untrained system of these oscillators will develop unstable regions of both attractors that grow and compete. We use photo-initiated inhibition to optically entrain the system with a projected + 2 π / 3 pattern in an attempt to force the system into the + 2 π / 3 attractor state. However, both the left and right handed variants of the 2 π / 3 attractor are present in the entrained system. Defining an order parameter e i 3 ϕ allows for a quantitation of the purity of the 2 π / 3 attractor state in the final system.
Robust Adaptive Algorithm by an Adaptive Zero Attractor Controller of ZA-LMS Algorithm
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Radhika Sivashanmugam
2016-01-01
Full Text Available This paper proposes a new approach to identify time varying sparse systems. The proposed approach uses Zero-Attracting Least Mean Square (ZA-LMS algorithm with an adaptive optimal zero attractor controller which can adapt dynamically to the sparseness level and provide appreciable performance in all environments ranging from sparse to nonsparse conditions. The optimal zero attractor controller is derived based on the criterion that confirms largest decrease in mean square deviation (MSD error. A simple update rule is also proposed to change the zero attractor controller based on the level of sparsity. It is found that, for nonsparse system, the proposed approach converges to LMS (as ZA-LMS cannot outperform LMS when the system is nonsparse and, for highly sparse system, as the proposed approach is based on optimal zero attractor controller, it converges either similar to ZA-LMS or even better than ZA-LMS (depending on the value of zero attractor controller chosen for ZA-LMS algorithm. The performance of the proposed algorithm is better than ZA-LMS and LMS when the system is semisparse. Simulations were performed to prove that the proposed algorithm is robust against variable sparsity level.
Wurdeman, Shane R; Myers, Sara A; Stergiou, Nicholas
2013-04-01
The amputation and subsequent prosthetic rehabilitation of a lower leg affects gait. Dynamical systems theory would predict the use of a prosthetic device should alter the functional attractor dynamics to which the system self-organizes. Therefore, the purpose of this study was to compare the largest Lyapunov exponent (a nonlinear tool for assessing attractor dynamics) for amputee gait compared to healthy non-amputee individuals. Fourteen unilateral, transtibial amputees and fourteen healthy, non-amputee individuals ambulated on a treadmill at preferred, self-selected walking speed. Our results showed that the sound hip (p = 0.013), sound knee (p = 0.05), and prosthetic ankle (p = 0.023) have significantly greater largest Lyapunov exponents than healthy non-amputees. Furthermore, the prosthetic ankle has a significantly greater (p = 0.0.17) largest Lyapunov exponent than the sound leg ankle. These findings indicate attractor states for amputee gait with increased divergence. The increased attractor divergence seems to coincide with decreased ability for motor control between the natural rhythms of the individual and those of the prosthetic device. Future work should consider the impact of different prostheses and rehabilitation on the attractor dynamics.
Controllable V-Shape Multi-Scroll Butterfly Attractor: System and Circuit Implementation
Zidan, Mohammed A.
2012-07-23
In this paper, a new controllable V-shape multiscroll attractor is presented, where a variety of symmetrical and unsymmetrical attractors with a variable number of scrolls can be controlled using new staircase nonlinear function and the parameters of the system. This attractor can be used to generate random signals with a variety of symbol distribution. Digital implementation of the proposed generator is also presented using a Xilinx Virtex® 4 Field Programmable Gate Array and experimental results are provided. The digital realization easily fits into a small area (<1.5% of the total area) and expresses a high throughput (4.3 Gbit/sec per state variable). © 2012 World Scientific Publishing Company.
Different routes to chaos via strange nonchaotic attractor in a quasiperiodically forced system
Venkatesan, A
1998-01-01
This paper focusses attention on the strange nonchaotic attractors (SNA) of a quasiperiodically forced dynamical system. Several routes, including the standard ones by which the appearance of strange nonchaotic attractors takes place, are shown to be realizable in the same model over a two parameters ($f-\\epsilon$) domain of the system. In particular, the transition through torus doubling to chaos via SNA, torus breaking to chaos via SNA and period doubling bifurcations of fractal torus are demonstrated with the aid of the two parameter ($f-\\epsilon$) phase diagram. More interestingly, in order to approach the strange nonchaotic attractor, the existence of several new bifurcations on the torus corresponding to the novel phenomenon of torus bubbling are described. Particularly, we point out the new routes to chaos, namely, (1) two frequency quasiperiodicity $\\to$ torus doubling $\\to$ torus merging followed by the gradual fractalization of torus to chaos, (2) two frequency quasiperiodicity $\\to$ torus doubling ...
Non-BPS Attractors in 5d and 6d Extended Supergravity
Andrianopoli, L.; Marrani, A.; Trigiante, M.
2008-01-01
We connect the attractor equations of a certain class of N=2, d=5 supergravities with their (1,0), d=6 counterparts, by relating the moduli space of non-BPS d=5 black hole/black string attractors to the moduli space of extremal dyonic black string d=6 non-BPS attractors. For d = 5 real special symmetric spaces and for N = 4,6,8 theories, we explicitly compute the flat directions of the black object potential corresponding to vanishing eigenvalues of its Hessian matrix. In the case N = 4, we study the relation to the (2,0), d=6 theory. We finally describe the embedding of the N=2, d=5 magic models in N=8, d=5 supergravity as well as the interconnection among the corresponding charge orbits.
SRB measures for a class of partially hyperbolic attractors in Hilbert spaces
Lian, Zeng; Liu, Peidong; Lu, Kening
2016-07-01
In this paper, we study the existence of SRB measures and their properties for infinite dimensional dynamical systems in a Hilbert space. We show several results including (i) if the system has a partially hyperbolic attractor with nontrivial finite dimensional unstable directions, then it has at least one SRB measure; (ii) if the attractor is uniformly hyperbolic and the system is topological mixing and the splitting is Hölder continuous, then there exists a unique SRB measure which is mixing; (iii) if the attractor is uniformly hyperbolic and the system is non-wondering and the splitting is Hölder continuous, then there exist at most finitely many SRB measures; (iv) for a given hyperbolic measure, there exist at most countably many ergodic components whose basin contains an observable set.
Radiation reaction induced spiral attractors in ultra-intense colliding laser beams
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Zheng Gong
2016-11-01
Full Text Available The radiation reaction effects on electron dynamics in counter-propagating circularly polarized laser beams are investigated through the linearization theorem and the results are in great agreement with numeric solutions. For the first time, the properties of fixed points in electron phase-space were analyzed with linear stability theory, showing that center nodes will become attractors if the classical radiation reaction is considered. Electron dynamics are significantly affected by the properties of the fixed points and the electron phase-space densities are found to be increasing exponentially near the attractors. The density growth rates are derived theoretically and further verified by particle-in-cell simulations, which can be detected in experiments to explore the effects of radiation reaction qualitatively. The attractor can also facilitate realizing a series of nanometer-scaled flying electron slices via adjusting the colliding laser frequencies.
Ohlson Timoudas, Thomas
2017-12-01
Let Φ be a quasi-periodically forced quadratic map, where the rotation constant ω is a Diophantine irrational. A strange non-chaotic attractor (SNA) is an invariant (under Φ) attracting graph of a nowhere continuous measurable function ψ from the circle {T} to [0, 1] . This paper investigates how a smooth attractor degenerates into a strange one, as a parameter \
Zhou, Shengfan
2017-08-01
We first establish some sufficient conditions for constructing a random exponential attractor for a continuous cocycle on a separable Banach space and weighted spaces of infinite sequences. Then we apply our abstract result to study the existence of random exponential attractors for non-autonomous first order dissipative lattice dynamical systems with multiplicative white noise.
A signature of attractor dynamics in the CA3 region of the hippocampus.
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César Rennó-Costa
2014-05-01
Full Text Available The notion of attractor networks is the leading hypothesis for how associative memories are stored and recalled. A defining anatomical feature of such networks is excitatory recurrent connections. These "attract" the firing pattern of the network to a stored pattern, even when the external input is incomplete (pattern completion. The CA3 region of the hippocampus has been postulated to be such an attractor network; however, the experimental evidence has been ambiguous, leading to the suggestion that CA3 is not an attractor network. In order to resolve this controversy and to better understand how CA3 functions, we simulated CA3 and its input structures. In our simulation, we could reproduce critical experimental results and establish the criteria for identifying attractor properties. Notably, under conditions in which there is continuous input, the output should be "attracted" to a stored pattern. However, contrary to previous expectations, as a pattern is gradually "morphed" from one stored pattern to another, a sharp transition between output patterns is not expected. The observed firing patterns of CA3 meet these criteria and can be quantitatively accounted for by our model. Notably, as morphing proceeds, the activity pattern in the dentate gyrus changes; in contrast, the activity pattern in the downstream CA3 network is attracted to a stored pattern and thus undergoes little change. We furthermore show that other aspects of the observed firing patterns can be explained by learning that occurs during behavioral testing. The CA3 thus displays both the learning and recall signatures of an attractor network. These observations, taken together with existing anatomical and behavioral evidence, make the strong case that CA3 constructs associative memories based on attractor dynamics.
Existence and regularity of a global attractor for doubly nonlinear parabolic equations
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Abderrahmane El Hachimi
2002-05-01
Full Text Available In this paper we consider a doubly nonlinear parabolic partial differential equation $$ frac{partial eta (u}{partial t}-Delta _{p}u+f(x,t,u=0 quad hbox{in }Omega imesmathbb{R}^{+}, $$ with Dirichlet boundary condition and initial data given. We prove the existence of a global compact attractor by using a dynamical system approach. Under additional conditions on the nonlinearities $Beta$, $f$, and on $p$, we prove more regularity for the global attractor and obtain stabilization results for the solutions.
Relativistic hydrodynamic attractors with broken symmetries: non-conformal and non-homogeneous
Romatschke, Paul
2017-12-01
Standard textbooks will state that hydrodynamics requires near-equilibrium to be applicable. Recently, however, out-of-equilibrium attractor solutions for hydrodynamics have been found in kinetic theory and holography in systems with a high degree of symmetry, suggesting the possibility of a genuine out-of-equilibrium formulation of hydrodynamics. This work demonstrates that attractor solutions also occur in non-conformal kinetic theory and spatially non-homogeneous systems, potentially having important implications for the interpretation of experimental data in heavy-ion and proton-proton collisions and relativistic fluid dynamics as a whole.
Predicting epileptic seizures from scalp EEG based on attractor state analysis.
Chu, Hyunho; Chung, Chun Kee; Jeong, Woorim; Cho, Kwang-Hyun
2017-05-01
Epilepsy is the second most common disease of the brain. Epilepsy makes it difficult for patients to live a normal life because it is difficult to predict when seizures will occur. In this regard, if seizures could be predicted a reasonable period of time before their occurrence, epilepsy patients could take precautions against them and improve their safety and quality of life. In this paper, we investigate a novel seizure precursor based on attractor state analysis for seizure prediction. We analyze the transition process from normal to seizure attractor state and investigate a precursor phenomenon seen before reaching the seizure attractor state. From the result of an analysis, we define a quantified spectral measure in scalp EEG for seizure prediction. From scalp EEG recordings, the Fourier coefficients of six EEG frequency bands are extracted, and the defined spectral measure is computed based on the coefficients for each half-overlapped 20-second-long window. The computed spectral measure is applied to seizure prediction using a low-complexity methodology. Within scalp EEG, we identified an early-warning indicator before an epileptic seizure occurs. Getting closer to the bifurcation point that triggers the transition from normal to seizure state, the power spectral density of low frequency bands of the perturbation of an attractor in the EEG, showed a relative increase. A low-complexity seizure prediction algorithm using this feature was evaluated, using ∼583h of scalp EEG in which 143 seizures in 16 patients were recorded. With the test dataset, the proposed method showed high sensitivity (86.67%) with a false prediction rate of 0.367h-1 and average prediction time of 45.3min. A novel seizure prediction method using scalp EEG, based on attractor state analysis, shows potential for application with real epilepsy patients. This is the first study in which the seizure-precursor phenomenon of an epileptic seizure is investigated based on attractor
Attractor and Boundedness of Switched Stochastic Cohen-Grossberg Neural Networks
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Chuangxia Huang
2016-01-01
Full Text Available We address the problem of stochastic attractor and boundedness of a class of switched Cohen-Grossberg neural networks (CGNN with discrete and infinitely distributed delays. With the help of stochastic analysis technology, the Lyapunov-Krasovskii functional method, linear matrix inequalities technique (LMI, and the average dwell time approach (ADT, some novel sufficient conditions regarding the issues of mean-square uniformly ultimate boundedness, the existence of a stochastic attractor, and the mean-square exponential stability for the switched Cohen-Grossberg neural networks are established. Finally, illustrative examples and their simulations are provided to illustrate the effectiveness of the proposed results.
Global attractors of non-autonomous quasi-homogeneous dynamical systems
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David N. Cheban
2002-01-01
Full Text Available It is shown that non-autonomous quasi-homogeneous dynamical systems admit a compact global attractor. The general results obtained here are applied to differential equations both in finite dimensional spaces and in infinite dimensional spaces, such as ordinary differential equations in Banach space and some types of evolutional partial differential equations.
Multistability and hidden attractors in a multilevel DC/DC converter
DEFF Research Database (Denmark)
Zhusubaliyev, Zhanybai T.; Mosekilde, Erik
2015-01-01
produce complicated structures of attracting and repelling states organized around the basic switching cycle. This leads us to suggest the existence of hidden attractors in such systems as well. In this case, the condition will be that the basin of attraction does not overlap with the fixed point...... that represents the basic switching cycle....
Decision-making neural circuits mediating social behaviors : An attractor network model.
Hurtado-López, Julián; Ramirez-Moreno, David F; Sejnowski, Terrence J
2017-06-29
We propose a mathematical model of a continuous attractor network that controls social behaviors. The model is examined with bifurcation analysis and computer simulations. The results show that the model exhibits stable steady states and thresholds for steady state transitions corresponding to some experimentally observed behaviors, such as aggression control. The performance of the model and the relation with experimental evidence are discussed.
Alternate attractors in the population dynamics of a tree-killing bark beetle
Sharon J. Martinson; Tiina Ylioja; Brian T. Sullivan; Ronald F. Billings; Matthew P. Ayres
2013-01-01
Among the most striking changes in ecosystems are those that happen abruptly and resist return to the original condition (i.e., regime shifts). This frequently involves conspicuous changes in the abundance of one species (e.g., an outbreaking pest or keystone species). Alternate attractors in population dynamics could explain switches between low and high levels of...
Lerner, Itamar; Bentin, Shlomo; Shriki, Oren
2012-01-01
Localist models of spreading activation (SA) and models assuming distributed representations offer very different takes on semantic priming, a widely investigated paradigm in word recognition and semantic memory research. In this study, we implemented SA in an attractor neural network model with distributed representations and created a unified…
Computation of Dimensions for Strange Attractors by the Box Counting Renormalization Method
Yang, Wei-Ming; Zheng, Wei-mou
1992-03-01
The scaling ansats for box counting functions is verified numerically for the reverse doubling sequence of the logistic map. A box counting renormalisation method is developed to calculate dimensions for strange attractors. The project supported by National Natural Science Foundation of China.
The necessity for a time local dimension in systems with time-varying attractors
DEFF Research Database (Denmark)
Særmark, Knud H; Ashkenazy, Y; Levitan, J
1997-01-01
We show that a simple non-linear system for ordinary differential equations may possess a time-varying attractor dimension. This indicates that it is infeasible to characterize EEG and MEG time series with a single time global dimension. We suggest another measure for the description of non...
Treatments of non-nuclear attractors within the theory of atoms in molecules
Alcoba, Diego R.; Lain, Luis; Torre, Alicia; Bochicchio, Roberto C.
2005-05-01
This Letter describes simple procedures to deal with non-nuclear attractors which are found in some results arising from topological population analyses of the molecular electron density. The proposed treatments have been applied to determine atomic electron populations and bond orders in the acetylene and dilithium molecules, achieving satisfactory chemical results. A detailed discussion of our proposals is reported.
The resident strikes back : Invader-induced switching of resident attractor
Mylius, S. D.; Diekmann, O
2001-01-01
The aim of this paper is two-fold: (a) by way of example, we elucidate the phenomenon of invader-induced switches in a resident attractor; (b) we expose in detail how resonance and phase have a strong impact when semelparous organisms (as, e.g. Pacific salmon) with different life-cycle lengths
Lorenz, HW; Nusse, HE
Goodwin's nonlinear accelerator model with periodic investment outlays is reconsidered and used as an economic example of the emergence of complex motion in nonlinear dynamical systems. In addition to chaotic attractors, the model can possess coexisting attracting periodic orbits or simple
Antimonotonicity, Chaos and Multiple Attractors in a Novel Autonomous Jerk Circuit
Kengne, J.; Negou, A. Nguomkam; Njitacke, Z. T.
2017-06-01
We perform a systematic analysis of a system consisting of a novel jerk circuit obtained by replacing the single semiconductor diode of the original jerk circuit described in [Sprott, 2011a] with a pair of semiconductor diodes connected in antiparallel. The model is described by a continuous time three-dimensional autonomous system with hyperbolic sine nonlinearity, and may be viewed as a control system with nonlinear velocity feedback. The stability of the (unique) fixed point, the local bifurcations, and the discrete symmetries of the model equations are discussed. The complex behavior of the system is categorized in terms of its parameters by using bifurcation diagrams, Lyapunov exponents, time series, Poincaré sections, and basins of attraction. Antimonotonicity, period doubling bifurcation, symmetry restoring crises, chaos, and coexisting bifurcations are reported. More interestingly, one of the key contributions of this work is the finding of various regions in the parameters’ space in which the proposed (“elegant”) jerk circuit experiences the unusual phenomenon of multiple competing attractors (i.e. coexistence of four disconnected periodic and chaotic attractors). The basins of attraction of various coexisting attractors display complexity (i.e. fractal basins boundaries), thus suggesting possible jumps between coexisting attractors in experiment. Results of theoretical analyses are perfectly traced by laboratory experimental measurements. To the best of the authors’ knowledge, the jerk circuit/system introduced in this work represents the simplest electrical circuit (only a quadruple op amplifier chip without any analog multiplier chip) reported to date capable of four disconnected periodic and chaotic attractors for the same parameters setting.
Laboratory and numerical simulation of internal wave attractors and their instability.
Brouzet, Christophe; Dauxois, Thierry; Ermanyuk, Evgeny; Joubaud, Sylvain; Sibgatullin, Ilias
2015-04-01
Internal wave attractors are formed as result of focusing of internal gravity waves in a confined domain of stably stratified fluid due to peculiarities of reflections properties [1]. The energy injected into domain due to external perturbation, is concentrated along the path formed by the attractor. The existence of attractors was predicted theoretically and proved both experimentally and numerically [1-4]. Dynamics of attractors is greatly influenced by geometrical focusing, viscous dissipation and nonlinearity. The experimental setup features Schmidt number equal to 700 which impose constraints on resolution in numerical schemes. Also for investigation of stability on large time intervals (about 1000 periods of external forcing) numerical viscosity may have significant impact. For these reasons, we have chosen spectral element method for investigation of this problem, what allows to carefully follow the nonlinear dynamics. We present cross-comparison of experimental observations and numerical simulations of long-term behavior of wave attractors. Fourier analysis and subsequent application of Hilbert transform are used for filtering of spatial components of internal-wave field [5]. The observed dynamics shows a complicated coupling between the effects of local instability and global confinement of the fluid domain. The unstable attractor is shown to act as highly efficient mixing box providing the efficient energy pathway from global-scale excitation to small-scale wave motions and mixing. Acknowledgement, IS has been partially supported by Russian Ministry of Education and Science (agreement id RFMEFI60714X0090) and Russian Foundation for Basic Research, grant N 15-01-06363. EVE gratefully acknowledges his appointment as a Marie Curie incoming fellow at Laboratoire de physique ENS de Lyon. This work has been partially supported by the ONLITUR grant (ANR-2011-BS04-006-01) and achieved thanks to the resources of PSMN from ENS de Lyon 1. Maas, L. R. M. & Lam, F
Energy Technology Data Exchange (ETDEWEB)
Márquez, Bicky A., E-mail: bmarquez@ivic.gob.ve; Suárez-Vargas, José J., E-mail: jjsuarez@ivic.gob.ve; Ramírez, Javier A. [Centro de Física, Instituto Venezolano de Investigaciones Científicas, km. 11 Carretera Panamericana, Caracas 1020-A (Venezuela, Bolivarian Republic of)
2014-09-01
Controlled transitions between a hierarchy of n-scroll attractors are investigated in a nonlinear optoelectronic oscillator. Using the system's feedback strength as a control parameter, it is shown experimentally the transition from Van der Pol-like attractors to 6-scroll, but in general, this scheme can produce an arbitrary number of scrolls. The complexity of every state is characterized by Lyapunov exponents and autocorrelation coefficients.
Periodicity, chaos, and multiple attractors in a memristor-based Shinriki's circuit
Energy Technology Data Exchange (ETDEWEB)
Kengne, J. [Laboratory of Automation and Applied Computer (LAIA), Department of Electrical Engineering, IUT-FV Bandjoun, University of Dschang, Dschang (Cameroon); Njitacke Tabekoueng, Z.; Kamdoum Tamba, V.; Nguomkam Negou, A. [Laboratory of Automation and Applied Computer (LAIA), Department of Electrical Engineering, IUT-FV Bandjoun, University of Dschang, Dschang (Cameroon); Department of Physics, Laboratory of Electronics and Signal Processing (LETS), Faculty of Science, University of Dschang, Dschang (Cameroon)
2015-10-15
In this contribution, a novel memristor-based oscillator, obtained from Shinriki's circuit by substituting the nonlinear positive conductance with a first order memristive diode bridge, is introduced. The model is described by a continuous time four-dimensional autonomous system with smooth nonlinearities. The basic dynamical properties of the system are investigated including equilibria and stability, phase portraits, frequency spectra, bifurcation diagrams, and Lyapunov exponents' spectrum. It is found that in addition to the classical period-doubling and symmetry restoring crisis scenarios reported in the original circuit, the memristor-based oscillator experiences the unusual and striking feature of multiple attractors (i.e., coexistence of a pair of asymmetric periodic attractors with a pair of asymmetric chaotic ones) over a broad range of circuit parameters. Results of theoretical analyses are verified by laboratory experimental measurements.
A SAT-based algorithm for finding attractors in synchronous Boolean networks.
Dubrova, Elena; Teslenko, Maxim
2011-01-01
This paper addresses the problem of finding attractors in synchronous Boolean networks. The existing Boolean decision diagram-based algorithms have limited capacity due to the excessive memory requirements of decision diagrams. The simulation-based algorithms can be applied to larger networks, however, they are incomplete. We present an algorithm, which uses a SAT-based bounded model checking to find all attractors in a Boolean network. The efficiency of the presented algorithm is evaluated by analyzing seven networks models of real biological processes, as well as 150,000 randomly generated Boolean networks of sizes between 100 and 7,000. The results show that our approach has a potential to handle an order of magnitude larger models than currently possible.
Sustaining high-energy orbits of bi-stable energy harvesters by attractor selection
Udani, Janav P.; Arrieta, Andres F.
2017-11-01
Nonlinear energy harvesters have the potential to efficiently convert energy over a wide frequency range; however, difficulties in attaining and sustaining high-energy oscillations restrict their applicability in practical scenarios. In this letter, we propose an actuation methodology to switch the state of bi-stable harvesters from the low-energy intra-well configuration to the coexisting high-energy inter-well configuration by controlled phase shift perturbations. The strategy is designed to introduce a change in the system state without creating distinct metastable attractors by exploiting the basins of attraction of the coexisting stable attractors. Experimental results indicate that the proposed switching strategy yields a significant improvement in energy transduction capabilities, is highly economical, enabling the rapid recovery of energy spent in the disturbance, and can be practically implemented with widely used low-strain piezoelectric transducers.
A birational mapping with a strange attractor: post-critical set and covariant curves
Energy Technology Data Exchange (ETDEWEB)
Bouamra, M; Hassani, S [Centre de Recherche Nucleaire d' Alger, 2 Bd. Frantz Fanon, BP 399, 16000 Alger (Algeria); Maillard, J-M [LPTMC, CNRS, Universite de Paris, Tour 24, 4eme etage, case 121, 4 Place Jussieu, 75252 Paris Cedex 05 (France)], E-mail: bouamrafr@yahoo.com, E-mail: maillard@lptmc.jussieu.fr, E-mail: maillard@lptl.jussieu.fr
2009-09-04
We consider some two-dimensional birational transformations. One of them is a birational deformation of the Henon map. For some of these birational mappings, the post-critical set (i.e. the iterates of the critical set) is infinite and we show that this gives straightforwardly the algebraic covariant curves of the transformation when they exist. These covariant curves are used to build the preserved meromorphic 2-form. One may also have an infinite post-critical set yielding a covariant curve which is not algebraic (transcendental). For two of the birational mappings considered, the post-critical set is finite and we claim that there is no algebraic covariant curve and no preserved meromorphic 2-form. For these two mappings with finite post-critical sets, attracting sets occur and we show that they pass the usual tests (Lyapunov exponents and the fractal dimension) for being strange attractors. The strange attractor of one of these two mappings is unbounded.
6d → 5d → 4d reduction of BPS attractors in flat gauged supergravities
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Kiril Hristov
2015-08-01
This is achieved starting from the BPS black string in 6d with an AdS3×S3 attractor and taking two different routes to arrive at a 1/2 BPS AdS2×S2 attractor of a non-BPS black hole in 4d N=2 flat gauged supergravity. The two inequivalent routes interchange the order of KK reduction on AdS3 and SS reduction on S3. We also find the commutator between the two operations after performing a duality transformation: on the level of the theory the result is the exchange of electric with magnetic gaugings; on the level of the solution we find a flip of the quartic invariant I4 to −I4.
Attractors for a Class of Abstract Evolution Equations with Fading Memory
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Xuan Wang
2017-01-01
Full Text Available In this paper, we study the dynamics of an abstract evolution equation with fading memory with a critical growing nonlinearity. By use of some new methods and asymptotic estimate techniques, we first verify the asymptotic compact of solution semigroup and then prove the existence of global attractors in weak topological space and strong topological space, while the forcing term only belongs to H-1(Ω or L2(Ω, respectively. The results are new and appear to be optimal.
Compact attractors for time-periodic age-structured population models
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Pierre Magal
2001-10-01
Full Text Available In this paper we investigate the existence of compact attractors for time-periodic age-structured models. So doing we investigate the eventual compactness of a class of abstract non-autonomous semiflow (non necessarily periodic. We apply this result to non-autonomous age-structured models. In the time periodic case, we obtain the existence of a periodic family of compact subsets that is invariant by the semiflow, and attract the solutions of the system.
A cortical attractor network with Martinotti cells driven by facilitating synapses.
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Pradeep Krishnamurthy
Full Text Available The population of pyramidal cells significantly outnumbers the inhibitory interneurons in the neocortex, while at the same time the diversity of interneuron types is much more pronounced. One acknowledged key role of inhibition is to control the rate and patterning of pyramidal cell firing via negative feedback, but most likely the diversity of inhibitory pathways is matched by a corresponding diversity of functional roles. An important distinguishing feature of cortical interneurons is the variability of the short-term plasticity properties of synapses received from pyramidal cells. The Martinotti cell type has recently come under scrutiny due to the distinctly facilitating nature of the synapses they receive from pyramidal cells. This distinguishes these neurons from basket cells and other inhibitory interneurons typically targeted by depressing synapses. A key aspect of the work reported here has been to pinpoint the role of this variability. We first set out to reproduce quantitatively based on in vitro data the di-synaptic inhibitory microcircuit connecting two pyramidal cells via one or a few Martinotti cells. In a second step, we embedded this microcircuit in a previously developed attractor memory network model of neocortical layers 2/3. This model network demonstrated that basket cells with their characteristic depressing synapses are the first to discharge when the network enters an attractor state and that Martinotti cells respond with a delay, thereby shifting the excitation-inhibition balance and acting to terminate the attractor state. A parameter sensitivity analysis suggested that Martinotti cells might, in fact, play a dominant role in setting the attractor dwell time and thus cortical speed of processing, with cellular adaptation and synaptic depression having a less prominent role than previously thought.
Alcoba, Diego R.; Lain, Luis; Torre, Alicia; Bochicchio, Roberto C.
2006-08-01
This work describes the partitioning of the electronic energy in systems in which the atoms in molecules theory predicts the existence of non-nuclear attractors. The procedure is based on our previous proposals within studies of topological population analysis [D.R. Alcoba, L. Lain, A. Torre, R.C. Bochicchio, Chem. Phys. Lett. 407 (2005) 379]. Numerical determinations in the acetylene and dilithium molecules are reported and compared with those arising from other approaches.
Pullback attractors for non-autonomous parabolic equations involving Grushin operators
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Cung The Anh
2010-01-01
Full Text Available Using the asymptotic a priori estimate method, we prove the existence of pullback attractors for a non-autonomous semilinear degenerate parabolic equation involving the Grushin operator in a bounded domain. We assume a polynomial type growth on the nonlinearity, and an exponential growth on the external force. The obtained results extend some existing results for non-autonomous reaction-diffusion equations.
Solving Stochastic Büchi Games on Infinite Arenas with a Finite Attractor
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Nathalie Bertrand
2013-06-01
Full Text Available We consider games played on an infinite probabilistic arena where the first player aims at satisfying generalized Büchi objectives almost surely, i.e., with probability one. We provide a fixpoint characterization of the winning sets and associated winning strategies in the case where the arena satisfies the finite-attractor property. From this we directly deduce the decidability of these games on probabilistic lossy channel systems.
Global attractors for the 2D hyperbolic Cahn–Hilliard equations
Khanmamedov, Azer; Yayla, Sema
2018-02-01
We consider the initial boundary value problem for the hyperbolic relaxation of the 2D Cahn-Hilliard equation with sub-cubic nonlinearity. Under mild regularity conditions on the nonlinearity, we prove the uniform (with respect to the initial data) boundedness of the weak solutions without assuming lower bound condition on the first derivative of the nonlinear term. Then, we prove the existence of the regular global attractor for the weak solutions.
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Mark Niedringhaus
Full Text Available Collective rhythmic dynamics from neurons is vital for cognitive functions such as memory formation but how neurons self-organize to produce such activity is not well understood. Attractor-based computational models have been successfully implemented as a theoretical framework for memory storage in networks of neurons. Additionally, activity-dependent modification of synaptic transmission is thought to be the physiological basis of learning and memory. The goal of this study is to demonstrate that using a pharmacological treatment that has been shown to increase synaptic strength within in vitro networks of hippocampal neurons follows the dynamical postulates theorized by attractor models. We use a grid of extracellular electrodes to study changes in network activity after this perturbation and show that there is a persistent increase in overall spiking and bursting activity after treatment. This increase in activity appears to recruit more "errant" spikes into bursts. Phase plots indicate a conserved activity pattern suggesting that a synaptic potentiation perturbation to the attractor leaves it unchanged. Lastly, we construct a computational model to demonstrate that these synaptic perturbations can account for the dynamical changes seen within the network.
An Attractor-Based Complexity Measurement for Boolean Recurrent Neural Networks
Cabessa, Jérémie; Villa, Alessandro E. P.
2014-01-01
We provide a novel refined attractor-based complexity measurement for Boolean recurrent neural networks that represents an assessment of their computational power in terms of the significance of their attractor dynamics. This complexity measurement is achieved by first proving a computational equivalence between Boolean recurrent neural networks and some specific class of -automata, and then translating the most refined classification of -automata to the Boolean neural network context. As a result, a hierarchical classification of Boolean neural networks based on their attractive dynamics is obtained, thus providing a novel refined attractor-based complexity measurement for Boolean recurrent neural networks. These results provide new theoretical insights to the computational and dynamical capabilities of neural networks according to their attractive potentialities. An application of our findings is illustrated by the analysis of the dynamics of a simplified model of the basal ganglia-thalamocortical network simulated by a Boolean recurrent neural network. This example shows the significance of measuring network complexity, and how our results bear new founding elements for the understanding of the complexity of real brain circuits. PMID:24727866
Hypercrater Bifurcations, Attractor Coexistence, and Unfolding in a 5D Model of Economic Dynamics
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Toichiro Asada
2011-01-01
Full Text Available Complex dynamical features are explored in a discrete interregional macrodynamic model proposed by Asada et al., using numerical methods. The model is five-dimensional with four parameters. The results demonstrate patterns of dynamical behaviour, such as bifurcation processes and coexistence of attractors, generated by high-dimensional discrete systems. In three cases of two-dimensional parameter subspaces the stability of equilibrium region is determined and its boundaries, the flip and Neimark-Hopf bifurcation curves, are identified by means of necessary coefficient criteria. In the first case closed invariant curves (CICs are found to occur through 5D-crater-type bifurcations, and for certain ranges of parameter values a stable equilibrium coexists with an unstable CIC associated with the subcritical bifurcation, as well as with an outer stable CIC. A remarkable feature of the second case is the coexistence of two attracting CICs outside the stability region. In both these cases the related hysteresis effects are illustrated by numerical simulations. In the third case a remarkable feature is the apparent unfolding of an attracting CIC before it evolves to a chaotic attractor. Examples of CICs and chaotic attractors are given in subspaces of phase space.
Alombah, N. Henry; Fotsin, Hilaire; Romanic, Kengne
In this paper, some complex nonlinear behaviors in a four-dimensional multiscroll autonomous memristor based chaotic system are investigated. This system is derived from the three-dimensional autonomous charge-controlled Muthuswamy-Chua simplest chaotic circuit. The system can generate four different coexisting attractors for a fixed set of parameters and different initial conditions. This phenomenon is relatively rare given that we have four different attractors namely: an equilibrium point, a stable limit cycle, a 16-peak limit cycle and a strange attractor that coexist in the system within a wide range of parameters. The nonlinear phenomenon of transient chaos is studied and revealed numerically in Matlab and Pspice environments. The complex transient dynamics of this memristive system under different initial states shows that the transient time depends strongly on the initial conditions. Moreover, this model displays spiking and bursting oscillations. The bursting behavior is classified according to the dynamics of separated slow and fast subsystems. It is shown to be of the fold-Hopf type. These complex dynamical behaviors of this system are investigated by means of numerical simulations and via Pspice circuit simulations. The use of bifurcation diagrams, Lyapunov exponents diagrams, power spectrums, phase portraits, time series, isospike diagram, basin of attraction, clearly shows these complex phenomena.
Hedrick, Kathryn R; Zhang, Kechen
2016-08-01
The problem of how the hippocampus encodes both spatial and nonspatial information at the cellular network level remains largely unresolved. Spatial memory is widely modeled through the theoretical framework of attractor networks, but standard computational models can only represent spaces that are much smaller than the natural habitat of an animal. We propose that hippocampal networks are built on a basic unit called a "megamap," or a cognitive attractor map in which place cells are flexibly recombined to represent a large space. Its inherent flexibility gives the megamap a huge representational capacity and enables the hippocampus to simultaneously represent multiple learned memories and naturally carry nonspatial information at no additional cost. On the other hand, the megamap is dynamically stable, because the underlying network of place cells robustly encodes any location in a large environment given a weak or incomplete input signal from the upstream entorhinal cortex. Our results suggest a general computational strategy by which a hippocampal network enjoys the stability of attractor dynamics without sacrificing the flexibility needed to represent a complex, changing world. Copyright © 2016 the American Physiological Society.
Hall attractor in axially symmetric magnetic fields in neutron star crusts.
Gourgouliatos, Konstantinos N; Cumming, Andrew
2014-05-02
We find an attractor for an axially symmetric magnetic field evolving under the Hall effect and subdominant Ohmic dissipation, resolving the question of the long-term fate of the magnetic field in neutron star crusts. The electron fluid is in isorotation, analogous to Ferraro's law, with its angular velocity being approximately proportional to the poloidal magnetic flux, Ω∝Ψ. This equilibrium is the long-term configuration of a magnetic field evolving because of the Hall effect and Ohmic dissipation. For an initial dipole-dominated field, the attractor consists mainly of a dipole and an octupole component accompanied by an energetically negligible quadrupole toroidal field. The field dissipates in a self-similar way: Although higher multipoles should decay faster, the toroidal field mediates transfer of energy into them from the lower ones, leading to an advection diffusion equilibrium and keeping the ratio of the poloidal multipoles almost constant. This has implications for the structure of the intermediate-age neutron stars, suggesting that their poloidal field should consist of a dipole and an octupole component accompanied by a very weak toroidal quadrupole. For initial conditions that have a higher multipole ℓ structure, the attractor consists mainly of ℓ and ℓ+2 poloidal components.
Modeling Multi-Agent Self-Organization through the Lens of Higher Order Attractor Dynamics.
Butner, Jonathan E; Wiltshire, Travis J; Munion, A K
2017-01-01
Social interaction occurs across many time scales and varying numbers of agents; from one-on-one to large-scale coordination in organizations, crowds, cities, and colonies. These contexts, are characterized by emergent self-organization that implies higher order coordinated patterns occurring over time that are not due to the actions of any particular agents, but rather due to the collective ordering that occurs from the interactions of the agents. Extant research to understand these social coordination dynamics (SCD) has primarily examined dyadic contexts performing rhythmic tasks. To advance this area of study, we elaborate on attractor dynamics, our ability to depict them visually, and quantitatively model them. Primarily, we combine difference/differential equation modeling with mixture modeling as a way to infer the underlying topological features of the data, which can be described in terms of attractor dynamic patterns. The advantage of this approach is that we are able to quantify the self-organized dynamics that agents exhibit, link these dynamics back to activity from individual agents, and relate it to other variables central to understanding the coordinative functionality of a system's behavior. We present four examples that differ in the number of variables used to depict the attractor dynamics (1, 2, and 6) and range from simulated to non-simulated data sources. We demonstrate that this is a flexible method that advances scientific study of SCD in a variety of multi-agent systems.
Geiyer, Daniel; Kauffman, Jeffrey L.
2016-04-01
Research in broadband nonlinear piezoelectric energy harvesting has gained traction in recent years as resonant, linear harvesters do not operate optimally in dynamic environments. By placing a linear harvester in a symmetric magnetic field, a nonlinear restoring force allows the system to realize motion across two potential wells. Different levels of excitation enable the system to oscillate solely in one potential well, periodically across both potential wells, or aperiodically across both potential wells. Periodic interwell motion is considered desirable for nonlinear energy harvesting systems, however, coexistent attractors inhibit uniqueness of such a solution. The authors have previously shown that chaotic, aperiodic motion between potential wells can be optimized for improved energy harvesting. The technique applied a chaotic controller to stabilize a large amplitude periodic orbit within the chaotic attractor. This work considers the basins of attraction of the two concurrent attractors and applies an intermittent control law in which the system is perturbed from a chaotic, aperiodic interwell response into the desirable large amplitude, periodic, interwell response.
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Paul eMiller
2013-05-01
Full Text Available Randomly connected recurrent networks of excitatory groups of neurons can possess a multitude of attractor states. When the internal excitatory synapses of these networks are depressing, the attractor states can be destabilized with increasing input. This leads to an itinerancy, where with either repeated transient stimuli, or increasing duration of a single stimulus, the network activity advances through sequences of attractor states. We find that the resulting network state, which persists beyond stimulus offset, can encode the number of stimuli presented via a distributed representation of neural activity with non-monotonic tuning curves for most neurons. Increased duration of a single stimulus is encoded via different distributed representations, so unlike an integrator, the network distinguishes separate successive presentations of a short stimulus from a single presentation of a longer stimulus with equal total duration. Moreover, different amplitudes of stimulus cause new, distinct activity patterns, such that changes in stimulus number, duration and amplitude can be distinguished from each other. These properties of the network depend on dynamic depressing synapses, as they disappear if synapses are static. Thus short-term synaptic depression allows a network to store separately the different dynamic properties of a spatially constant stimulus.
An attractor-based complexity measurement for Boolean recurrent neural networks.
Cabessa, Jérémie; Villa, Alessandro E P
2014-01-01
We provide a novel refined attractor-based complexity measurement for Boolean recurrent neural networks that represents an assessment of their computational power in terms of the significance of their attractor dynamics. This complexity measurement is achieved by first proving a computational equivalence between Boolean recurrent neural networks and some specific class of ω-automata, and then translating the most refined classification of ω-automata to the Boolean neural network context. As a result, a hierarchical classification of Boolean neural networks based on their attractive dynamics is obtained, thus providing a novel refined attractor-based complexity measurement for Boolean recurrent neural networks. These results provide new theoretical insights to the computational and dynamical capabilities of neural networks according to their attractive potentialities. An application of our findings is illustrated by the analysis of the dynamics of a simplified model of the basal ganglia-thalamocortical network simulated by a Boolean recurrent neural network. This example shows the significance of measuring network complexity, and how our results bear new founding elements for the understanding of the complexity of real brain circuits.
Using cell fate attractors to uncover transcriptional regulation of HL60 neutrophil differentiation
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Kauffman Stuart A
2009-02-01
Full Text Available Abstract Background The process of cellular differentiation is governed by complex dynamical biomolecular networks consisting of a multitude of genes and their products acting in concert to determine a particular cell fate. Thus, a systems level view is necessary for understanding how a cell coordinates this process and for developing effective therapeutic strategies to treat diseases, such as cancer, in which differentiation plays a significant role. Theoretical considerations and recent experimental evidence support the view that cell fates are high dimensional attractor states of the underlying molecular networks. The temporal behavior of the network states progressing toward different cell fate attractors has the potential to elucidate the underlying molecular mechanisms governing differentiation. Results Using the HL60 multipotent promyelocytic leukemia cell line, we performed experiments that ultimately led to two different cell fate attractors by two treatments of varying dosage and duration of the differentiation agent all-trans-retinoic acid (ATRA. The dosage and duration combinations of the two treatments were chosen by means of flow cytometric measurements of CD11b, a well-known early differentiation marker, such that they generated two intermediate populations that were poised at the apparently same stage of differentiation. However, the population of one treatment proceeded toward the terminally differentiated neutrophil attractor while that of the other treatment reverted back toward the undifferentiated promyelocytic attractor. We monitored the gene expression changes in the two populations after their respective treatments over a period of five days and identified a set of genes that diverged in their expression, a subset of which promotes neutrophil differentiation while the other represses cell cycle progression. By employing promoter based transcription factor binding site analysis, we found enrichment in the set of divergent
Cocaine-Induced Changes in Low-Dimensional Attractors of Local Field Potentials in Optogenetic Mice
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Sorinel A. Oprisan
2018-01-01
Full Text Available Optogenetically evoked local field potential (LFP recorded from the medial prefrontal cortex (mPFC of mice during basal conditions and following a systemic cocaine administration were analyzed. Blue light stimuli were delivered to mPFC through a fiber optic every 2 s and each trial was repeated 100 times. As in the previous study, we used a surrogate data method to check that nonlinearity was present in the experimental LFPs and only used the last 1.5 s of steady activity to measure the LFPs phase resetting induced by the brief 10 ms light stimulus. We found that the steady dynamics of the mPFC in response to light stimuli could be reconstructed in a three-dimensional phase space with topologically similar “8”-shaped attractors across different animals. Therefore, cocaine did not change the complexity of the recorded nonlinear data compared to the control case. The phase space of the reconstructed attractor is determined by the LFP time series and its temporally shifted versions by a multiple of some lag time. We also compared the change in the attractor shape between cocaine-injected and control using (1 dendrogram clustering and (2 Frechet distance. We found about 20% overlap between control and cocaine trials when classified using dendrogram method, which suggest that it may be possible to describe mathematically both data sets with the same model and slightly different model parameters. We also found that the lag times are about three times shorter for cocaine trials compared to control. As a result, although the phase space trajectories for control and cocaine may look similar, their dynamics is significantly different.
Huang, Sui
2006-03-01
During development of multicellular organisms, multipotent stem and progenitor cells undergo a series of hierarchically organized ``somatic speciation'' processes consisting of binary branching events to achieve the diversity of discretely distinct differentiated cell types in the body. Current paradigms of genetic regulation of development do not explain this discreteness, nor the time-irreversibility of differentiation. Each cell contains the same genome with the same N (˜ 25,000) genes and each cell type k is characterized by a distinct stable gene activation pattern, expressed as the cell state vector Sk(t) = xk1(t) ,.. xki(t),.. xkN(t), where xki is the activation state of gene i in cell type k. Because genes are engaged in a network of mutual regulatory interactions, the movement of Sk(t) in the N-dimensional state space is highly constrained and the organism can only realize a tiny fraction of all possible configurations Sk. Then, the trajectories of Sk reflect the diversifying developmental paths and the mature cell types are high-dimensional attractor states. Experimental results based on gene expression profile measurements during blood cell differentiation using DNA microarrays are presented that support the old idea that cell types are attractors. This basic notion is extended to treat binary fate decisions as bifurcations in the dynamics of networks circuits. Specifically, during cell fate decision, the metastable progenitor attractor is destabilized, poising the cell on a `watershed state' so that it can stochastically or in response to deterministic perturbations enter either one of two alternative fates. Overall, the model and supporting experimental data provide an overarching conceptual framework that helps explain how the specifics of gene network architecture produces discreteness and robustness of cell types, allows for both stochastic and deterministic cell fate decision and ensures directionality of organismal development.
AHaH Computing–From Metastable Switches to Attractors to Machine Learning
Nugent, Michael Alexander; Molter, Timothy Wesley
2014-01-01
Modern computing architecture based on the separation of memory and processing leads to a well known problem called the von Neumann bottleneck, a restrictive limit on the data bandwidth between CPU and RAM. This paper introduces a new approach to computing we call AHaH computing where memory and processing are combined. The idea is based on the attractor dynamics of volatile dissipative electronics inspired by biological systems, presenting an attractive alternative architecture that is able to adapt, self-repair, and learn from interactions with the environment. We envision that both von Neumann and AHaH computing architectures will operate together on the same machine, but that the AHaH computing processor may reduce the power consumption and processing time for certain adaptive learning tasks by orders of magnitude. The paper begins by drawing a connection between the properties of volatility, thermodynamics, and Anti-Hebbian and Hebbian (AHaH) plasticity. We show how AHaH synaptic plasticity leads to attractor states that extract the independent components of applied data streams and how they form a computationally complete set of logic functions. After introducing a general memristive device model based on collections of metastable switches, we show how adaptive synaptic weights can be formed from differential pairs of incremental memristors. We also disclose how arrays of synaptic weights can be used to build a neural node circuit operating AHaH plasticity. By configuring the attractor states of the AHaH node in different ways, high level machine learning functions are demonstrated. This includes unsupervised clustering, supervised and unsupervised classification, complex signal prediction, unsupervised robotic actuation and combinatorial optimization of procedures–all key capabilities of biological nervous systems and modern machine learning algorithms with real world application. PMID:24520315
AHaH computing-from metastable switches to attractors to machine learning.
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Michael Alexander Nugent
Full Text Available Modern computing architecture based on the separation of memory and processing leads to a well known problem called the von Neumann bottleneck, a restrictive limit on the data bandwidth between CPU and RAM. This paper introduces a new approach to computing we call AHaH computing where memory and processing are combined. The idea is based on the attractor dynamics of volatile dissipative electronics inspired by biological systems, presenting an attractive alternative architecture that is able to adapt, self-repair, and learn from interactions with the environment. We envision that both von Neumann and AHaH computing architectures will operate together on the same machine, but that the AHaH computing processor may reduce the power consumption and processing time for certain adaptive learning tasks by orders of magnitude. The paper begins by drawing a connection between the properties of volatility, thermodynamics, and Anti-Hebbian and Hebbian (AHaH plasticity. We show how AHaH synaptic plasticity leads to attractor states that extract the independent components of applied data streams and how they form a computationally complete set of logic functions. After introducing a general memristive device model based on collections of metastable switches, we show how adaptive synaptic weights can be formed from differential pairs of incremental memristors. We also disclose how arrays of synaptic weights can be used to build a neural node circuit operating AHaH plasticity. By configuring the attractor states of the AHaH node in different ways, high level machine learning functions are demonstrated. This includes unsupervised clustering, supervised and unsupervised classification, complex signal prediction, unsupervised robotic actuation and combinatorial optimization of procedures-all key capabilities of biological nervous systems and modern machine learning algorithms with real world application.
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Anhui Gu
2013-01-01
Full Text Available The long time behavior of solutions of the nonautonomous three-components reversible Gray-Scott system defined on the entire space ℝn is studied when the external forcing terms are unbounded in a phase space. The existence of a pullback global attractor for the equation is established in L2ℝn3 and H1ℝn3, respectively. The pullback asymptotic compactness of solutions is proved by using uniform estimates on the tails of solutions on unbounded domains.
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V.-T. Pham
2014-11-01
Full Text Available Memristor-based systems and their potential applications, in which memristor is both a nonlinear element and a memory element, have been received significant attention recently. A memristor-based hyperchaotic system with hidden attractor is studied in this paper. The dynamics properties of this hyperchaotic system are discovered through equilibria, Lyapunov exponents, bifurcation diagram, Poincaré map and limit cycles. In addition, its anti-synchronization scheme via adaptive control method is also designed and MATLAB simulations are shown. Finally, an electronic circuit emulating the memristor-based hyperchaotic system has been designed using off-the-shelf components.
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A. Weissblut
2012-03-01
Full Text Available This article – introduction to the structural theory of general view dynamical systems, based on construction of dynamic quantum models (DQM, offered by the author. This model is simply connected with traditional model of quantum mechanics (i.e. with the Schrodinger equation. At the same time obtained thus non – Hamiltonian quantum dynamics is easier than classical one: it allow building the clear structural theory and effective algorithms of research for concrete systems. This article is devoted mainly to such task. The algorithm of search for DQM attractors, based on this approach, is offered here.
CMB constraints on the inflaton couplings and reheating temperature in α-attractor inflation
Drewes, Marco; Kang, Jin U.; Mun, Ui Ri
2017-11-01
We study reheating in α-attractor models of inflation in which the inflaton couples to other scalars or fermions. We show that the parameter space contains viable regions in which the inflaton couplings to radiation can be determined from the properties of CMB temperature fluctuations, in particular the spectral index. This may be the only way to measure these fundamental microphysical parameters, which shaped the universe by setting the initial temperature of the hot big bang and contain important information about the embedding of a given model of inflation into a more fundamental theory of physics. The method can be applied to other models of single field inflation.
Global Attractors for Semilinear Parabolic Problems Involving X-Elliptic Operators
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Stefanie Sonner
2015-12-01
Full Text Available We consider semilinear parabolic equations involving an operator that is X-elliptic with respect to a family of vector fields X with suitable properties. The vector fields determine the natural functional setting associated to the problem and the admissible growth of the non-linearity. We prove the global existence of solutions and characterize their longtime behavior. In particular, we show the existence and finite fractal dimension of the global attractor of the generated semigroup and the convergence of solutions to an equilibrium solution when time tends to infinity.
Global attractor for the lattice dynamical system of a nonlinear Boussinesq equation
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Ahmed Y. Abdallah
2005-01-01
Full Text Available We will study the lattice dynamical system of a nonlinear Boussinesq equation. Our objective is to explore the existence of the global attractor for the solution semiflow of the introduced lattice system and to investigate its upper semicontinuity with respect to a sequence of finite-dimensional approximate systems. As far as we are aware, our result here is the first concerning the lattice dynamical system corresponding to a differential equation of second order in time variable and fourth order in spatial variable with nonlinearity involving the gradients.
Volatility Clustering and Scaling for Financial Time Series due to Attractor Bubbling
Krawiecki, A.; Hołyst, J. A.; Helbing, D.
2002-09-01
A microscopic model of financial markets is considered, consisting of many interacting agents (spins) with global coupling and discrete-time heat bath dynamics, similar to random Ising systems. The interactions between agents change randomly in time. In the thermodynamic limit, the obtained time series of price returns show chaotic bursts resulting from the emergence of attractor bubbling or on-off intermittency, resembling the empirical financial time series with volatility clustering. For a proper choice of the model parameters, the probability distributions of returns exhibit power-law tails with scaling exponents close to the empirical ones.
Shi, Pengliang
2008-03-01
In this paper, we investigate three kinds of numerical artifacts: period-like, strange-nonchaotic-attractor-like, and chaos-like behaviors in an extended logistic map system. These artificial behaviors appear in double precision and change into other real attractors in high-precision simulations. All of them are generated by a complicated dynamical process of the system and round-off truncation errors in numerical computations. A quantity β, which is closely related to the local Lyapunov exponent, is proposed to measure the extremum of large expansion or contraction dynamical capability. Eventually, we find the artifacts will emerge if the relation is not kept: αβ <γ, where γ is the attractor size of the system and α is the computational precision digit, for instance, α =2×10-16 for double precision, which has a unit round-off of 2×10-16.
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Zhonglin Wang
2014-01-01
Full Text Available A permanent magnet synchronous motor (PMSM model with smooth air gap and an exogenous periodic input is introduced and analyzed in this paper. With a simple mathematical transformation, a new nonautonomous Lorenz-like system is derived from this PMSM model, and this new three-dimensional system can display the complicated dynamics such as the chaotic attractor and the multiperiodic orbits by adjusting the frequency and amplitude of the exogenous periodic inputs. Moreover, this new system shows a double-deck chaotic attractor that is completely different from the four-wing chaotic attractors on topological structures, although the phase portrait shapes of the new attractor and the four-wing chaotic attractors are similar. The exotic phenomenon has been well demonstrated and investigated by numerical simulations, bifurcation analysis, and electronic circuit implementation.
Design of LED fish lighting attractors using horizontal/vertical LIDC mapping method.
Shen, S C; Huang, H J
2012-11-19
This study employs a sub-module concept to develop high-brightness light-emitting diode (HB-LED) fishing light arrays to replace traditional fishing light attractors. The horizontal/vertical (H/V) plane light intensity distribution curve (LIDC) of a LED light source are mapped to assist in the design of a non-axisymmetric lens with a fish-attracting light pattern that illuminates sufficiently large areas and alternates between bright and dark. These LED fishing light attractors are capable of attracting schools of fish toward the perimeter of the luminous zone surrounding fishing boats. Three CT2 boats (10 to 20 ton capacity) were recruited to conduct a field test for 1 y on the sea off the southwestern coast of Taiwan. Field tests show that HB-LED fishing light array installed 5 m above the boat deck illuminated a sea surface of 5 × 12 m and achieved an illuminance of 2000 lx. The test results show that the HB-LED fishing light arrays increased the mean catch of the three boats by 5% to 27%. In addition, the experimental boats consumed 15% to 17% less fuel than their counterparts.
DeCross, Matthew P.; Kaiser, David I.; Prabhu, Anirudh; Prescod-Weinstein, Chanda; Sfakianakis, Evangelos I.
2018-01-01
This is the first of a three-part series of papers, in which we study the preheating phase for multifield models of inflation involving nonminimal couplings. In this paper, we study the single-field attractor behavior that these models exhibit during inflation and quantify its strength and parameter dependence. We further demonstrate that the strong single-field attractor behavior persists after the end of inflation. Preheating in such models therefore generically avoids the "dephasing" that typically affects multifield models with minimally coupled fields, allowing efficient transfer of energy from the oscillating inflaton condensate(s) to coupled perturbations across large portions of parameter space. We develop a doubly covariant formalism for studying the preheating phase in such models and identify several features specific to multifield models with nonminimal couplings, including effects that arise from the nontrivial field-space manifold. In papers II and III, we apply this formalism to study how the amplification of adiabatic and isocurvature perturbations varies with parameters, highlighting several distinct regimes depending on the magnitude of the nonminimal couplings ξI.
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Bocheng Bao
2017-08-01
Full Text Available A new hyperbolic-type memristor emulator is presented and its frequency-dependent pinched hysteresis loops are analyzed by numerical simulations and confirmed by hardware experiments. Based on the emulator, a novel hyperbolic-type memristor based 3-neuron Hopfield neural network (HNN is proposed, which is achieved through substituting one coupling-connection weight with a memristive synaptic weight. It is numerically shown that the memristive HNN has a dynamical transition from chaotic, to periodic, and further to stable point behaviors with the variations of the memristor inner parameter, implying the stabilization effect of the hyperbolic-type memristor on the chaotic HNN. Of particular interest, it should be highly stressed that for different memristor inner parameters, different coexisting behaviors of asymmetric attractors are emerged under different initial conditions, leading to the existence of multistable oscillation states in the memristive HNN. Furthermore, by using commercial discrete components, a nonlinear circuit is designed and PSPICE circuit simulations and hardware experiments are performed. The results simulated and captured from the realization circuit are consistent with numerical simulations, which well verify the facticity of coexisting asymmetric attractors' behaviors.
Guided Self-Organization in a Dynamic Embodied System Based on Attractor Selection Mechanism
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Surya G. Nurzaman
2014-05-01
Full Text Available Guided self-organization can be regarded as a paradigm proposed to understand how to guide a self-organizing system towards desirable behaviors, while maintaining its non-deterministic dynamics with emergent features. It is, however, not a trivial problem to guide the self-organizing behavior of physically embodied systems like robots, as the behavioral dynamics are results of interactions among their controller, mechanical dynamics of the body, and the environment. This paper presents a guided self-organization approach for dynamic robots based on a coupling between the system mechanical dynamics with an internal control structure known as the attractor selection mechanism. The mechanism enables the robot to gracefully shift between random and deterministic behaviors, represented by a number of attractors, depending on internally generated stochastic perturbation and sensory input. The robot used in this paper is a simulated curved beam hopping robot: a system with a variety of mechanical dynamics which depends on its actuation frequencies. Despite the simplicity of the approach, it will be shown how the approach regulates the probability of the robot to reach a goal through the interplay among the sensory input, the level of inherent stochastic perturbation, i.e., noise, and the mechanical dynamics.
Higher derivative corrections to BPS black hole attractors in 4d gauged supergravity
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Hristov, Kiril [Institute for Nuclear Research and Nuclear Energy, Bulgarian Academy of Sciences, Tsarigradsko Chaussee 72, 1784 Sofia (Bulgaria); Katmadas, Stefanos [Dipartimento di Fisica, Università di Milano-Bicocca,I-20126 Milano (Italy); INFN, Sezione di Milano-Bicocca,I-20126 Milano (Italy); Lodato, Ivano [Department of Physics, IISER Pune,Homi Bhaba Road, Pashan, Pune (India)
2016-05-30
We analyze BPS black hole attractors in 4d gauged supergravity in the presence of higher derivative supersymmetric terms, including a Weyl-squared-type action, and determine the resulting corrections to the Bekenstein-Hawking entropy. The near-horizon geometry AdS{sub 2}×S{sup 2} (or other Riemann surface) preserves half of the supercharges in N=2 supergravity with Fayet-Iliopoulos gauging. We derive a relation between the entropy and the black hole charges that suggests via AdS/CFT how subleading corrections contribute to the supersymmetric index in the dual microscopic picture. Depending on the model, the attractors are part of full black hole solutions with different asymptotics, such as Minkowski, AdS{sub 4}, and hvLif{sub 4}. We give explicit examples for each of the asymptotic cases and comment on the implications. Among other results, we find that the Weyl-squared terms spoil the exact two-derivative relation to non-BPS asymptotically flat black holes in ungauged supergravity.
Noise-induced escape from attractors in one-dimensional maps
Beale, Paul D.
1989-10-01
The addition of external noise to a dynamical system described by an iterated map causes the orbit to escape from the attractor. The escape time τ has the behavior τ~=τ0exp(E0/Γ), where Γ is the noise temperature, E0 is the minimum escape energy, and τ0 is the inverse of the attempt rate. We will describe an analytical method for calculating the mean escape time based on the principle of minimum escape energy. Analytical solutions for E0 are presented for values of the mapping control parameter a close to tangent bifurcations and interior crises. The minimum escape energy displays a power-law dependence on the control parameter near tangent bifurcations (E0~||a-at||3/2) and near interior crises (E0~||a-ac||2). Numerical solutions are given for control-parameter values throughout the range of the attractor. The results agree with the results of Monte Carlo simulations of the logistic map and with independent work on the noise stability of rf-driven Josephson junctions.
Mirror Fermat Calabi-Yau Threefolds and Landau-Ginzburg Black Hole Attractors
Bellucci, S; Marrani, A; Yeranyan, A H
2006-01-01
We study black hole attractor equations for one-(complex structure)modulus Calabi-Yau spaces which are the mirror dual of Fermat Calabi-Yau threefolds (CY_{3}s). When exploring non-degenerate solutions near the Landau-Ginzburg point of the moduli space of such 4-dimensional compactifications, we always find two species of extremal black hole attractors, depending on the choice of the Sp(4,Z) symplectic charge vector, one 1/2-BPS (which is always stable, according to general results of special Kahler geometry) and one non-BPS. The latter turns out to be stable (local minimum of the ``effective black hole potential'' V_{BH}) for non-vanishing central charge, whereas it is unstable (saddle point of V_{BH}) for the case of vanishing central charge. This is to be compared to the large volume limit of one-modulus CY_{3}-compactifications (of Type II A superstrings), in which the homogeneous symmetric special Kahler geometry based on cubic prepotential admits (beside the 1/2-BPS ones) only non-BPS extremal black hol...
Distortions in recall from visual memory: two classes of attractors at work.
Huang, Jie; Sekuler, Robert
2010-02-24
In a trio of experiments, a matching procedure generated direct, analogue measures of short-term memory for the spatial frequency of Gabor stimuli. Experiment 1 showed that when just a single Gabor was presented for study, a retention interval of just a few seconds was enough to increase the variability of matches, suggesting that noise in memory substantially exceeds that in vision. Experiment 2 revealed that when a pair of Gabors was presented on each trial, the remembered appearance of one of the Gabors was influenced by: (1) the relationship between its spatial frequency and the spatial frequency of the accompanying, task-irrelevant non-target stimulus; and (2) the average spatial frequency of Gabors seen on previous trials. These two influences, which work on very different time scales, were approximately additive in their effects, each operating as an attractor for remembered appearance. Experiment 3 showed that a timely pre-stimulus cue allowed selective attention to curtail the influence of a task-irrelevant non-target, without diminishing the impact of the stimuli seen on previous trials. It appears that these two separable attractors influence distinct processes, with perception being influenced by the non-target stimulus and memory being influenced by stimuli seen on previous trials.
Rohlin distance and the evolution of influenza A virus: weak attractors and precursors.
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Raffaella Burioni
Full Text Available The evolution of the hemagglutinin amino acids sequences of Influenza A virus is studied by a method based on an informational metrics, originally introduced by Rohlin for partitions in abstract probability spaces. This metrics does not require any previous functional or syntactic knowledge about the sequences and it is sensitive to the correlated variations in the characters disposition. Its efficiency is improved by algorithmic tools, designed to enhance the detection of the novelty and to reduce the noise of useless mutations. We focus on the USA data from 1993/94 to 2010/2011 for A/H3N2 and on USA data from 2006/07 to 2010/2011 for A/H1N1. We show that the clusterization of the distance matrix gives strong evidence to a structure of domains in the sequence space, acting as weak attractors for the evolution, in very good agreement with the epidemiological history of the virus. The structure proves very robust with respect to the variations of the clusterization parameters, and extremely coherent when restricting the observation window. The results suggest an efficient strategy in the vaccine forecast, based on the presence of "precursors" (or "buds" populating the most recent attractor.
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Rajpoot, Subhash [California State University, Long Beach, CA (United States); Vacaru, Sergiu I. [Quantum Gravity Research, Topanga, CA (United States); University ' ' Al.I. Cuza' ' , Project IDEI, Iasi (Romania)
2017-05-15
Applying the anholonomic frame deformation method, we construct various classes of cosmological solutions for effective Einstein-Yang-Mills-Higgs, and two measure theories. The types of models considered are Freedman-Lemaitre-Robertson-Walker, Bianchi, Kasner and models with attractor configurations. The various regimes pertaining to plateau-type inflation, quadratic inflation, Starobinsky type and Higgs type inflation are presented. (orig.)
BOUNDARY CRISIS OF ATTRACTOR IN THE SIMULATION CAUSES OF THE DEGRADATION OF COMMERCIAL BIORESOURCES
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A. Yu. Perevarukha
2015-01-01
Full Text Available The article describes the computational model that unites the formalization of ecological features of the reproductive cycle of anadromous fish and the possibility of studying nonlinear effects in the population dynamics under anthropogenic impact. Event-driven component implemented in continuous time has allowed us to take into account changes in the survival generation in interrelation with the factors of growth rate. Discrete component trajectory of the dynamical system has two areas of attraction and is characterized by the reverse tangent bifurcation due to the impact of fishing, which dramatically transforms the population with the condition of irregular fluctuations in low numbers. The further emergence of «boundary crisis» for the interval attractor describes a common scenario an irreversible degradation of biological resources.
Internal wave attractors examined using laboratory experiments and 3D numerical simulations
Brouzet, Christophe; Scolan, H; Ermanyuk, E V; Dauxois, Thierry
2016-01-01
In the present paper, we combine numerical and experimental approaches to study the dynamics of stable and unstable internal wave attractors. The problem is considered in a classic trapezoidal setup filled with a uniformly stratified fluid. Energy is injected into the system at global scale by the small-amplitude motion of a vertical wall. Wave motion in the test tank is measured with the help of conventional synthetic schlieren and PIV techniques. The numerical setup closely reproduces the experimental one in terms of geometry and the operational range of the Reynolds and Schmidt numbers. The spectral element method is used as a numerical tool to simulate the nonlinear dynamics of a viscous salt-stratified fluid. We show that the results of three-dimensional calculations are in excellent qualitative and quantitative agreement with the experimental data, including the spatial and temporal parameters of the secondary waves produced by triadic resonance instability. Further, we explore experimentally and numeri...
d=4 Black Hole Attractors in N=2 Supergravity with Fayet-Iliopoulos Terms
Bellucci, S; Marrani, A; Yeranyan, A
2008-01-01
We generalize the description of the d=4 Attractor Mechanism based on an effective black hole (BH) potential to the presence of a gauging which does not modify the derivatives of the scalars and does not involve hypermultiplets. The obtained results do not rely necessarily on supersymmetry, and they can be extended to d>4, as well. Thence, we work out the example of the stu model of N=2 supergravity in the presence of Fayet-Iliopoulos terms, for the supergravity analogues of the magnetic and D0-D6 BH charge configurations, and in three different symplectic frames: the SO(1,1)^{2}, SO(2,2) covariant and SO(8)-truncated ones. The attractive nature of the critical points, related to the semi-positive definiteness of the Hessian matrix, is also studied.
Discontinuous attractor dimension at the synchronization transition of time-delayed chaotic systems.
Zeeb, Steffen; Dahms, Thomas; Flunkert, Valentin; Schöll, Eckehard; Kanter, Ido; Kinzel, Wolfgang
2013-04-01
The attractor dimension at the transition to complete synchronization in a network of chaotic units with time-delayed couplings is investigated. In particular, we determine the Kaplan-Yorke dimension from the spectrum of Lyapunov exponents for iterated maps and for two coupled semiconductor lasers. We argue that the Kaplan-Yorke dimension must be discontinuous at the transition and compare it to the correlation dimension. For a system of Bernoulli maps, we indeed find a jump in the correlation dimension. The magnitude of the discontinuity in the Kaplan-Yorke dimension is calculated for networks of Bernoulli units as a function of the network size. Furthermore, the scaling of the Kaplan-Yorke dimension as well as of the Kolmogorov entropy with system size and time delay is investigated.
Allawala, Altan; Marston, J B
2016-11-01
We investigate the Fokker-Planck description of the equal-time statistics of the three-dimensional Lorenz attractor with additive white noise. The invariant measure is found by computing the zero (or null) mode of the linear Fokker-Planck operator as a problem of sparse linear algebra. Two variants are studied: a self-adjoint construction of the linear operator and the replacement of diffusion with hyperdiffusion. We also access the low-order statistics of the system by a perturbative expansion in equal-time cumulants. A comparison is made to statistics obtained by the standard approach of accumulation via direct numerical simulation. Theoretical and computational aspects of the Fokker-Planck and cumulant expansion methods are discussed.
Unraveling chaotic attractors by complex networks and measurements of stock market complexity.
Cao, Hongduo; Li, Ying
2014-03-01
We present a novel method for measuring the complexity of a time series by unraveling a chaotic attractor modeled on complex networks. The complexity index R, which can potentially be exploited for prediction, has a similar meaning to the Kolmogorov complexity (calculated from the Lempel-Ziv complexity), and is an appropriate measure of a series' complexity. The proposed method is used to research the complexity of the world's major capital markets. None of these markets are completely random, and they have different degrees of complexity, both over the entire length of their time series and at a level of detail. However, developing markets differ significantly from mature markets. Specifically, the complexity of mature stock markets is stronger and more stable over time, whereas developing markets exhibit relatively low and unstable complexity over certain time periods, implying a stronger long-term price memory process.
Cosmological attractor inflation from the RG-improved Higgs sector of finite gauge theory
Elizalde, E; Pozdeeva, E O; Vernov, S Yu
2015-01-01
The possibility to construct an inflationary scenario for renormalization-group improved potentials corresponding to the Higgs sector of finite gauge models is investigated. Taking into account quantum corrections to the renormalization-group potential which sums all leading logs of perturbation theory is essential for a successful realization of the inflationary scenario, with very reasonable parameters values. The inflationary models thus obtained are seen to be in good agreement with the most recent and accurate observational data. More specifically, the values of the relevant inflationary parameters, $n_s$ and $r$, are close to the corresponding ones in the $R^2$ and Higgs-driven inflation scenarios. It is shown that the model here constructed and Higgs-driven inflation belong to the same class of cosmological attractors.
Toward pole inflation and attractors in supergravity: Chiral matter field inflation
Kobayashi, T.; Seto, O.; Tatsuishi, T. H.
2017-12-01
In string-inspired supergravity theory, the Kähler metric of chiral matter fields often has a pole. Such a Kähler metric is interesting from the viewpoint of the framework of the pole inflation, where the scalar potential can be stretched out to be flat around the pole for a canonically normalized field and inflation can be realized. However, when the Kähler metric has a pole, the scalar potential can also have a pole at the same point in supergravity theory. We study such supergravity models with a pole, and provide numerical analysis of inflationary dynamics and resultant density perturbation. In contrast with the usual pole inflation models, inflation in this supergravity-based model occurs not on the pole but in a region apart from the pole. We show that the existence of the pole in the scalar potential is crucial nevertheless. We also examine attractor behavior of our model.
Cosmological attractor inflation from the RG-improved Higgs sector of finite gauge theory
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Elizalde, Emilio; Odintsov, Sergei D. [Instituto de Ciencias del Espacio (ICE/CSIC) and Institut d' Estudis Espacials de Catalunya (IEEC), Campus UAB, Carrer de Can Magrans, s/n, Cerdanyola del Vallès, Barcelona, 08193 Spain (Spain); Pozdeeva, Ekaterina O.; Vernov, Sergey Yu., E-mail: elizalde@ieec.uab.es, E-mail: odintsov@ieec.uab.es, E-mail: pozdeeva@www-hep.sinp.msu.ru, E-mail: svernov@theory.sinp.msu.ru [Skobeltsyn Institute of Nuclear Physics, Lomonosov Moscow State University, Leninskie Gory 1, Moscow, 119991 (Russian Federation)
2016-02-01
The possibility to construct an inflationary scenario for renormalization-group improved potentials corresponding to the Higgs sector of finite gauge models is investigated. Taking into account quantum corrections to the renormalization-group potential which sums all leading logs of perturbation theory is essential for a successful realization of the inflationary scenario, with very reasonable parameter values. The inflationary models thus obtained are seen to be in good agreement with the most recent and accurate observational data. More specifically, the values of the relevant inflationary parameters, n{sub s} and r, are close to the corresponding ones in the R{sup 2} and Higgs-driven inflation scenarios. It is shown that the model here constructed and Higgs-driven inflation belong to the same class of cosmological attractors.
Attractor of Beam Equation with Structural Damping under Nonlinear Boundary Conditions
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Danxia Wang
2015-01-01
Full Text Available Simultaneously, considering the viscous effect of material, damping of medium, and rotational inertia, we study a kind of more general Kirchhoff-type extensible beam equation utt-uxxtt+uxxxx-σ(∫0l(ux2dxuxx-ϕ(∫0l(ux2dxuxxt=q(x, in [0,L]×R+ with the structural damping and the rotational inertia term. Little attention is paid to the longtime behavior of the beam equation under nonlinear boundary conditions. In this paper, under nonlinear boundary conditions, we prove not only the existence and uniqueness of global solutions by prior estimates combined with some inequality skills, but also the existence of a global attractor by the existence of an absorbing set and asymptotic compactness of corresponding solution semigroup. In addition, the same results also can be proved under the other nonlinear boundary conditions.
DEFF Research Database (Denmark)
Isaeva, Olga B.; Kuznetsov, Sergey P.; Mosekilde, Erik
2011-01-01
model corresponds to the situation of equality of natural frequencies of the partial oscillators, and another to a nonresonant ratio of the oscillation frequencies relating to each of the two pairs. Dynamics of all models are illustrated with diagrams indicating the transformation of the angular......The paper proposes an approach to constructing feasible examples of dynamical systems with hyperbolic chaotic attractors based on the successive transfer of excitation between two pairs of self-oscillators that are alternately active. An angular variable that measures the relations of the current...... amplitudes for the two oscillators of each pair undergoes a transformation in accordance with the expanding circle map during each cycle of the process. We start with equations describing the dynamics in terms of complex or real amplitudes and then examine two models based on van der Pol oscillators. One...
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Laura Dempere-Marco
Full Text Available The study of working memory capacity is of outmost importance in cognitive psychology as working memory is at the basis of general cognitive function. Although the working memory capacity limit has been thoroughly studied, its origin still remains a matter of strong debate. Only recently has the role of visual saliency in modulating working memory storage capacity been assessed experimentally and proved to provide valuable insights into working memory function. In the computational arena, attractor networks have successfully accounted for psychophysical and neurophysiological data in numerous working memory tasks given their ability to produce a sustained elevated firing rate during a delay period. Here we investigate the mechanisms underlying working memory capacity by means of a biophysically-realistic attractor network with spiking neurons while accounting for two recent experimental observations: 1 the presence of a visually salient item reduces the number of items that can be held in working memory, and 2 visually salient items are commonly kept in memory at the cost of not keeping as many non-salient items. Our model suggests that working memory capacity is determined by two fundamental processes: encoding of visual items into working memory and maintenance of the encoded items upon their removal from the visual display. While maintenance critically depends on the constraints that lateral inhibition imposes to the mnemonic activity, encoding is limited by the ability of the stimulated neural assemblies to reach a sufficiently high level of excitation, a process governed by the dynamics of competition and cooperation among neuronal pools. Encoding is therefore contingent upon the visual working memory task and has led us to introduce the concept of effective working memory capacity (eWMC in contrast to the maximal upper capacity limit only reached under ideal conditions.
Path integration and cognitive mapping in a continuous attractor neural network model.
Samsonovich, A; McNaughton, B L
1997-08-01
A minimal synaptic architecture is proposed for how the brain might perform path integration by computing the next internal representation of self-location from the current representation and from the perceived velocity of motion. In the model, a place-cell assembly called a "chart" contains a two-dimensional attractor set called an "attractor map" that can be used to represent coordinates in any arbitrary environment, once associative binding has occurred between chart locations and sensory inputs. In hippocampus, there are different spatial relations among place fields in different environments and behavioral contexts. Thus, the same units may participate in many charts, and it is shown that the number of uncorrelated charts that can be encoded in the same recurrent network is potentially quite large. According to this theory, the firing of a given place cell is primarily a cooperative effect of the activity of its neighbors on the currently active chart. Therefore, it is not particularly useful to think of place cells as encoding any particular external object or event. Because of its recurrent connections, hippocampal field CA3 is proposed as a possible location for this "multichart" architecture; however, other implementations in anatomy would not invalidate the main concepts. The model is implemented numerically both as a network of integrate-and-fire units and as a "macroscopic" (with respect to the space of states) description of the system, based on a continuous approximation defined by a system of stochastic differential equations. It provides an explanation for a number of hitherto perplexing observations on hippocampal place fields, including doubling, vanishing, reshaping in distorted environments, acquiring directionality in a two-goal shuttling task, rapid formation in a novel environment, and slow rotation after disorientation. The model makes several new predictions about the expected properties of hippocampal place cells and other cells of the
Dempere-Marco, Laura; Melcher, David P.; Deco, Gustavo
2012-01-01
The study of working memory capacity is of outmost importance in cognitive psychology as working memory is at the basis of general cognitive function. Although the working memory capacity limit has been thoroughly studied, its origin still remains a matter of strong debate. Only recently has the role of visual saliency in modulating working memory storage capacity been assessed experimentally and proved to provide valuable insights into working memory function. In the computational arena, attractor networks have successfully accounted for psychophysical and neurophysiological data in numerous working memory tasks given their ability to produce a sustained elevated firing rate during a delay period. Here we investigate the mechanisms underlying working memory capacity by means of a biophysically-realistic attractor network with spiking neurons while accounting for two recent experimental observations: 1) the presence of a visually salient item reduces the number of items that can be held in working memory, and 2) visually salient items are commonly kept in memory at the cost of not keeping as many non-salient items. Our model suggests that working memory capacity is determined by two fundamental processes: encoding of visual items into working memory and maintenance of the encoded items upon their removal from the visual display. While maintenance critically depends on the constraints that lateral inhibition imposes to the mnemonic activity, encoding is limited by the ability of the stimulated neural assemblies to reach a sufficiently high level of excitation, a process governed by the dynamics of competition and cooperation among neuronal pools. Encoding is therefore contingent upon the visual working memory task and has led us to introduce the concept of effective working memory capacity (eWMC) in contrast to the maximal upper capacity limit only reached under ideal conditions. PMID:22952608
Dempere-Marco, Laura; Melcher, David P; Deco, Gustavo
2012-01-01
The study of working memory capacity is of outmost importance in cognitive psychology as working memory is at the basis of general cognitive function. Although the working memory capacity limit has been thoroughly studied, its origin still remains a matter of strong debate. Only recently has the role of visual saliency in modulating working memory storage capacity been assessed experimentally and proved to provide valuable insights into working memory function. In the computational arena, attractor networks have successfully accounted for psychophysical and neurophysiological data in numerous working memory tasks given their ability to produce a sustained elevated firing rate during a delay period. Here we investigate the mechanisms underlying working memory capacity by means of a biophysically-realistic attractor network with spiking neurons while accounting for two recent experimental observations: 1) the presence of a visually salient item reduces the number of items that can be held in working memory, and 2) visually salient items are commonly kept in memory at the cost of not keeping as many non-salient items. Our model suggests that working memory capacity is determined by two fundamental processes: encoding of visual items into working memory and maintenance of the encoded items upon their removal from the visual display. While maintenance critically depends on the constraints that lateral inhibition imposes to the mnemonic activity, encoding is limited by the ability of the stimulated neural assemblies to reach a sufficiently high level of excitation, a process governed by the dynamics of competition and cooperation among neuronal pools. Encoding is therefore contingent upon the visual working memory task and has led us to introduce the concept of effective working memory capacity (eWMC) in contrast to the maximal upper capacity limit only reached under ideal conditions.
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Theiler, J. [Los Alamos National Lab., NM (United States)]|[Santa Fe Inst., NM (United States); Nichols, S. [Georgia Inst. of Tech., Atlanta, GA (United States). School of Physics
1993-09-01
The sensitivity to noise of the coherent (or in-phase) attractor for a set of N globally coupled maps is studied; these discrete-time maps are associated with the continuous-time equations of motion for a series array of Josephson junction oscillators. We investigate both geometrical properties of the basin of attraction in the large N limit, and the implications of this geometry on the average time for the system to ``escape`` from the coherently oscillating mode. Our main results are that the attractor basin maintains a box-shaped ``core`` of finite radius even as N {yields} {infinity}, and that the in-phase attractor of a large N array is much less vulnerable to noise than are the out-of-phase attractors.
Hjelmfelt, Allen; Harding, Robert H.; Tsujimoto, Kim K.; Ross, John
1990-03-01
Periodic perturbations are applied to the input fluxes of reactants in a system which exhibits autonomous oscillations, the combustion of acetaldehyde (ACH) and oxygen, and a system which exhibits damped oscillations, the combustion of methane and oxygen. The ACH system is studied by experiments and numerical analysis and the methane system is studied by numerical analysis. The periodic perturbations are in the form of a two-term Fourier series. Such perturbations may generate multiple attractors, which are either periodic or chaotic. We discuss two types of bistable responses: a new phase bistability, in which a subharmonic frequency is added to a sinusoidal perturbation at different phases relative to the periodic response; and jump phenomena, in which the resonant frequency of a nonlinear oscillator depends on the amplitude of the periodic perturbation. Both the ACH and the methane systems confirm the phase bistability. The additional complex behavior of bistability due to jump phenomena is seen only in calculations in the methane system. In both types of bistability a hysteresis loop is formed as we vary the form of the periodic perturbation. In the methane system, we find period doubling to chaos occuring on one branch of the hysteresis loop while the other branch remains periodic. The methane system has been studied in the context of the efficiency of power production. We calculate the efficiency corresponding to each bistable attractor and find one branch of each pair to be the more efficient mode of operation. In the case of the coexisting periodic and chaotic attractors the chaotic attractor is the more efficient mode of operation.
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Richard Eleftherios Boyatzis
2015-05-01
Full Text Available Personal and shared vision have a long history in management and organizational practices yet only recently have we begun to build a systematic body of empirical knowledge about the role of personal and shared vision in organizations. As the introductory paper for this special topic in Frontiers in Psychology, we present a theoretical argument as to the existence and critical role of two states in which a person, dyad, team, or organization may find themselves when engaging in the creation of a personal or shared vision: the positive emotional attractor (PEA and the negative emotional attractor (NEA. These two primary states are strange attractors, each characterized by three dimensions: (1 positive versus negative emotional arousal; (2 endocrine arousal of the parasympathetic nervous system versus sympathetic nervous system; and (3 neurological activation of the default mode network versus the task positive network. We argue that arousing the PEA is critical when creating or affirming a personal vision (i.e., sense of one’s purpose and ideal self. We begin our paper by reviewing the underpinnings of our PEA-NEA theory, briefly review each of the papers in this special issue, and conclude by discussing the practical implications of the theory.
Boyatzis, Richard E; Rochford, Kylie; Taylor, Scott N
2015-01-01
Personal and shared vision have a long history in management and organizational practices yet only recently have we begun to build a systematic body of empirical knowledge about the role of personal and shared vision in organizations. As the introductory paper for this special topic in Frontiers in Psychology, we present a theoretical argument as to the existence and critical role of two states in which a person, dyad, team, or organization may find themselves when engaging in the creation of a personal or shared vision: the positive emotional attractor (PEA) and the negative emotional attractor (NEA). These two primary states are strange attractors, each characterized by three dimensions: (1) positive versus negative emotional arousal; (2) endocrine arousal of the parasympathetic nervous system versus sympathetic nervous system; and (3) neurological activation of the default mode network versus the task positive network. We argue that arousing the PEA is critical when creating or affirming a personal vision (i.e., sense of one's purpose and ideal self). We begin our paper by reviewing the underpinnings of our PEA-NEA theory, briefly review each of the papers in this special issue, and conclude by discussing the practical implications of the theory.
Boyatzis, Richard E.; Rochford, Kylie; Taylor, Scott N.
2015-01-01
Personal and shared vision have a long history in management and organizational practices yet only recently have we begun to build a systematic body of empirical knowledge about the role of personal and shared vision in organizations. As the introductory paper for this special topic in Frontiers in Psychology, we present a theoretical argument as to the existence and critical role of two states in which a person, dyad, team, or organization may find themselves when engaging in the creation of a personal or shared vision: the positive emotional attractor (PEA) and the negative emotional attractor (NEA). These two primary states are strange attractors, each characterized by three dimensions: (1) positive versus negative emotional arousal; (2) endocrine arousal of the parasympathetic nervous system versus sympathetic nervous system; and (3) neurological activation of the default mode network versus the task positive network. We argue that arousing the PEA is critical when creating or affirming a personal vision (i.e., sense of one’s purpose and ideal self). We begin our paper by reviewing the underpinnings of our PEA–NEA theory, briefly review each of the papers in this special issue, and conclude by discussing the practical implications of the theory. PMID:26052300
Study of the attractor structure of an agent-based sociological model
Timpanaro, André M.; Prado, Carmen P. C.
2011-03-01
The Sznajd model is a sociophysics model that is based in the Potts model, and used for describing opinion propagation in a society. It employs an agent-based approach and interaction rules favouring pairs of agreeing agents. It has been successfully employed in modeling some properties and scale features of both proportional and majority elections (see for instance the works of A. T. Bernardes and R. N. Costa Filho), but its stationary states are always consensus states. In order to explain more complicated behaviours, we have modified the bounded confidence idea (introduced before in other opinion models, like the Deffuant model), with the introduction of prejudices and biases (we called this modification confidence rules), and have adapted it to the discrete Sznajd model. This generalized Sznajd model is able to reproduce almost all of the previous versions of the Sznajd model, by using appropriate choices of parameters. We solved the attractor structure of the resulting model in a mean-field approach and made Monte Carlo simulations in a Barabási-Albert network. These simulations show great similarities with the mean-field, for the tested cases of 3 and 4 opinions. The dynamical systems approach that we devised allows for a deeper understanding of the potential of the Sznajd model as an opinion propagation model and can be easily extended to other models, like the voter model. Our modification of the bounded confidence rule can also be readily applied to other opinion propagation models.
Vestibular and Attractor Network Basis of the Head Direction Cell Signal in Subcortical Circuits
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Benjamin J Clark
2012-03-01
Full Text Available Accurate navigation depends on a network of neural systems that encode the moment-to-moment changes in an animal’s directional orientation and location in space. Within this navigation system are head direction (HD cells, which fire persistently when an animal’s head is pointed in a particular direction (Sharp et al., 2001a; Taube, 2007. HD cells are widely thought to underlie an animal’s sense of spatial orientation, and research over the last 25+ years has revealed that this robust spatial signal is widely distributed across subcortical and cortical limbic areas. Much of this work has been directed at understanding the functional organization of the HD cell circuitry, and precisely how this signal is generated from sensory and motor systems. The purpose of the present review is to summarize some of the recent studies arguing that the HD cell circuit is largely processed in a hierarchical fashion, following a pathway involving the dorsal tegmental nuclei → lateral mammillary nuclei → anterior thalamus → parahippocampal and retrosplenial cortical regions. We also review recent work identifying bursting cellular activity in the HD cell circuit after lesions of the vestibular system, and relate these observations to the long held view that attractor network mechanisms underlie HD signal generation. Finally, we summarize the work to date suggesting that this network architecture may reside within the tegmento-mammillary circuit.
Baladi, Viviane; Kuna, Tobias; Lucarini, Valerio
2017-03-01
We consider a smooth one-parameter family t\\mapsto ≤ft( {{f}t}:M\\to M\\right) of diffeomorphisms with compact transitive Axiom A attractors {{ Λ }t} , denoting by \\text{d}{ρt} the SRB measure of {{f}t}{{|}{{ Λ t}}} . Our first result is that for any function θ in the Sobolev space Hpr(M) , with 1 and 0 < r < 1/p, the map t\\mapsto {\\int}θ \\text{d}{ρt} is α-Hölder continuous for all α . This applies to θ (x)=h(x) \\Theta ≤ft(g(x)-a\\right) (for all α <1 ) for h and g smooth and \\Theta the Heaviside function, if a is not a critical value of g. Our second result says that for any such function θ (x)=h(x) \\Theta ≤ft(g(x)-a\\right) so that in addition the intersection of ≤ft\\{x|g(x)=a\\right\\} with the support of h is foliated by ‘admissible stable leaves’ of f t , the map t\\mapsto {\\int}θ \\text{d}{ρt} is differentiable. (We provide distributional linear response and fluctuation-dissipation formulas for the derivative.) Obtaining linear response or fractional response for such observables θ is motivated by extreme-value theory.
Cancer as quasi-attractor in the gene expression phase space
Giuliani, A.
2017-09-01
It takes no more than 250 tissue types to build up a metazoan, and each tissue has a specific and largely invariant gene expression signature. This implies the `viable configurations' correspondent to a given activated/inactivated expression pattern over the entire genome are very few. This points to the presence of few `low energy deep valleys' correspondent to the allowed states of the system and is a direct consequence of the fact genes do not work by alone but embedded into genetic expression networks. Statistical thermodynamics formalism focusing on the changes in the degree of correlation of the studied systems allows to detect transition behavior in gene expression phase space resembling the phase transition of physical-chemistry studies. In this realm cancer can be intended as a sort of `parasite' sub-attractor of the corresponding healthy tissue that, in the case of disease, is `kinetically entrapped' into a sub-optimal solution. The consequences of such a state of affair for cancer therapies are potentially huge.
Solanka, Lukas; van Rossum, Mark CW; Nolan, Matthew F
2015-01-01
Neural computations underlying cognitive functions require calibration of the strength of excitatory and inhibitory synaptic connections and are associated with modulation of gamma frequency oscillations in network activity. However, principles relating gamma oscillations, synaptic strength and circuit computations are unclear. We address this in attractor network models that account for grid firing and theta-nested gamma oscillations in the medial entorhinal cortex. We show that moderate intrinsic noise massively increases the range of synaptic strengths supporting gamma oscillations and grid computation. With moderate noise, variation in excitatory or inhibitory synaptic strength tunes the amplitude and frequency of gamma activity without disrupting grid firing. This beneficial role for noise results from disruption of epileptic-like network states. Thus, moderate noise promotes independent control of multiplexed firing rate- and gamma-based computational mechanisms. Our results have implications for tuning of normal circuit function and for disorders associated with changes in gamma oscillations and synaptic strength. DOI: http://dx.doi.org/10.7554/eLife.06444.001 PMID:26146940
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Brajendra K Singh
Full Text Available Simple models of insect populations with non-overlapping generations have been instrumental in understanding the mechanisms behind population cycles, including wild (chaotic fluctuations. The presence of deterministic chaos in natural populations, however, has never been unequivocally accepted. Recently, it has been proposed that the application of chaos control theory can be useful in unravelling the complexity observed in real population data. This approach is based on structural perturbations to simple population models (population skeletons. The mechanism behind such perturbations to control chaotic dynamics thus far is model dependent and constant (in size and direction through time. In addition, the outcome of such structurally perturbed models is [almost] always equilibrium type, which fails to commensurate with the patterns observed in population data.We present a proportional feedback mechanism that is independent of model formulation and capable of perturbing population skeletons in an evolutionary way, as opposed to requiring constant feedbacks. We observe the same repertoire of patterns, from equilibrium states to non-chaotic aperiodic oscillations to chaotic behaviour, across different population models, in agreement with observations in real population data. Model outputs also indicate the existence of multiple attractors in some parameter regimes and this coexistence is found to depend on initial population densities or the duration of transient dynamics. Our results suggest that such a feedback mechanism may enable a better understanding of the regulatory processes in natural populations.
A mismatch-based model for memory reconsolidation and extinction in attractor networks.
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Remus Osan
Full Text Available The processes of memory reconsolidation and extinction have received increasing attention in recent experimental research, as their potential clinical applications begin to be uncovered. A number of studies suggest that amnestic drugs injected after reexposure to a learning context can disrupt either of the two processes, depending on the behavioral protocol employed. Hypothesizing that reconsolidation represents updating of a memory trace in the hippocampus, while extinction represents formation of a new trace, we have built a neural network model in which either simple retrieval, reconsolidation or extinction of a stored attractor can occur upon contextual reexposure, depending on the similarity between the representations of the original learning and reexposure sessions. This is achieved by assuming that independent mechanisms mediate Hebbian-like synaptic strengthening and mismatch-driven labilization of synaptic changes, with protein synthesis inhibition preferentially affecting the former. Our framework provides a unified mechanistic explanation for experimental data showing (a the effect of reexposure duration on the occurrence of reconsolidation or extinction and (b the requirement of memory updating during reexposure to drive reconsolidation.
Emergent properties of gene evolution: Species as attractors in phenotypic space
Reuveni, Eli; Giuliani, Alessandro
2012-02-01
The question how the observed discrete character of the phenotype emerges from a continuous genetic distance metrics is the core argument of two contrasted evolutionary theories: punctuated equilibrium (stable evolution scattered with saltations in the phenotype) and phyletic gradualism (smooth and linear evolution of the phenotype). Identifying phenotypic saltation on the molecular levels is critical to support the first model of evolution. We have used DNA sequences of ∼1300 genes from 6 isolated populations of the budding yeast Saccharomyces cerevisiae. We demonstrate that while the equivalent measure of the genetic distance show a continuum between lineage distance with no evidence of discrete states, the phenotypic space illustrates only two (discrete) possible states that can be associated with a saltation of the species phenotype. The fact that such saltation spans large fraction of the genome and follows by continuous genetic distance is a proof of the concept that the genotype-phenotype relation is not univocal and may have severe implication when looking for disease related genes and mutations. We used this finding with analogy to attractor-like dynamics and show that punctuated equilibrium could be explained in the framework of non-linear dynamics systems.
Effect of synapse dilution on the memory retrieval in structured attractor neural networks
Brunel, N.
1993-08-01
We investigate a simple model of structured attractor neural network (ANN). In this network a module codes for the category of the stored information, while another group of neurons codes for the remaining information. The probability distribution of stabilities of the patterns and the prototypes of the categories are calculated, for two different synaptic structures. The stability of the prototypes is shown to increase when the fraction of neurons coding for the category goes down. Then the effect of synapse destruction on the retrieval is studied in two opposite situations : first analytically in sparsely connected networks, then numerically in completely connected ones. In both cases the behaviour of the structured network and that of the usual homogeneous networks are compared. When lesions increase, two transitions are shown to appear in the behaviour of the structured network when one of the patterns is presented to the network. After the first transition the network recognizes the category of the pattern but not the individual pattern. After the second transition the network recognizes nothing. These effects are similar to syndromes caused by lesions in the central visual system, namely prosopagnosia and agnosia. In both types of networks (structured or homogeneous) the stability of the prototype is greater than the stability of individual patterns, however the first transition, for completely connected networks, occurs only when the network is structured.
Using machine learning to replicate chaotic attractors and calculate Lyapunov exponents from data
Pathak, Jaideep; Lu, Zhixin; Hunt, Brian R.; Girvan, Michelle; Ott, Edward
2017-12-01
We use recent advances in the machine learning area known as "reservoir computing" to formulate a method for model-free estimation from data of the Lyapunov exponents of a chaotic process. The technique uses a limited time series of measurements as input to a high-dimensional dynamical system called a "reservoir." After the reservoir's response to the data is recorded, linear regression is used to learn a large set of parameters, called the "output weights." The learned output weights are then used to form a modified autonomous reservoir designed to be capable of producing an arbitrarily long time series whose ergodic properties approximate those of the input signal. When successful, we say that the autonomous reservoir reproduces the attractor's "climate." Since the reservoir equations and output weights are known, we can compute the derivatives needed to determine the Lyapunov exponents of the autonomous reservoir, which we then use as estimates of the Lyapunov exponents for the original input generating system. We illustrate the effectiveness of our technique with two examples, the Lorenz system and the Kuramoto-Sivashinsky (KS) equation. In the case of the KS equation, we note that the high dimensional nature of the system and the large number of Lyapunov exponents yield a challenging test of our method, which we find the method successfully passes.
Seven-Disk Manifold, alpha-attractors and B-modes
Ferrara, Sergio
2016-01-01
Cosmological alpha-attractor models in \\cN=1 supergravity are based on hyperbolic geometry of a Poincar\\'e disk with the radius square {\\cal R}^2=3\\alpha. The predictions for the B-modes, r\\approx 3\\alpha {4\\over N^2}, depend on moduli space geometry and are robust for a rather general class of potentials. Here we notice that starting with M-theory compactified on a 7-manifold with G_2 holonomy, with a special choice of Betti numbers, one can obtain d=4 \\cN=1 supergravity with rank 7 scalar coset \\Big[{SL(2)\\over SO(2)}\\Big]^7. In a model where these 7 unit size Poincar\\'e disks have identified moduli one finds that 3 alpha =7. Assuming that the moduli space geometry of the phenomenological models is inherited from this version of M-theory, one would predict r \\approx 10^{-2} for 53 e-foldings. We also describe the related maximal supergravity and M/string theory models leading to preferred values 3 alpha =1,2,3,4,5,6,7.
Noise in attractor networks in the brain produced by graded firing rate representations.
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Tristan J Webb
Full Text Available Representations in the cortex are often distributed with graded firing rates in the neuronal populations. The firing rate probability distribution of each neuron to a set of stimuli is often exponential or gamma. In processes in the brain, such as decision-making, that are influenced by the noise produced by the close to random spike timings of each neuron for a given mean rate, the noise with this graded type of representation may be larger than with the binary firing rate distribution that is usually investigated. In integrate-and-fire simulations of an attractor decision-making network, we show that the noise is indeed greater for a given sparseness of the representation for graded, exponential, than for binary firing rate distributions. The greater noise was measured by faster escaping times from the spontaneous firing rate state when the decision cues are applied, and this corresponds to faster decision or reaction times. The greater noise was also evident as less stability of the spontaneous firing state before the decision cues are applied. The implication is that spiking-related noise will continue to be a factor that influences processes such as decision-making, signal detection, short-term memory, and memory recall even with the quite large networks found in the cerebral cortex. In these networks there are several thousand recurrent collateral synapses onto each neuron. The greater noise with graded firing rate distributions has the advantage that it can increase the speed of operation of cortical circuitry.
Red Queen strange attractors in host-parasite replicator gene-for-gene coevolution
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Sardanyes, Josep [Complex Systems Lab (ICREA-UPF), Barcelona Biomedical Research Park (PRBB-GRIB), Dr. Aiguader 88, 08003 Barcelona (Spain)]. E-mail: josep.sardanes@upf.edu; Sole, Ricard V. [Complex Systems Lab (ICREA-UPF), Barcelona Biomedical Research Park (PRBB-GRIB), Dr. Aiguader 88, 08003 Barcelona (Spain); Santa Fe Institute, 1399 Hyde Park Road, Santa Fe, NM 87501 (United States)
2007-06-15
We study a continuous time model describing gene-for-gene, host-parasite interactions among self-replicating macromolecules evolving in both neutral and rugged fitness landscapes. Our model considers polymorphic genotypic populations of sequences with 3 bits undergoing mutation and incorporating a 'type II' non-linear functional response in the host-parasite interaction. We show, for both fitness landscapes, a wide range of chaotic coevolutionary dynamics governed by Red Queen strange attractors. The analysis of a rugged fitness landscape for parasite sequences reveals that fittest genotypes achieve lower stationary concentration values, as opposed to the flattest ones, which undergo a higher stationary concentration. Our model also shows that the increase of parasites pressure (higher self-replication and mutation rates) generically involves a simplification of the host-parasite dynamical behavior, involving the transition from a chaotic to an ordered coevolutionary phase. Moreover, the same transition can also be found when hosts 'run' faster through the hypercube. Our results, in agreement with previous studies in host-parasite coevolution, suggest that chaos might be common in coevolutionary dynamics of changing self-replicating entities undergoing a host-parasite ecology.
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Kazuyuki Aihara
2011-04-01
Full Text Available The classical information-theoretic measures such as the entropy and the mutual information (MI are widely applicable to many areas in science and engineering. Csiszar generalized the entropy and the MI by using the convex functions. Recently, we proposed the grid occupancy (GO and the quasientropy (QE as measures of independence. The QE explicitly includes a convex function in its definition, while the expectation of GO is a subclass of QE. In this paper, we study the effect of different convex functions on GO, QE, and Csiszar’s generalized mutual information (GMI. A quality factor (QF is proposed to quantify the sharpness of their minima. Using the QF, it is shown that these measures can have sharper minima than the classical MI. Besides, a recursive algorithm for computing GMI, which is a generalization of Fraser and Swinney’s algorithm for computing MI, is proposed. Moreover, we apply GO, QE, and GMI to chaotic time series analysis. It is shown that these measures are good criteria for determining the optimum delay in strange attractor reconstruction.
Attractors in Sequence Space: Agent-Based Exploration of MHC I Binding Peptides.
Jäger, Natalie; Wisniewska, Joanna M; Hiss, Jan A; Freier, Anja; Losch, Florian O; Walden, Peter; Wrede, Paul; Schneider, Gisbert
2010-01-12
Ant Colony Optimization (ACO) is a meta-heuristic that utilizes a computational analogue of ant trail pheromones to solve combinatorial optimization problems. The size of the ant colony and the representation of the ants' pheromone trails is unique referring to the given optimization problem. In the present study, we employed ACO to generate novel peptides that stabilize MHC I protein on the plasma membrane of a murine lymphoma cell line. A jury of feedforward neural network classifiers served as fitness function for peptide design by ACO. Bioactive murine MHC I H-2K(b) stabilizing as well as nonstabilizing octapeptides were designed, synthesized and tested. These peptides reveal residue motifs that are relevant for MHC I receptor binding. We demonstrate how the performance of the implemented ACO algorithm depends on the colony size and the size of the search space. The actual peptide design process by ACO constitutes a search path in sequence space that can be visualized as trajectories on a self-organizing map (SOM). By projecting the sequence space on a SOM we visualize the convergence of the different solutions that emerge during the optimization process in sequence space. The SOM representation reveals attractors in sequence space for MHC I binding peptides. The combination of ACO and SOM enables systematic peptide optimization. This technique allows for the rational design of various types of bioactive peptides with minimal experimental effort. Here, we demonstrate its successful application to the design of MHC-I binding and nonbinding peptides which exhibit substantial bioactivity in a cell-based assay. Copyright © 2010 WILEY-VCH Verlag GmbH & Co. KGaA, Weinheim.
Low-dimensional attractor for neural activity from local field potentials in optogenetic mice.
Oprisan, Sorinel A; Lynn, Patrick E; Tompa, Tamas; Lavin, Antonieta
2015-01-01
We used optogenetic mice to investigate possible nonlinear responses of the medial prefrontal cortex (mPFC) local network to light stimuli delivered by a 473 nm laser through a fiber optics. Every 2 s, a brief 10 ms light pulse was applied and the local field potentials (LFPs) were recorded with a 10 kHz sampling rate. The experiment was repeated 100 times and we only retained and analyzed data from six animals that showed stable and repeatable response to optical stimulations. The presence of nonlinearity in our data was checked using the null hypothesis that the data were linearly correlated in the temporal domain, but were random otherwise. For each trail, 100 surrogate data sets were generated and both time reversal asymmetry and false nearest neighbor (FNN) were used as discriminating statistics for the null hypothesis. We found that nonlinearity is present in all LFP data. The first 0.5 s of each 2 s LFP recording were dominated by the transient response of the networks. For each trial, we used the last 1.5 s of steady activity to measure the phase resetting induced by the brief 10 ms light stimulus. After correcting the LFPs for the effect of phase resetting, additional preprocessing was carried out using dendrograms to identify "similar" groups among LFP trials. We found that the steady dynamics of mPFC in response to light stimuli could be reconstructed in a three-dimensional phase space with topologically similar "8"-shaped attractors across different animals. Our results also open the possibility of designing a low-dimensional model for optical stimulation of the mPFC local network.
Attractor learning in synchronized chaotic systems in the presence of unresolved scales
Wiegerinck, W.; Selten, F. M.
2017-12-01
Recently, supermodels consisting of an ensemble of interacting models, synchronizing on a common solution, have been proposed as an alternative to the common non-interactive multi-model ensembles in order to improve climate predictions. The connection terms in the interacting ensemble are to be optimized based on the data. The supermodel approach has been successfully demonstrated in a number of simulation experiments with an assumed ground truth and a set of good, but imperfect models. The supermodels were optimized with respect to their short-term prediction error. Nevertheless, they produced long-term climatological behavior that was close to the long-term behavior of the assumed ground truth, even in cases where the long-term behavior of the imperfect models was very different. In these supermodel experiments, however, a perfect model class scenario was assumed, in which the ground truth and imperfect models belong to the same model class and only differ in parameter setting. In this paper, we consider the imperfect model class scenario, in which the ground truth model class is more complex than the model class of imperfect models due to unresolved scales. We perform two supermodel experiments in two toy problems. The first one consists of a chaotically driven Lorenz 63 oscillator ground truth and two Lorenz 63 oscillators with constant forcings as imperfect models. The second one is more realistic and consists of a global atmosphere model as ground truth and imperfect models that have perturbed parameters and reduced spatial resolution. In both problems, we find that supermodel optimization with respect to short-term prediction error can lead to a long-term climatological behavior that is worse than that of the imperfect models. However, we also show that attractor learning can remedy this problem, leading to supermodels with long-term behavior superior to the imperfect models.
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Jose eDavila-Velderrain
2015-04-01
Full Text Available Robust temporal and spatial patterns of cell types emerge in the course of normal development in multicellular organisms. The onset of degenerative diseases may result from altered cell fate decisions that give rise to pathological phenotypes. Complex networks of genetic and non-genetic components underlie such normal and altered morphogenetic patterns. Here we focus on the networks of regulatory interactions involved in cell-fate decisions. Such networks modeled as dynamical non-linear systems attain particular stable configurations on gene activity that have been interpreted as cell-fate states. The network structure also restricts the most probable transition patterns among such states. The so-called Epigenetic Landscape (EL, originally proposed by C.H. Waddington, was an early attempt to conceptually explain the emergence of developmental choices as the result of intrinsic constraints (regulatory interactions shaped during evolution. Thanks to the wealth of molecular genetic and genomic studies, we are now able to postulate gene regulatory networks (GRN grounded on experimental data, and to derive EL models for specific cases. This, in turn, has motivated several mathematical and computational modeling approaches inspired by the EL concept, that may be useful tools to understand and predict cell-fate decisions and emerging patterns. In order to distinguish between the classical metaphorical EL proposal of Waddington, we refer to the Epigenetic Attractors Landscape (EAL, a proposal that is formally framed in the context of GRNs and dynamical systems theory. In this review we discuss recent EAL modeling strategies, their conceptual basis and their application in studying the emergence of both normal and pathological developmental processes. In addition, we discuss how model predictions can shed light into rational strategies for cell fate regulation, and we point to challenges ahead.
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Jairo A Díaz
Full Text Available In a previous research, we have described and documented self-assembly of geometric triangular chiral hexagon crystal-like complex organizations (GTCHC in human pathological tissues. This article documents and gathers insights into the magnetic field in cancer tissues and also how it generates an invariant functional geometric attractor constituted for collider partners in their entangled environment. The need to identify this hierarquic attractor was born out of the concern to understand how the vascular net of these complexes are organized, and to determine if the spiral vascular subpatterns observed adjacent to GTCHC complexes and their assembly are interrelational. The study focuses on cancer tissues and all the macroscopic and microscopic material in which GTCHC complexes are identified, which have been overlooked so far, and are rigorously revised. This revision follows the same parameters that were established in the initial phase of the investigation, but with a new item: the visualization and documentation of external dorsal serous vascular bed areas in spatial correlation with the localization of GTCHC complexes inside the tumors. Following the standard of the electro-optical collision model, we were able to reproduce and replicate collider patterns, that is, pairs of left and right hand spin-spiraled subpatterns, associated with the orientation of the spinning process that can be an expansion or contraction disposition of light particles. Agreement between this model and tumor data is surprisingly close; electromagnetic spiral patterns generated were identical at the spiral vascular arrangement in connection with GTCHC complexes in malignant tumors. These findings suggest that the framework of collagen type 1 - vasoactive vessels that structure geometric attractors in cancer tissues with invariant morphology sets generate collider partners in their magnetic domain with opposite biological behavior. If these principles are incorporated
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Matthew O’Lemmon
2013-01-01
Full Text Available The 2004 Indian Ocean Tsunami was epic in scale and scope and will go down as one of the largest natural disasters in human history. This paper presents an analysis of media coverage of the disaster and surveys of 206 local and international tourists in Khao Lak, Thailand, through the framework of chaos theory. Specifically, this paper examines the role of expert analysis as a periodic attractor during and after the tsunami. It will demonstrate how expert analysis brought disparate images and eyewitness testimony into greater focus, creating order in an otherwise chaotic environment.
True, Hans
2013-03-01
In recent years, several authors have proposed 'easier numerical methods' to find the critical speed in railway dynamical problems. Actually, the methods do function in some cases, but in most cases it is really a gamble. In this article, the methods are discussed and the pros and contras are commented upon. I also address the questions when a linearisation is allowed and the curious fact that the hunting motion is more robust than the ideal stationary-state motion on the track. Concepts such as 'multiple attractors', 'subcritical and supercritical bifurcations', 'permitted linearisation', 'the danger of running at supercritical speeds' and 'chaotic motion' are addressed.
Allouba, Hassan; Langa, Jose A.
2010-01-01
We delve deeper into the study of semimartingale attractors that we recently introduced in Allouba and Langa [4] H. Allouba and J.A. Langa, Semimartingale attractors for generalized Allen-Cahn SPDEs driven by space-time white noise, C. R. Acad. Sci. Paris, Ser. I 337 (2003), 201-206. In this article we focus on second order SPDEs of the Allen-Cahn type. After proving existence, uniqueness, and detailed regularity results for our SPDEs and a corresponding random PDE of Allen-Cahn type, we prov...
Nature of non-nuclear (3, -3) π-attractor and π-bonding: Theoretical analysis on π-electron density
Lv, Jiao; Yang, Lihua; Sun, Zheng; Meng, Lingpeng; Li, Xiaoyan
2018-01-01
Understanding the nature of π-electron density is important to characterize the conjugate π molecular systems. In this work, the π-electron densities of some typical conjugated π molecular systems were separated from their total electron densities; the positions and natures of non-nuclear (3, -3) π-attractors and the π-bond critical points (π-BCPs) are investigated. The calculated results show that for the same element, the position of the π-attractor is constant, regardless of the chemical surroundings. The position of the π-BCP is closer to the atom with the larger electronegativity.
Unstable Orbits and Milnor Attractors in the Discontinuous Flat Top Tent Map
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Schanz Michael
2012-08-01
Full Text Available In this work we consider the discontinuous flat top tent map which represents an example for discontinuous piecewise-smooth maps, whereby the system function is constant on some interval. Such maps show several characteristics caused by this constant value which are still insufficiently investigated. In this work we demonstrate that in the discontinuous flat top tent map every unstable periodic orbit may become a Milnor attractor. Moreover, it turns out that there exists a strong connection between stable and unstable orbits and that the appearance of a single unstable orbit may cause an infinite number of stable orbits to appear. Based on this connection we provide a more precise explanation of the recently discovered self-similar bifurcation scenario occurring in the discontinuous flat top tent map denoted as the nested period incrementing scenario. Dans ce travail nous considérons l’application discontinue de tente à haut plat qui représente un exemple d’application régulière par morceaux discontinue, où la fonction du système est constante sur un intervalle. De telles applications montrent plusieurs aspects causés par cette valeur constante qui ne sont toujours pas suffisamment compris. Dans ce travail nous démontrons que pour l’applicatiion discontinue de tente à haut plat toutes les orbites périodiques instables peuvent devenir un attracteur de Milnor. De plus, il apparaît qu’il y a un forte connexion entre les orbites stables et instables et que l’apparition d’une seule orbite instable peut provoquer l’apparition d’un nombre infini d’orbites stables. Sur la base de cette connexion nous proposons une explication précisée du scénario de bifurcation auto-similaire découvert récemment pour l’applicatiion discontinue de tente à haut plat, le scénario d’incrément de période nichée.
Nicolis, John S.; Katsikas, Anastassis A.
Collective parameters such as the Zipf's law-like statistics, the Transinformation, the Block Entropy and the Markovian character are compared for natural, genetic, musical and artificially generated long texts from generating partitions (alphabets) on homogeneous as well as on multifractal chaotic maps. It appears that minimal requirements for a language at the syntactical level such as memory, selectivity of few keywords and broken symmetry in one dimension (polarity) are more or less met by dynamically iterating simple maps or flows e.g. very simple chaotic hardware. The same selectivity is observed at the semantic level where the aim refers to partitioning a set of enviromental impinging stimuli onto coexisting attractors-categories. Under the regime of pattern recognition and classification, few key features of a pattern or few categories claim the lion's share of the information stored in this pattern and practically, only these key features are persistently scanned by the cognitive processor. A multifractal attractor model can in principle explain this high selectivity, both at the syntactical and the semantic levels.
Kengne, J.; Njitacke Tabekoueng, Z.; Fotsin, H. B.
2016-07-01
We perform a systematic analysis of a system consisting of an autonomous third order Duffing-Holmes type chaotic oscillator recently introduced by Tamasevicius et al. (2009). In this type of oscillators, the symmetrical characteristics of the nonlinear component necessary for generating chaotic oscillations is synthesized by using a pair of semiconductor diodes connected in anti-parallel. Based on the Shockley diode equation and a judicious choice of state variables, we derive a smooth mathematical model (involving hyperbolic sine and cosine functions) for a better description of both the regular and chaotic dynamics of the oscillator. The bifurcation analysis shows that chaos is achieved via the classical period-doubling and symmetry restoring crisis scenarios. More interestingly, some regions of the parameter space corresponding to the coexistence of multiple attractors (e.g. coexistence of four different attractors for the same values of system parameters) are discovered. This striking phenomenon is unique and has not yet been reported previously in an electrical circuit (the universal Chua's circuit included, in spite the immense amount of related research work), and thus represents a meaningful contribution to the understanding of the behavior of nonlinear dynamical systems in general. Some PSpice simulations of the nonlinear dynamics of the oscillator are carried out to verify the theoretical analysis.
Huang, Sui; Ingber, Donald E
It is commonly assumed that somatic evolution drives the multi-step process that produces metastatic cancer. But it is difficult to reconcile the inexorable progression towards metastasis in virtually all carcinomas and the associated complex change of cancer cell phenotype, characterized by an epithelial-to-mesenchymal transition, with the random nature of gene mutations. Given their irreversible nature, it is also difficult to explain why certain metastatic carcinomas can reform normal tissue boundaries and remain dormant for years at distant sites. Here we propose an encompassing conceptual framework based on system-level dynamics of gene regulatory networks that may help reconcile these inconsistencies. The concepts of gene expression state space and attractors are introduced which provide a mathematical and molecular basis for an "epigenetic landscape". We then describe how cancer cells are trapped in "embryonic attractors" because of distortions of this landscape caused by mutational rewiring of the regulatory network. The implications of this concept for a new integrative understanding of tumor formation and metastatic progression are discussed. This formal framework of cancer progression unites mainstream genetic determinism with alternative ideas that emphasize non-genetic influences, including chronic growth stimulation,extracellular matrix remodeling, alteration of cell mechanics and disruption of tissue architecture.
Directory of Open Access Journals (Sweden)
Mohadeseh Kanafchian
2017-04-01
In this paper, we first give a brief introduction into chaotic image encryption and then we investigate some important properties and behaviour of the logistic map. The logistic map, aperiodic trajectory, or random-like fluctuation, could not be obtained with some choice of initial condition. Therefore, a noisy logistic map with an additive system noise is introduced. The proposed scheme is based on the extended map of the Clifford strange attractor, where each dimension has a specific role in the encryption process. Two dimensions are used for pixel permutation and the third dimension is used for pixel diffusion. In order to optimize the Clifford encryption system we increase the space key by using the noisy logistic map and a novel encryption scheme based on the Clifford attractor and the noisy logistic map for secure transfer images is proposed. This algorithm consists of two parts: the noisy logistic map shuffle of the pixel position and the pixel value. We use times for shuffling the pixel position and value then we generate the new pixel position and value by the Clifford system. To illustrate the efficiency of the proposed scheme, various types of security analysis are tested. It can be concluded that the proposed image encryption system is a suitable choice for practical applications.
Hausmann, Anna; Toivonen, Tuuli; Heikinheimo, Vuokko; Tenkanen, Henrikki; Slotow, Rob; Di Minin, Enrico
2017-04-10
Charismatic megafauna are arguably considered the primary attractor of ecotourists to sub-Saharan African protected areas. However, the lack of visitation data across the whole continent has thus far prevented the investigation of whether charismatic species are indeed a key attractor of ecotourists to protected areas. Social media data can now be used for this purpose. We mined data from Instagram, and used generalized linear models with site- and country-level deviations to explore which socio-economic, geographical and biological factors explain social media use in sub-Saharan African protected areas. We found that charismatic species richness did not explain social media usage. On the other hand, protected areas that were more accessible, had sparser vegetation, where human population density was higher, and that were located in wealthier countries, had higher social media use. Interestingly, protected areas with lower richness in non-charismatic species had more users. Overall, our results suggest that more factors than simply charismatic species might explain attractiveness of protected areas, and call for more in-depth content analysis of the posts. With African countries projected to develop further in the near-future, more social media data will become available, and could be used to inform protected area management and marketing.
Fisher, Aaron J.; Newman, Michelle G.; Molenaar, Peter C. M.
2011-01-01
Objective: The present article aimed to demonstrate that the establishment of dynamic patterns during the course of psychotherapy can create attractor states for continued adaptive change following the conclusion of treatment. Method: This study is a secondary analysis of T. D. Borkovec and E. Costello (1993). Of the 55 participants in the…
Algaba, Antonio; Fernández-Sánchez, Fernando; Merino, Manuel; Rodríguez-Luis, Alejandro J.
2013-09-01
In this paper, we show, by means of a linear scaling in time and coordinates, that the Chen system, given by ẋ=a(y-x), ẏ=(c-a)x+cy-xz, ż=-bz+xy, is, generically (c ≠0), a special case of the Lorenz system. First, we infer that it is enough to consider two parameters to study its dynamics. Furthermore, we prove that there exists a homothetic transformation between the Chen and the Lorenz systems and, accordingly, all the dynamical behavior exhibited by the Chen system is present in the Lorenz system (since the former is a special case of the second). We illustrate our results relating Hopf bifurcations, periodic orbits, invariant surfaces, and chaotic attractors of both systems. Since there has been a large literature that has ignored this equivalence, the aim of this paper is to review and clarify this field. Unfortunately, a lot of the previous papers on the Chen system are unnecessary or incorrect.
Zuk, Pawel J; Kochańczyk, Marek; Jaruszewicz, Joanna; Bednorz, Witold; Lipniacki, Tomasz
2012-10-01
Living cells may be considered as biochemical reactors of multiple steady states. Transitions between these states are enabled by noise, or, in spatially extended systems, may occur due to the traveling wave propagation. We analyze a one-dimensional bistable stochastic birth-death process by means of potential and temperature fields. The potential is defined by the deterministic limit of the process, while the temperature field is governed by noise. The stable steady state in which the potential has its global minimum defines the global deterministic attractor. For the stochastic system, in the low noise limit, the stationary probability distribution becomes unimodal, concentrated in one of two stable steady states, defined in this study as the global stochastic attractor. Interestingly, these two attractors may be located in different steady states. This observation suggests that the asymptotic behavior of spatially extended stochastic systems depends on the substrate diffusivity and size of the reactor. We confirmed this hypothesis within kinetic Monte Carlo simulations of a bistable reaction- diffusion model on the hexagonal lattice. In particular, we found that although the kinase-phosphatase system remains inactive in a small domain, the activatory traveling wave may propagate when a larger domain is considered.
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Kiran Sree Pokkuluri
2014-01-01
Full Text Available Protein coding and promoter region predictions are very important challenges of bioinformatics (Attwood and Teresa, 2000. The identification of these regions plays a crucial role in understanding the genes. Many novel computational and mathematical methods are introduced as well as existing methods that are getting refined for predicting both of the regions separately; still there is a scope for improvement. We propose a classifier that is built with MACA (multiple attractor cellular automata and MCC (modified clonal classifier to predict both regions with a single classifier. The proposed classifier is trained and tested with Fickett and Tung (1992 datasets for protein coding region prediction for DNA sequences of lengths 54, 108, and 162. This classifier is trained and tested with MMCRI datasets for protein coding region prediction for DNA sequences of lengths 252 and 354. The proposed classifier is trained and tested with promoter sequences from DBTSS (Yamashita et al., 2006 dataset and nonpromoters from EID (Saxonov et al., 2000 and UTRdb (Pesole et al., 2002 datasets. The proposed model can predict both regions with an average accuracy of 90.5% for promoter and 89.6% for protein coding region predictions. The specificity and sensitivity values of promoter and protein coding region predictions are 0.89 and 0.92, respectively.
The 3-Attractor Water Model: Monte-Carlo Simulations with a New, Effective 2-Body Potential (BMW
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Francis Muguet
2003-02-01
Full Text Available According to the precepts of the 3-attractor (3-A water model, effective 2-body water potentials should feature as local minima the bifurcated and inverted water dimers in addition to the well-known linear water dimer global minimum. In order to test the 3-A model, a new pair wise effective intermolecular rigid water potential has been designed. The new potential is part of new class of potentials called BMW (Bushuev-Muguet-Water which is built by modifying existing empirical potentials. This version (BMW v. 0.1 has been designed by modifying the SPC/E empirical water potential. It is a preliminary version well suited for exploratory Monte-Carlo simulations. The shape of the potential energy surface (PES around each local minima has been approximated with the help of Gaussian functions. Classical Monte Carlo simulations have been carried out for liquid water in the NPT ensemble for a very wide range of state parameters up to the supercritical water regime. Thermodynamic properties are reported. The radial distributions functions (RDFs have been computed and are compared with the RDFs obtained from Neutron Scattering experimental data. Our preliminary Monte-Carlo simulations show that the seemingly unconventional hypotheses of the 3-A model are most plausible. The simulation has also uncovered a totally new role for 2-fold H-bonds.
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Jun Ma
Full Text Available In this paper, a new four-variable dynamical system is proposed to set chaotic circuit composed of memristor and Josephson junction, and the dependence of chaotic behaviors on nonlinearity is investigated. A magnetic flux-controlled memristor is used to couple with the RCL-shunted junction circuit, and the dynamical behaviors can be modulated by changing the coupling intensity between the memristor and the RCL-shunted junction. Bifurcation diagram and Lyapunov exponent are calculated to confirm the emergence of chaos in the improved dynamical system. The outputs and dynamical behaviors can be controlled by the initial setting and external stimulus as well. As a result, chaos can be suppressed and spiking occurs in the sampled outputs under negative feedback, while applying positive feedback type via memristor can be effective to trigger chaos. Furthermore, it is found that the number of multi-attractors in the Jerk circuit can be modulated when memristor coupling is applied on the circuit. These results indicate that memristor coupling can be effective to control chaotic circuits and it is also useful to reproduce dynamical behaviors for neuronal activities.
A revised catalog of CfA galaxy groups in the Virgo/Great Attractor flow field
Nolthenius, Richard
1993-01-01
A new identification of groups and clusters in the CfAl Catalog of Huchra, et al. (1983) is presented, using a percolation algorithm to identify density enhancements. The procedure differs from that of the original Geller and Huchra (1983; GH) catalog in several important respects; galaxy distances are calculated from the Virgo-Great Attractor flow model of Faber and Burnstein (1988), the adopted distance linkage criteria is only approx. 1/4 as large as in the Geller and Huchra catalog, the sky link relation is taken from Nolthenius and White (1987), correction for interstellar extinction is included, and 'by-hand' adjustments to group memberships are made in the complex regions of Virgo/Coma I/Ursa Major and Coma/A1367 (to allow for varying group velocity dispersions and to trim unphysical 'spider arms'). Since flow model distances are poorly determined in these same regions, available distances from the IR Tully-Fisher planetary nebula luminosity function and surface brightness resolution methods are adopted if possible.
Moussas, X.; Coustenis, A.; Solomonidou, A.; Bampasidis, G.; Bratsolis, E.; Stamogiorgos, S.
2012-04-01
People have always been charmed by the beauty of the starry sky, the Sun, the Moon, the planets, the Solar System and the mystery of the birth and the evolution of the Cosmos. As the deep space is believed to be the only territory unexplored by the mankind, the humanity has always been looking forward to the discoveries of Space Science. However, due to the complicated character of modern Science and Technology, people usually are alienated from scientific issues. Dealing with this situation, the Space Group of the National and Kapodistrian University of Athens in collaboration with LESIA of the Observatoire de Paris-Meudon, have been performing several campaigns to raise the public awareness of Science and Astronomy with emphasis to the Solar System exploration. The Space Group of the University of Athens has scientific impact in both the Space Physics field and the public outreach of Astronomy throughout Europe, Northern Africa and the United States of America. Using the Antikythera Mechanism as central object and as a great attractor of children and the general public to astronomy and even philosophy, we have performed numerous outreach activities focalized on the general audience in order to conceptualize astronomical phenomena and change their prior usually not very clear knowledge and intuition. These Solar System events, conducted by our Group, help young people to develop their critical thinking, self-expression and creative talents and eventually to love astronomy and to develop an interest the planets. Their introduction into the space field seems essential for cultivation of these skills.
CONVERSION OF THE HYDRO-CLIMATIC RESOURCES IN TOURISM ATTRACTORS IN ROŞIA MONTANĂ-ABRUD MINING AREA
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JURJ MARIA-ADINA
2015-03-01
Full Text Available This paper aims to analyze water and climate resources from Roşia Montană-Abrud mining area and to emphasize the necessity to transform these resources into tourism attractors. The most significant water resources are the antrophogenic lakes called ”tăuri” which represent elements of great originality created for mining purposes. The first man-made lakes were created in order to activate the stamping mills used to grind the auriferous ores and occurred in this area since ancient times. These lakes have had an fundamental role during the millenary mining exploitation until the middle of 20th century, after which they had lost their significance during the industrial process, as a consequence of the 1948 nationalization. Previous research identified traces of a big number of lakes, out of which there are active only 9 in the present. Although these lakes play no role in modern mining, they have a high cultural value which can be capitalized through tourism activities. The mentioned area, due to its altitude, is also appropriate for practising mountain climatic therapy. Given the fact that water and climate resources inherently have a significant role when concerning outdoor activities, Roşia Montană-Abrud area is suitable for recreational nautical tourism, winter sports and mountain cure, but one has to consider that hidro-climatic resources are also important for rural tourism, agritourism, ecotourism etc., for which reason it is imperative to be provided adequate tourism planning and tourism promotion in order to capitalize them properly.
Huang, S.; Ingber, D. E.
2000-01-01
Development of characteristic tissue patterns requires that individual cells be switched locally between different phenotypes or "fates;" while one cell may proliferate, its neighbors may differentiate or die. Recent studies have revealed that local switching between these different gene programs is controlled through interplay between soluble growth factors, insoluble extracellular matrix molecules, and mechanical forces which produce cell shape distortion. Although the precise molecular basis remains unknown, shape-dependent control of cell growth and function appears to be mediated by tension-dependent changes in the actin cytoskeleton. However, the question remains: how can a generalized physical stimulus, such as cell distortion, activate the same set of genes and signaling proteins that are triggered by molecules which bind to specific cell surface receptors. In this article, we use computer simulations based on dynamic Boolean networks to show that the different cell fates that a particular cell can exhibit may represent a preprogrammed set of common end programs or "attractors" which self-organize within the cell's regulatory networks. In this type of dynamic network model of information processing, generalized stimuli (e.g., mechanical forces) and specific molecular cues elicit signals which follow different trajectories, but eventually converge onto one of a small set of common end programs (growth, quiescence, differentiation, apoptosis, etc.). In other words, if cells use this type of information processing system, then control of cell function would involve selection of preexisting (latent) behavioral modes of the cell, rather than instruction by specific binding molecules. Importantly, the results of the computer simulation closely mimic experimental data obtained with living endothelial cells. The major implication of this finding is that current methods used for analysis of cell function that rely on characterization of linear signaling pathways or
Pierini, Stefano; Ghil, Michael; Chekroun, Mickael D.
2017-04-01
A low-order quasigeostrophic model captures several key features of intrinsic low-frequency variability of the oceans' wind-driven circulation. This double-gyre model is used here as a prototype of an unstable and nonlinear dynamical system with time-dependent forcing to explore basic features of climate change in the presence of natural variability [1,2]. The studies rely on the theoretical framework of nonautonomous dynamical systems and of their pullback attractors (PBAs), namely the time-dependent invariant sets that attract all trajectories initialized in the remote past. Ensemble simulations help us explore these PBAs. The chaotic PBAs of the periodically forced model [1] are found to be cyclo-stationary and cyclo-ergodic. Two parameters are then introduced to analyze the topological structure of the PBAs as a function of the forcing period; their joint use allows one to identify four distinct forms of sensitivity to initial state that correspond to distinct system behaviors. The model's response to periodic forcing turns out to be, in most cases, very sensitive to the initial state. The system is then forced by a synthetic aperiodic forcing [2]. The existence of a global PBA is rigorously demonstrated. We then assess the convergence of trajectories to this PBA by computing the probability density function (PDF) of trajectory localization in the model's phase space. A sensitivity analysis with respect to forcing amplitude shows that the global PBA experiences large modifications if the underlying autonomous system is dominated by small-amplitude limit cycles, while the changes are less dramatic in a regime characterized by large-amplitude relaxation oscillations. The dependence of the attracting sets on the choice of the ensemble of initial states is then analyzed. Two types of basins of attraction coexist for certain parameter ranges; they contain chaotic and nonchaotic trajectories, respectively. The statistics of the former does not depend on the initial
Conductivities from attractors
Energy Technology Data Exchange (ETDEWEB)
Erdmenger, Johanna [Max-Planck-Institut für Physik (Werner-Heisenberg-Institut), Föhringer Ring 6, D-80805 Munich (Germany); Institut für Theoretische Physik und Astrophysik, Julius-Maximilians-Universität Würzburg, Am Hubland, 97074 Würzburg (Germany); Fernández, Daniel [Max-Planck-Institut für Physik (Werner-Heisenberg-Institut), Föhringer Ring 6, D-80805 Munich (Germany); Science Institute, University of Iceland, Dunhaga 3, 107 Reykjavík (Iceland); Goulart, Prieslei [Max-Planck-Institut für Physik (Werner-Heisenberg-Institut), Föhringer Ring 6, D-80805 Munich (Germany); Instituto de Física Teórica, UNESP-Universidade Estadual Paulista,R. Dr. Bento T. Ferraz 271, Bl. II, São Paulo 01140-070, SP (Brazil); Witkowski, Piotr [Max-Planck-Institut für Physik (Werner-Heisenberg-Institut), Föhringer Ring 6, D-80805 Munich (Germany)
2017-03-28
In the context of applications of the AdS/CFT correspondence to condensed matter physics, we compute conductivities for field theory duals of dyonic planar black holes in 3+1-dimensional Einstein-Maxwell-dilaton theories at zero temperature. We combine the near-horizon data obtained via Sen’s entropy function formalism with known expressions for conductivities. In this way we express the conductivities in terms of the extremal black hole charges. We apply our approach to three different examples for dilaton theories for which the background geometry is not known explicitly. For a constant scalar potential, the thermoelectric conductivity explicitly scales as α{sub xy}∼N{sup 3/2}, as expected. For the same model, our approach yields a finite result for the heat conductivity κ/T∝N{sup 3/2} even for T→0.
Recurrences of strange attractors
Indian Academy of Sciences (India)
2015-11-27
Nov 27, 2015 ... Author Affiliations. E J Ngamga1 A Nandi2 R Ramaswamy2 M C Romano3 M Thiel3 J Kurths1. Nonlinear Dynamics Group, Institute of Physics, University of Potsdam, Potsdam 14415, Germany; School of Physical Sciences, Jawaharlal Nehru University, New Delhi 110 067, India; Department of Physics, ...
Recurrences of strange attractors
Indian Academy of Sciences (India)
order to detect the transitions from or to SNAs too. The outline of this paper is as follows: in §2, we present the recurrence approach to detect the different transitions. This approach is applied in §3 to detect transi- tions to SNAs in the quasiperiodically forced logistic map. Section 4 examines the transition from SNAs to chaos.
Schlünzen, N.; Joost, J.-P.; Bonitz, M.
2017-09-01
In a recent Rapid Communication [A. Stan, Phys. Rev. B 93, 041103(R) (2016), 10.1103/PhysRevB.93.041103], the reliability of the Keldysh-Kadanoff-Baym equations (KBE) using correlated self-energy approximations applied to linear and nonlinear response has been questioned. In particular, the existence of a universal attractor has been predicted that would drive the dynamics of any correlated system towards an unphysical homogeneous density distribution regardless of the system type, the interaction, and the many-body approximation. Moreover, it was conjectured that even the mean-field dynamics would be damped. Here, by performing accurate solutions of the KBE for situations studied in that paper, we prove these claims wrong, being caused by numerical inaccuracies.
Energy Technology Data Exchange (ETDEWEB)
Garcia Velarde, M.
1977-07-01
Thermo convective instabilities in horizontal fluid layers are discussed with emphasis on the Rayleigh-Bernard model problem. Steady solutions and time-dependent phenomena (relaxation oscillations and transition to turbulence) are studied within the nonlinear Boussinesq-Oberbeck approximation. Homogeneous steady solutions, limit cycles, and inhomogeneous (ordered) spatial structures are also studied in simple reaction-diffusion systems. Lastly, the non-periodic attractor that appears at large Rayleigh numbers in the truncated Boussinesq-Oberbeck model of Lorenz, is constructed, and a discussion of turbulent behavior is given. (Author) 105 refs.
Free Energy, Value, and Attractors
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Karl Friston
2012-01-01
Full Text Available It has been suggested recently that action and perception can be understood as minimising the free energy of sensory samples. This ensures that agents sample the environment to maximise the evidence for their model of the world, such that exchanges with the environment are predictable and adaptive. However, the free energy account does not invoke reward or cost-functions from reinforcement-learning and optimal control theory. We therefore ask whether reward is necessary to explain adaptive behaviour. The free energy formulation uses ideas from statistical physics to explain action in terms of minimising sensory surprise. Conversely, reinforcement-learning has its roots in behaviourism and engineering and assumes that agents optimise a policy to maximise future reward. This paper tries to connect the two formulations and concludes that optimal policies correspond to empirical priors on the trajectories of hidden environmental states, which compel agents to seek out the (valuable states they expect to encounter.
Photonic analogies of gravitational attractors
San-Román-Alerigi, Damián P.
2013-01-01
In our work we demonstrate a Gaussian-like refractive index mapping to realize light trapping. Our study shows that this centro-symmetrical photonic structure is able to mime the light geodesics described by celestial mechanics. Possible applications are discussed. © 2013 IEEE.
Unity of Cosmological Inflation Attractors
Galante, Mario; Kallosh, Renata; Linde, Andrei; Roest, Diederik
2015-01-01
Recently, several broad classes of inflationary models have been discovered whose cosmological predictions, in excellent agreement with Planck, are stable with respect to significant modifications of the inflaton potential. Some classes of models are based on a nonminimal coupling to gravity. These
Misra, A
2008-01-01
We consider two sets of issues in this paper. The first has to do with moduli stabilization, existence of “area codes” [A. Giryavets, New attractors and area codes, JHEP 0603 (2006) 020, hep-th/0511215] and the possibility of getting a non-supersymmetric dS minimum without the addition of -branes as in KKLT for type II flux compactifications. The second has to do with the “inverse problem” [K. Saraikin, C. Vafa, Non-supersymmetric black holes and topological strings, hep-th/0703214] and “fake superpotentials” [A. Ceresole, G. Dall'Agata, Flow equations for non-BPS extremal black holes, JHEP 0703 (2007) 110, hep-th/0702088] for extremal (non-)supersymmetric black holes in type II compactifications. We use (orientifold of) a “Swiss cheese” Calabi–Yau [J.P. Conlon, F. Quevedo, K. Suruliz, Large-volume flux compactifications: Moduli spectrum and D3/D7 soft supersymmetry breaking, JHEP 0508 (2005) 007, hep-th/0505076] expressed as a degree-18 hypersurface in WCP4[1,1,1,6,9] in the “large-volume...
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Peter Krøjgaard
2013-01-01
Full Text Available We report a replication experiment of a mechanized version of the seminal wide-screen/narrow-screen design of Wilcox and Baillargeon (1998 with 9.5-month-old infants (N=80. Two different methodologies were employed simultaneously: (a the standard looking time paradigm and (b eye tracking. Across conditions with three different screen sizes, the results from both methodologies revealed a clear and interesting pattern: the looking times increased as a significantly linear function of reduced screen sizes, that is, independently of the number of different objects involved. There was no indication in the data that the infants made use of the featural differences between the different-looking objects involved. The results suggest a simple, novel, and thought-provoking interpretation of the infants’ looking behavior in the wide-screen/narrow-screen design: moving objects are attractors, and the more space left for visible object movement in the visual field, the longer are infants’ looks. Consequently, no cognitive interpretation may be needed.
Thanassoulas, C; Verveniotis, G; Zymaris, N
2008-01-01
In order to investigate the capability of the preseismic electric field "strange attractor like" precursor as a time predictor of a large EQ within a short time window (short-term prediction), the specific methodology was applied on the Earth's electric field recorded during a rather long seismically active period (December 1st, 2007 - April 30th, 2008) of Greece. During this period of time a number (8) of large (Ms > 5.5R) earthquakes took place. The particular analysis is presented in detail for the following EQs: the Monemvasia EQ (January 6th 2008, Ms = 6.6R), the Methoni EQs (February 14th 2008 Ms = 6.7R, February 19th 2008 Ms = 5.6R, February 20th 2008 Ms = 6.5R, February 26th 2008 Ms = 5.7R), the Skyros EQ (March 19th 2008 Ms = 5.5R) and the Mid Southern Creta EQ (March 28th 2008 Ms = 5.6R). The obtained results from the analysis of the afore mentioned EQs, in conjunction to the ones obtained from an earlier presentation of the particular methodology (Thanassoulas et al. 2008a), suggest: an average tim...
From Anosov dynamics to hyperbolic attractors
Indian Academy of Sciences (India)
For conservative systems, hyperbolic chaos is represented by Anosov dynamics, when a .... site faces of the cubic cell may be thought as identified, and in this sense we deal with a compact ..... The scale along the vertical axis is indicated at the top in the right part of the figure. Here k is the steepness factor of frequency ...
Symmetric Encryption Model Based on Chaotic Attractors
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Edilma Isabel Amaya Barrera
2016-10-01
Conclusions: the algorithm is presented as an alternative to traditional algorithms demonstrating greater efficiency in the management of computing resources and raises the groundwork for continuing their study on the interested academic community due to the variety of dynamical systems nonlinear.
Attractors for equations of mathematical physics
Chepyzhov, Vladimir V
2001-01-01
One of the major problems in the study of evolution equations of mathematical physics is the investigation of the behavior of the solutions to these equations when time is large or tends to infinity. The related important questions concern the stability of solutions or the character of the instability if a solution is unstable. In the last few decades, considerable progress in this area has been achieved in the study of autonomous evolution partial differential equations. For a number of basic evolution equations of mathematical physics, it was shown that the long time behavior of their soluti
A plethora of strange nonchaotic attractors
Indian Academy of Sciences (India)
, 1977). [38] V I Arnold, Geometrical methods in the theory of ordinary differential equations (Springer. Verlag, Berlin, 1983). [39] A S Cassol, F L S Veiga and M H R Tragtenberg, LANL archives, cond-mat/0002329. 56. Pramana – J. Phys., Vol.
Attractors, bifurcations, & chaos nonlinear phenomena in economics
Puu, Tönu
2003-01-01
The present book relies on various editions of my earlier book "Nonlinear Economic Dynamics", first published in 1989 in the Springer series "Lecture Notes in Economics and Mathematical Systems", and republished in three more, successively revised and expanded editions, as a Springer monograph, in 1991, 1993, and 1997, and in a Russian translation as "Nelineynaia Economicheskaia Dinamica". The first three editions were focused on applications. The last was differ ent, as it also included some chapters with mathematical background mate rial -ordinary differential equations and iterated maps -so as to make the book self-contained and suitable as a textbook for economics students of dynamical systems. To the same pedagogical purpose, the number of illus trations were expanded. The book published in 2000, with the title "A ttractors, Bifurcations, and Chaos -Nonlinear Phenomena in Economics", was so much changed, that the author felt it reasonable to give it a new title. There were two new math ematics ch...
Ferrara, S.; Sagnotti, A.
2014-01-01
We derive new types of $U(1)^n$ Born-Infeld actions based on N=2 special geometry in four dimensions. As in the single vector multiplet (n=1) case, the non--linear actions originate, in a particular limit, from quadratic expressions in the Maxwell fields. The dynamics is encoded in a set of coefficients $d_{ABC}$ related to the third derivative of the holomorphic prepotential and in an SU(2) triplet of N=2 Fayet-Iliopoulos charges, which must be suitably chosen to preserve a residual N=1 supersymmetry.
Learning chaotic attractors by neural networks
Bakker, R; Schouten, JC; Giles, CL; Takens, F; van den Bleek, CM
2000-01-01
An algorithm is introduced that trains a neural network to identify chaotic dynamics from a single measured time series. During training, the algorithm learns to short-term predict the time series. At the same time a criterion, developed by Diks, van Zwet, Takens, and de Goede (1996) is monitored
Coupled chaotic attractors and driving-induced bistability: A brief ...
Indian Academy of Sciences (India)
2015-02-04
Feb 4, 2015 ... system. Hence, it is also called as drive–response or master–slave interaction. Coupled nonlinear dynamical systems display a range of interesting ... symmetry elements. The celebrated Lorenz [19] oscillator is one such systems with some inherent symmetry. The governing equations of this system are.
Memories of sandalwood: Malacca, Timor attractor and Solor's channel
Casquilho, José Pinto
2014-01-01
In this work we present a somewhat extensive review, mainly of historical nature, focusing on the period that Malacca was under Portuguese suzerainty (1511-1641), concerning the subject of sandalwood routes from Timor, making warehouse in the archipelago of Solor. In the sixteenth century and seventeenth-century Lusitanian writings, there are no doubts about the indexical equivalence between Timor island and white sandalwood (Santalum album L.), then notable for its abundance and quality, thu...
Teaching as a career choice: attractors and deterrents identified by ...
African Journals Online (AJOL)
Erna Kinsey
Promotion of the teaching profession. In this article I argue for greater attention to be focused on aspects that learners regard as ... article I report on a research project that aimed to analyse and assess the opinions and per- ceptions of Grade 11 learners .... Sufficient overhead projectors. Well-equipped computer room.
Entropy function and attractors for AdS black holes
Morales, J F; Morales, Jose F.; Samtleben, Henning
2006-01-01
We apply Sen's entropy formalism to the study of the near horizon geometry and the entropy of asymptotically AdS black holes in gauged supergravities. In particular, we consider non-supersymmetric electrically charged black holes with AdS_2 xS^{d-2} horizons in U(1)^4 and U(1)^3 gauged supergravities in d=4 and d=5 dimensions, respectively. We study several cases including static/rotating, BPS and non-BPS black holes in Einstein as well as in Gauss-Bonnet gravity. In all examples, the near horizon geometry and black hole entropy are derived by extremizing the entropy function and are given entirely in terms of the gauge coupling, the electric charges and the angular momentum of the black hole.
A possible approach on optical analogues of gravitational attractors
San-Román-Alerigi, Damián P.
2013-04-01
In this paper we report on the feasibility of light confinement in orbital geodesics on stationary, planar, and centro-symmetric refractive index mappings. Constrained to fabrication and [meta]material limitations, the refractive index, n, has been bounded to the range: 0.8 ? n(r) ? 3.5. Mappings are obtained through the inverse problem to the light geodesics equations, considering trappings by generalized orbit conditions defined a priori. Our simulation results show that the above mentioned refractive index distributions trap light in an open orbit manifold, both perennial and temporal, in regards to initial conditions. Moreover, due to their characteristics, these mappings could be advantageous to optical computing and telecommunications, for example, providing an on-demand time delay or optical memories. Furthermore, beyond their practical applications to photonics, these mappings set forth an attractive realm to construct a panoply of celestial mechanics analogies and experiments in the laboratory. © 2013 Optical Society of America.
Power of Criminal Attractors: Modeling the Pull of Activity Nodes
Richard Frank; Vahid Dabbaghian; Andrew Reid; Suraj Singh; Jonathan Cinnamon; Patricia Brantingham
2011-01-01
The spatial distribution of crime has been a long-standing interest in the field of criminology. Research in this area has shown that activity nodes and travel paths are key components that help to define patterns of offending. Little research, however, has considered the influence of activity nodes on the spatial distribution of crimes in crime neutral areas - those where crimes are more haphazardly dispersed. Further, a review of the literature has revealed a lack of research in determining...
Detection of strong attractors in social media networks
National Research Council Canada - National Science Library
Qasem, Ziyaad; Jansen, Marc; Hecking, Tobias; Hoppe, H Ulrich
2016-01-01
Detection of influential actors in social media such as Twitter or Facebook plays an important role for improving the quality and efficiency of work and services in many fields such as education and marketing...
Attractor Signaling Models for Discovery of Combinatorial Therapies
2013-09-01
phoma using either naive or memory B-cells as a control for both p = 1 and p = 2. RBL2 disregulation has been recently associated with many types of...47]. Our analysis identified BCL6 as an im- portant drug target for both DLBCL and follicular lym- phoma using either naive or memory B-cells as a...R. Sapienza, et al., “Gene expression analysis uncovers similarity and di↵erences among burkitt lym- phoma subtypes,” ibid. 117, 3596–3608 (2011). 15
Damping of 3D internal wave attractors by lateral walls
Beckebanze, F.|info:eu-repo/dai/nl/411109472; Maas, L R M|info:eu-repo/dai/nl/07267069X
2016-01-01
The reflection of internal gravity waves at sloping boundaries leads to focusing or defo- cusing. In closed domains, focusing dominates and projects the wave energy onto ’wave attractors’. Previous theoretical and experimental work on 2D steady state wave attrac- tors has demonstrated that geometric
Symposium on Nonlinear Semigroups, Partial Differential Equations and Attractors
Zachary, Woodford
1987-01-01
The original idea of the organizers of the Washington Symposium was to span a fairly narrow range of topics on some recent techniques developed for the investigation of nonlinear partial differential equations and discuss these in a forum of experts. It soon became clear, however, that the dynamical systems approach interfaced significantly with many important branches of applied mathematics. As a consequence, the scope of this resulting proceedings volume is an enlarged one with coverage of a wider range of research topics.
Hidden attractors without equilibrium and adaptive reduced-order ...
Indian Academy of Sciences (India)
2017-03-10
Mar 10, 2017 ... 1Guangxi Colleges and Universities Key Laboratory of Complex System Optimization and Big Data Processing,. Yulin Normal University, Yulin 537000, People's Republic of China .... As an important analysis technique, the Poincaré map can reflect bifurcation and folding properties of chaos. When c = 4, m ...
Attractor Signaling Models for Discovery of Combinatorial Therapies
2014-11-01
doi:10.1371/journal.pone.0105842 Editor: Mariko Okada (Hatakeyama), Rikagaku Kenkyūsho Center for Allergy and Immunology , Japan Received June 10, 2014...acquired!drug!resistance!still!makes!the!5-year!survival!rate!for!this!disease! less!than!15%.!Over!the!years,!many!specific! mechanisms !associated!with!drug...RPMI 1640 (Hyclone) supplemented with 10% Canadian characterized fetal bovine serum (Hyclone), 1% 200 mM L-glutamine (Omega), and 1% penicillin
Solitonlike attractor for blood vessel tip density in angiogenesis
Bonilla, L. L.; Carretero, M.; Terragni, F.
2016-12-01
Recently, numerical simulations of a stochastic model have shown that the density of vessel tips in tumor-induced angiogenesis adopts a solitonlike profile [Sci. Rep. 6, 31296 (2016), 10.1038/srep31296]. In this work, we derive and solve the equations for the soliton collective coordinates that indicate how the soliton adapts its shape and velocity to varying chemotaxis and diffusion. The vessel tip density can be reconstructed from the soliton formulas. While the stochastic model exhibits large fluctuations, we show that the location of the maximum vessel tip density for different replicas follows closely the soliton peak position calculated either by ensemble averages or by solving an alternative deterministic description of the density. The simple soliton collective coordinate equations may also be used to ascertain the response of the vessel network to changes in the parameters and thus to control it.
Hidden attractors without equilibrium and adaptive reduced-order ...
Indian Academy of Sciences (India)
Guangxi Colleges and Universities Key Laboratory of Complex System Optimization and Big Data Processing, Yulin Normal University, Yulin 537000, People's Republic of China; School of Statistics and Management, Shanghai University of Finance and Economics, Shanghai 200433, People's Republic of China ...
Moduli and (un)attractor black hole thermodynamics
Astefanesei, D.; Goldstein, K.D.; Mahapatra, S.
2008-01-01
We investigate four-dimensional spherically symmetric black hole solutions in gravity theories with massless, neutral scalars non-minimally coupled to gauge fields. In the non-extremal case, we explicitly show that, under the variation of the moduli, the scalar charges appear in the first law of
Estimation of dynamic properties of attractors observed in hollow ...
Indian Academy of Sciences (India)
Understanding of the basic nature of arc root ﬂuctuation is still one of the unsolved problems in thermal arc plasma physics. It has direct impact on myriads of thermal plasma applications being implemented at present. Recently, chaotic nature of arc root behavior has been reported through the analysis of voltages, acoustic ...
Directory of Open Access Journals (Sweden)
Moisés Damián Perales Escudero
2013-01-01
Full Text Available Previous L1 and L2 research on inferential comprehension has tended to follow a quantitative orientation. By contrast, L2 research on critical reading is qualitative and tends to ignore inferences. This paper presents a qualitative, design-based study of a critical reading intervention focused on promoting generative rhetorical inferences and investigating co-adaptation and emergence of new meaning-making capacities. Complexity theory (CT constructs were used to research processes of co-adaptation between the participants' comprehension and the teacher-researcher's understanding of learning and instructional needs. Identification of attractor states and control parameters in classroom discourse were used to explore unpredicted factors influencing the participants' inferential comprehension and further refine the intervention. The results indicate that rhetorical genre knowledge acted as a control parameter driving the students' comprehension to attractor states characterized by implausible inferences, and that this knowledge explains the emergence of pragmatic meaning (rhetorical inferences from semantic meaning. The paper illustrates the usefulness of CT constructs in doing design-based research qualitatively in a manner that informs both theory and practice.As pesquisas anteriores em L1 e L2 sobre compreensão inferencial tendem a uma orientação quantitativa. Por outro lado, a pesquisa sobre leitura crítica em L2 é qualitativa e tende a ignorar as inferências. Este artigo apresenta um estudo qualitativo (design-based research sobre uma intervenção de leitura crítica com foco na promoção de geração de inferências retóricas, investigando a co-adaptação e a emergência de capacidades de produção de novos significados. Os construtos da teoria da complexidade foram usados ??para investigar processos de co-adaptação entre a compreensão de aprendizagem e necessidades instrucionais dos participantes e do professor pesquisador. A
Multistable Attractors in a Network of Phase Oscillators with Three-Body Interactions
Tanaka, Takuma; Aoyagi, Toshio
2011-06-01
Three-body interactions have been found in physics, biology, and sociology. To investigate their effect on dynamical systems, as a first step, we study numerically and theoretically a system of phase oscillators with a three-body interaction. As a result, an infinite number of multistable synchronized states appear above a critical coupling strength, while a stable incoherent state always exists for any coupling strength. Owing to the infinite multistability, the degree of synchrony in an asymptotic state can vary continuously within some range depending on the initial phase pattern.
N=8 non-BPS Attractors, Fixed Scalars and Magic Supergravities
Ferrara, Sergio
2008-01-01
We analyze the Hessian matrix of the black hole potential of N=8, d=4 supergravity, and determine its rank at non-BPS critical points, relating the resulting spectrum to non-BPS solutions (with non-vanishing central charge) of N=2, d=4 magic supergravities and their ``mirror'' duals. We find agreement with the known degeneracy splitting of N=2 non-BPS spectrum of generic special Kahler geometries with cubic holomorphic prepotential. We also relate non-BPS critical points with vanishing central charge in N=2 magic supergravities to a particular reduction of the N=8, 1/8-BPS critical points.
Imura, Jun-ichi; Ueta, Tetsushi
2015-01-01
This book is the first to report on theoretical breakthroughs on control of complex dynamical systems developed by collaborative researchers in the two fields of dynamical systems theory and control theory. As well, its basic point of view is of three kinds of complexity: bifurcation phenomena subject to model uncertainty, complex behavior including periodic/quasi-periodic orbits as well as chaotic orbits, and network complexity emerging from dynamical interactions between subsystems. Analysis and Control of Complex Dynamical Systems offers a valuable resource for mathematicians, physicists, and biophysicists, as well as for researchers in nonlinear science and control engineering, allowing them to develop a better fundamental understanding of the analysis and control synthesis of such complex systems.
Recurrent motifs as resonant attractor states in the narrative field: a testable model of archetype.
Goodwyn, Erik
2013-06-01
At the most basic level, archetypes represented Jung's attempt to explain the phenomenon of recurrent myths and folktale motifs (Jung 1956, 1959, para. 99). But the archetype remains controversial as an explanation of recurrent motifs, as the existence of recurrent motifs does not prove that archetypes exist. Thus, the challenge for contemporary archetype theory is not merely to demonstrate that recurrent motifs exist, since that is not disputed, but to demonstrate that archetypes exist and cause recurrent motifs. The present paper proposes a new model which is unlike others in that it postulates how the archetype creates resonant motifs. This model necessarily clarifies and adapts some of Jung's seminal ideas on archetype in order to provide a working framework grounded in contemporary practice and methodologies. For the first time, a model of archetype is proposed that can be validated on empirical, rather than theoretical grounds. This is achieved by linking the archetype to the hard data of recurrent motifs rather than academic trends in other fields. © 2013, The Society of Analytical Psychology.
Symmetron and de Sitter attractor in a teleparallel model of cosmology
Sadjadi, H Mohseni
2016-01-01
In the teleparallel framework of cosmology, a quintessence with non-minimal couplings to the scalar torsion and a boundary term is considered. A conformal coupling to matter density is also taken into account. It is shown that the model can describe onset of cosmic acceleration after an epoch of matter dominated era, where dark energy is negligible, via $Z_2$ symmetry breaking. While the conformal coupling holds the Universe in a vacuum with zero dark energy density in the early epoch, the non-minimal couplings lead the Universe to a stable state with de Sitter expansion at late time.
Directory of Open Access Journals (Sweden)
Fei Yu
2013-06-01
Full Text Available Through introducing two piecewise-linear triangular wave functions in a three-dimensional spiral chaotic Colpittsoscillator model, a four-dimensional grid multiscroll hyperchaotic system is constructed. Interestingly, by adjusting abuild-in parameter in a variable of one triangle wave function, the control of the gradient of the multiscroll grid isachieved. Whereas by deploying the zero points of the two triangular wave functions to extend the saddle-focusequilibrium points with index-2 in phase space the scroll numbers do not only increase along with the number ofturning points, but they can also generate arbitrary multiples of products. The basic dynamical behaviors of theproposed four-dimensional multiscroll hyperchaotic system are analyzed. Finally, the hardware experimental circuit isdesigned and the interrelated circuit implementation is realized. The experimental results are in agreement with boththeoretical analyses and numerical simulations, which verify the feasibility of the design methods.
Luminescent threat: toxicity of light stick attractors used in pelagic fishery.
de Oliveira, Tiago Franco; da Silva, Amanda Lucila Medeiros; de Moura, Rafaela Alves; Bagattini, Raquel; de Oliveira, Antonio Anax Falcão; de Medeiros, Marisa Helena Gennari; Di Mascio, Paolo; de Arruda Campos, Ivan Pérsio; Barretto, Fabiano Prado; Bechara, Etelvino José Henriques; Loureiro, Ana Paula de Melo
2014-06-19
Light sticks (LS) are sources of chemiluminescence commonly used in pelagic fishery, where hundreds are discarded and reach the shores. Residents from fishing villages report an improper use of LS contents on the skin. Given the scarce information regarding LS toxicity, the effects of LS solutions in cell cultures were evaluated herein. Loss of viability, cell cycle changes and DNA fragmentation were observed in HepG2 cell line and skin fibroblasts. A non-cytotoxic LS concentration increased the occurrence of the mutagenic lesion 1,N(6)-εdAdo in HepG2 DNA by three-fold. Additionally, in vitro incubations of spent LS contents with DNA generated dGuo-LS adducts, whose structure elucidation revealed the presence of a reactive chlorinated product. In conclusion, the LS contents were found to be highly cyto- and genotoxic. Our data indicate an urgent need for LS waste management guidelines and for adequate information regarding toxic outcomes that may arise from human exposure.
Tomasino, Arthur P.
2013-01-01
In spite of the best efforts of researchers and practitioners, Information Systems (IS) developers are having problems "getting it right". IS developments are challenged by the emergence of unanticipated IS characteristics undermining managers ability to predict and manage IS change. Because IS are complex, development formulas, best…
The Aspect Ratio Dependence of the Attractor Dimension in Taylor-Couette Flow
1988-01-01
and G. Iooss,"Calcul des solutions bifurquees pour le probl~me de Couette-Taylor avec les deux cylindres en rotation", J. Mec. theor applique Numero ...Procaccia and Badii-Politi algorithms. The aspect ratio was varied between 19.9 and 34.48 and the inner cylinder Reynolds numbers ranged between R/Rej...11 and R/Rc = 15, where Rc is the critical Reynolds number for the primary instability.) The variation of the dimension with Reynolds number was
Lunkenheimer, E.S.; Hollenstein, T.P.; Wang, J.; Shields, A.M.
2012-01-01
Familial emotion socialization practices relate to children's emotion regulation (ER) skills in late childhood, however, we have more to learn about how the context and structure of these interactions relates to individual differences in children's ER. The present study examined flexibility and
Reactivation in Working Memory: An Attractor Network Model of Free Recall
Lansner, Anders; Marklund, Petter; Sikström, Sverker; Nilsson, Lars-Göran
2013-01-01
The dynamic nature of human working memory, the general-purpose system for processing continuous input, while keeping no longer externally available information active in the background, is well captured in immediate free recall of supraspan word-lists. Free recall tasks produce several benchmark memory phenomena, like the U-shaped serial position curve, reflecting enhanced memory for early and late list items. To account for empirical data, including primacy and recency as well as contiguity effects, we propose here a neurobiologically based neural network model that unifies short- and long-term forms of memory and challenges both the standard view of working memory as persistent activity and dual-store accounts of free recall. Rapidly expressed and volatile synaptic plasticity, modulated intrinsic excitability, and spike-frequency adaptation are suggested as key cellular mechanisms underlying working memory encoding, reactivation and recall. Recent findings on the synaptic and molecular mechanisms behind early LTP and on spiking activity during delayed-match-to-sample tasks support this view. PMID:24023690
Attractor switching in neuron networks and Spatiotemporal filters for motion processing
Subramanian, Easwara Naga
2008-01-01
From a broader perspective, we address two important questions, viz., (a) what kind of mechanism would enable a neuronal network to switch between various tasks or stored patterns? (b) what are the properties of neurons that are used by the visual system in early motion detection? To address (a) we
Deviant talk in adolescent friendships: A step toward measuring a pathogenic attractor process
Granic, I.; Dishion, T.J.
2003-01-01
Deviant talk in adolescent friendships has been previously found to predict escalations in substance use, delinquency, and violence. The current paper extends past work on deviant talk by examining its dynamic, self-organizing properties. From the direct observations of peer interactions, a simple
Dynamical systems, attractors, and neural circuits [version 1; referees: 3 approved
Directory of Open Access Journals (Sweden)
Paul Miller
2016-05-01
Full Text Available Biology is the study of dynamical systems. Yet most of us working in biology have limited pedagogical training in the theory of dynamical systems, an unfortunate historical fact that can be remedied for future generations of life scientists. In my particular field of systems neuroscience, neural circuits are rife with nonlinearities at all levels of description, rendering simple methodologies and our own intuition unreliable. Therefore, our ideas are likely to be wrong unless informed by good models. These models should be based on the mathematical theories of dynamical systems since functioning neurons are dynamic—they change their membrane potential and firing rates with time. Thus, selecting the appropriate type of dynamical system upon which to base a model is an important first step in the modeling process. This step all too easily goes awry, in part because there are many frameworks to choose from, in part because the sparsely sampled data can be consistent with a variety of dynamical processes, and in part because each modeler has a preferred modeling approach that is difficult to move away from. This brief review summarizes some of the main dynamical paradigms that can arise in neural circuits, with comments on what they can achieve computationally and what signatures might reveal their presence within empirical data. I provide examples of different dynamical systems using simple circuits of two or three cells, emphasizing that any one connectivity pattern is compatible with multiple, diverse functions.
Attractor-Based Obstructions to Growth in Homogeneous Cyclic Boolean Automata.
Khan, Bilal; Cantor, Yuri; Dombrowski, Kirk
2015-11-01
We consider a synchronous Boolean organism consisting of N cells arranged in a circle, where each cell initially takes on an independently chosen Boolean value. During the lifetime of the organism, each cell updates its own value by responding to the presence (or absence) of diversity amongst its two neighbours' values. We show that if all cells eventually take a value of 0 (irrespective of their initial values) then the organism necessarily has a cell count that is a power of 2. In addition, the converse is also proved: if the number of cells in the organism is a proper power of 2, then no matter what the initial values of the cells are, eventually all cells take on a value of 0 and then cease to change further. We argue that such an absence of structure in the dynamical properties of the organism implies a lack of adaptiveness, and so is evolutionarily disadvantageous. It follows that as the organism doubles in size (say from m to 2m) it will necessarily encounter an intermediate size that is a proper power of 2, and suffers from low adaptiveness. Finally we show, through computational experiments, that one way an organism can grow to more than twice its size and still avoid passing through intermediate sizes that lack structural dynamics, is for the organism to depart from assumptions of homogeneity at the cellular level.
Galich, Nikolay E.
2008-07-01
Communication contains the description of the immunology data treatment. New nonlinear methods of immunofluorescence statistical analysis of peripheral blood neutrophils have been developed. We used technology of respiratory burst reaction of DNA fluorescence in the neutrophils cells nuclei due to oxidative activity. The histograms of photon count statistics the radiant neutrophils populations' in flow cytometry experiments are considered. Distributions of the fluorescence flashes frequency as functions of the fluorescence intensity are analyzed. Statistic peculiarities of histograms set for women in the pregnant period allow dividing all histograms on the three classes. The classification is based on three different types of smoothing and long-range scale averaged immunofluorescence distributions, their bifurcation and wavelet spectra. Heterogeneity peculiarities of long-range scale immunofluorescence distributions and peculiarities of wavelet spectra allow dividing all histograms on three groups. First histograms group belongs to healthy donors. Two other groups belong to donors with autoimmune and inflammatory diseases. Some of the illnesses are not diagnosed by standards biochemical methods. Medical standards and statistical data of the immunofluorescence histograms for identifications of health and illnesses are interconnected. Peculiarities of immunofluorescence for women in pregnant period are classified. Health or illness criteria are connected with statistics features of immunofluorescence histograms. Neutrophils populations' fluorescence presents the sensitive clear indicator of health status.
Reactivation in working memory: an attractor network model of free recall.
Lansner, Anders; Marklund, Petter; Sikström, Sverker; Nilsson, Lars-Göran
2013-01-01
The dynamic nature of human working memory, the general-purpose system for processing continuous input, while keeping no longer externally available information active in the background, is well captured in immediate free recall of supraspan word-lists. Free recall tasks produce several benchmark memory phenomena, like the U-shaped serial position curve, reflecting enhanced memory for early and late list items. To account for empirical data, including primacy and recency as well as contiguity effects, we propose here a neurobiologically based neural network model that unifies short- and long-term forms of memory and challenges both the standard view of working memory as persistent activity and dual-store accounts of free recall. Rapidly expressed and volatile synaptic plasticity, modulated intrinsic excitability, and spike-frequency adaptation are suggested as key cellular mechanisms underlying working memory encoding, reactivation and recall. Recent findings on the synaptic and molecular mechanisms behind early LTP and on spiking activity during delayed-match-to-sample tasks support this view.
Remarks and examples on transient processes and attractors in biological evolution
Directory of Open Access Journals (Sweden)
Philippe Lherminier
2015-11-01
Full Text Available We present a model for the competition of two biological entities into the same species (polyphasie, clonal/sex, cancerous cells, the first one with a birth ratio higher than the second when the resources are abundant, whereas the situation is reversed for scarce resources. The first one rapidly exhausts the resources, improving growth of the second, leading to a auto-sustained cyclic process (ESS = Evolutionary Stable Strategy. We use known models of population dynamics for three agents: two phases asexual and sexual (for instance of the same species and one of resources. The main feature of the model (for certain values of the parameters is the very long and entangled transient process, which involves a long period where one of the forms is practically absent, before emerging again to join a stable cycle which implies preservation of both forms. This model should throw some light on the biological problem of the maintenance of sexuality in competition with asexual clones, as well as on the alternated fast growth versus latency in cancer tumors.
Directory of Open Access Journals (Sweden)
Francis F. Muguet
2005-04-01
Full Text Available MC simulations of a set of zigzag ((9,0-(14,0 and armchair ((6,6-(10,10carbon nanotubes immersed in water have been carried out in an NpT-ensemble (512 watermolecules, p=1 bar, T=298 K. Intermolecular interactions were described by BMWpotential according to which, besides the well-known linear water dimer bifurcated andinverted water dimers are metastable. In all cases, it was found that there are large periodicfluctuations of water occupancy inside the nanotubes. Decrease in the size of the nanotubediameter leads to a significant destruction of the H-bond network, and to a bifucarted dimerpopulation increase. Inverted dimer concentration relationship with the nanotube diameter ismore complicated. Population maximum for inverted dimers occurs for diameters of 10-11 ÃƒÂ¥. Water features different intermolecular structures not only inside carbon nanotubesbut also in the outer first hydration shells. The amount of bifurcated and inverted dimers issignificantly more important in the first hydration shell than in bulk water.
Directory of Open Access Journals (Sweden)
Joseph G. Meert
2014-03-01
A second possibility is that our views of older supercontinents are shaped by well-known connections documented for the most recent supercontinent, Pangea. It is intriguing that three of the four ‘lonely wanderers’ (Tarim, North China, South China did not unite until just before, or slightly after the breakup of Pangea. The fourth ‘lonely wanderer’, the Kalahari (and core Kaapvaal craton has a somewhat unique Archean-age geology compared to its nearest neighbors in Gondwana, but very similar to that in western Australia.
Lorenz's attractor applied to the stream cipher (Ali-Pacha generator)
Energy Technology Data Exchange (ETDEWEB)
Ali-Pacha, Adda [University of Sciences and Technology of Oran USTO, BP 1505, El M' Naouer, Oran 31036 (Algeria)]. E-mail: alipacha@yahoo.com; Hadj-Said, Naima [University of Sciences and Technology of Oran USTO, BP 1505, El M' Naouer, Oran 31036 (Algeria); M' Hamed, A. [National Institute of Telecommunications, Evry, Paris (France); Belgoraf, A. [University of Sciences and Technology of Oran USTO, BP 1505, El M' Naouer, Oran 31036 (Algeria)
2007-08-15
The safety of information is primarily founded today on the calculation of algorithms whose confidentiality depends on the number of the necessary bits for the definition of a cryptographic key. If this type of system has proved reliable, then the increasing power of the means of calculation threatens the confidentiality of these methods. The powerful computers are certainly able to quantify and decipher information quickly, but their computing speed allows parallel cryptanalysis, which aims 'to break' a code by discovering the key, for example, by testing all the possible keys. The only evocation of the principle of the quantum computer, with the potentially colossal capacities of calculation, has started a shock, even in the most savaged who are convinced of algorithmic cryptography. To mitigate this concern, we will introduce in this article a new cryptographic system based on chaotic concepts.
State-dependence of climate sensitivity : attractor constraints and palaeoclimate regimes
von der Heydt, Anna|info:eu-repo/dai/nl/245567526; Ashwin, Peter
2016-01-01
Equilibrium climate sensitivity (ECS) is a key predictor of climate change. However, it is not very well constrained, either by climate models or by observational data. The reasons for this include strong internal variability and forcing on many time scales. In practise this means that the
Multistability and hidden attractors in an impulsive Goodwin oscillator with time delay
DEFF Research Database (Denmark)
Zhusubaliyev, Z. T.; Mosekilde, Erik; Churilov, A. N.
2015-01-01
are subject to a negative feedback regulation that is capable of modifying the intermittent bursts into more regular pulse trains. Bifurcation analysis of a hybrid model that attempts to integrate the intermittent bursting activity with a continuous hormone secretion has recently demonstrated a number......The release of luteinizing hormone (LH) is driven by intermittent bursts of activity in the hypothalamic nerve centers of the brain. Luteinizing hormone again stimulates release of the male sex hormone testosterone (Te) and, via the circulating concentration of Te, the hypothalamic nerve centers...
The use of supernatural entities in moral conversations as a cultural-psychological attractor.
Tófalvy, Tamás; Viciana, Hugo
2009-06-01
Social behavior in most human societies is characterized by the following of moral rules explicitly justified by religious belief systems. These systems constitute the diverse domain of human sacred values. Supernatural entities as founders or warranty of moral principles may be seen as a form of "conversation stoppers," considerations that can be dropped into a moral decision process in order to prevent endlessly reconsidering and endlessly asking for further justification. In this article we offer a general naturalistic framework toward answering the question of why supernatural entities are so attractive in moral argumentation. We present an explanatory model based on the phenomena of multiple channels of moral reasoning, the suspension of epistemic vigilance, and relevance assumptions through the attractiveness of the sacred, moral dumbfounding, and the expression of social coalitionary commitment. Thus, in light of much of current cognitive theory, sacred values make sense as basins in the evolutionary landscape of human morality.
Directory of Open Access Journals (Sweden)
Jian-feng Zhao
2017-01-01
Full Text Available This paper presents a three-dimensional autonomous chaotic system with high fraction dimension. It is noted that the nonlinear characteristic of the improper fractional-order chaos is interesting. Based on the continuous chaos and the discrete wavelet function map, an image encryption algorithm is put forward. The key space is formed by the initial state variables, parameters, and orders of the system. Every pixel value is included in secret key, so as to improve antiattack capability of the algorithm. The obtained simulation results and extensive security analyses demonstrate the high level of security of the algorithm and show its robustness against various types of attacks.
Krawiecki, A.
A multi-agent spin model for changes of prices in the stock market based on the Ising-like cellular automaton with interactions between traders randomly varying in time is investigated by means of Monte Carlo simulations. The structure of interactions has topology of a small-world network obtained from regular two-dimensional square lattices with various coordination numbers by randomly cutting and rewiring edges. Simulations of the model on regular lattices do not yield time series of logarithmic price returns with statistical properties comparable with the empirical ones. In contrast, in the case of networks with a certain degree of randomness for a wide range of parameters the time series of the logarithmic price returns exhibit intermittent bursting typical of volatility clustering. Also the tails of distributions of returns obey a power scaling law with exponents comparable to those obtained from the empirical data.
Directory of Open Access Journals (Sweden)
Claudia Elena TUDORACHE
2016-10-01
Full Text Available The municipality of Târgu Jiu, as an ensemble of urban space organization, is strictly dependent on the physical environment in which it is located, starting with relief, hydrography and so on. The peri-central part of the city hada developed the urban tissue poorly at the start of the 19th century, with a deficient historical, cultural and architectural load. Landscape improvement owes heavily to the central axis of the city, represented by the "Calea Eroilor" Cultural Ensemble, which brings a touch of uniqueness to the urban context. The article hopes to emphasize the discrepancies between the two banks of the River Jiu, which are extremely contrasting from both an architectural and a functional points of view. The left bank has administrative and architectural roles, while the right side is a former industrial area. In its entirety, the project aims to combine the two components, economic and social. The existing patrimony will help bring a harmonization and anew dynamic to the western part of the city, in terms of profits as well as in terms of the social course. The urban structure of the city as a whole must correspond to a territorial harmony and operational status so that a revitalization of the analysed area can transform the entire city. The specific objectives are the increase in real-estate action in the implementation area and developing the infrastructure, which will eventually lead to more entrepreneurial activities for a sustainable development.
N. V., Kuznetsov; G. A., Leonov; M. V., Yuldashev; R. V., Yuldashev
2017-10-01
During recent years it has been shown that hidden oscillations, whose basin of attraction does not overlap with small neighborhoods of equilibria, may significantly complicate simulation of dynamical models, lead to unreliable results and wrong conclusions, and cause serious damage in drilling systems, aircrafts control systems, electromechanical systems, and other applications. This article provides a survey of various phase-locked loop based circuits (used in satellite navigation systems, optical, and digital communication), where such difficulties take place in MATLAB and SPICE. Considered examples can be used for testing other phase-locked loop based circuits and simulation tools, and motivate the development and application of rigorous analytical methods for the global analysis of phase-locked loop based circuits.
Baladi, Viviane; Kuna, Tobias; Lucarini, Valerio
2017-08-01
The first main result of Baladi et al (2017 Nonlinearity 30 1204-20) is modified as follows: For any θ in the Sobolev space H^r_p(M) , with 1 and 0, the map t\\mapsto \\int θ dρt is α-Hölder continuous for all \
DEFF Research Database (Denmark)
True, Hans
2013-01-01
In recent years, several authors have proposed easier numerical methods to find the critical speed in railway dynamical problems. Actually, the methods do function in some cases, but in most cases it is really a gamble. In this article, the methods are discussed and the pros and contras are comme......In recent years, several authors have proposed easier numerical methods to find the critical speed in railway dynamical problems. Actually, the methods do function in some cases, but in most cases it is really a gamble. In this article, the methods are discussed and the pros and contras...
Richard Eleftherios Boyatzis; Kylie eRochford; Scott eTaylor
2015-01-01
Personal and shared vision have a long history in management and organizational practices yet only recently have we begun to build a systematic body of empirical knowledge about the role of personal and shared vision in organizations. As the introductory paper for this special topic in Frontiers in Psychology, we present a theoretical argument as to the existence and critical role of two states in which a person, dyad, team, or organization may find themselves when engaging in the creation of...
Boyatzis, Richard E.; Rochford, Kylie; Taylor, Scott N.
2015-01-01
Personal and shared vision have a long history in management and organizational practices yet only recently have we begun to build a systematic body of empirical knowledge about the role of personal and shared vision in organizations. As the introductory paper for this special topic in Frontiers in Psychology, we present a theoretical argument as to the existence and critical role of two states in which a person, dyad, team, or organization may find themselves when engaging in the creation of...
Marconi, Pier Luigi
369 patients, selected within a set of 1215 outpatients, were studied. The data were clustered into two set: the baseline set and the endpoint set. The clinical parameters had a higher variability at the baseline than at the endpoint. 4 to 5 factors were extracted in total group and 3 subgroups (190 "affective", 34 type-B personality, 166 without any of both disorders). In all subgroups there was a background pattern of 6 components: 3 components confirming the trifactorial temperamental model of Cloninger; 1 component related to the quality of social relationships; 2 components (that are the main components of factorial model about in all groups) relating to quality of life and adjustment self perceived by patients, and to pattern of dysfunctional behavior, inner feelings, and thought processes externally evaluated. These background components seem to aggregate differently in the subgroups in accordance to the clinical diagnosis. These patterns may be interpreted as expression of an increased "coherence" among parameters due to a lack of flexibility caused by the illness. The different class of illness can be further distinguished by intensity of maladjustment, that is related to the intensity of clinical signs just only at the baseline. These data suggest that the main interfering factors are clinical psychopathology at baseline and stable personality traits at endpoint. This persistent chronic maladjustment personality-driven is evidenced after the clinical disorder was cured by treatment. An interpretative model is presented by the author.
Pucilowski, Sebastian; Tordesillas, Antoinette; Froyland, Gary
2017-06-01
In transitive metastable chaotic dynamical systems, there are no invariant neighbourhoods in the phase space. The best that one can do is look for metastable or almost-invariant (AI) regions as a means to decompose the system into its basic self-organising building blocks. Here we study the metastable dynamics of a dense granular material embodying strain localization in 3D from the perspective of its conformational landscape: the state space of all observed conformations as defined by the local topology of individual grains relative to their first ring of contacting neighbors. We determine the metastable AI sets that divide this conformational landscape, such that grain rearrangements from one conformation to another conformation in the same AI set occurs with high probability: by contrast, grain rearrangements involving conformational transitions between AI sets are unlikely. The great majority of conformational transitions are identity transitions: grains rearrange and exchange contacts to preserve those topological properties with the greatest influence on cluster stability, namely, the number of contacts and 3-cycles. Force chains show a clear preference for that AI set with the most number of accessible and highly connected conformations. Here force chains continually explore the conformational landscape, wandering from one rarely inhabited conformation to another. As force chains become overloaded and buckle, the energy released enables member grains to overcome the high dynamical barriers that separate metastable regions and subsequently escape one region to enter another in the conformational landscape. Thus, compared to grains locked in stable force chains, those in buckling force chains, confined to the shear band, show a greater propensity for not only non-identity transitions within each metastable region but also inter-transitions between metastable regions.
Heyman, R E; Wojda, A K; Eddy, J M; Haydt, N C; Geiger, J F; Slep, A M Smith
2018-02-01
Over 1 in 5 dental patients report moderate to severe dental fear. Although the efficacy of cognitive-behavioral treatment (CBT) for dental fear has been examined in over 20 randomized controlled trials-with 2 meta-analyses finding strong average effect sizes ( d > 1)-CBT has received almost no dissemination beyond the specialty clinics that tested it. The challenge, then, is not how to treat dental fear but how to disseminate and implement such an evidence-based treatment in a way that recognizes the rewards and barriers in the US health care system. This mixed-method study investigated the potential of disseminating CBT through care from a mental health provider from within the dental home, a practice known as evidence-based collaborative care (EBCC). Two preadoption studies were conducted with practicing dentists drawn from a self-organized Practice-Based Research Network in the New York City metropolitan area. The first comprised 3 focus groups ( N = 17), and the second involved the administration of a survey ( N = 46). Focus group participants agreed that CBT for dental fear is worthy of consideration but identified several concerns regarding its appeal, feasibility, and application in community dental practices. Survey participants indicated endorsement of factors promoting the use of EBCC as a mechanism for CBT dissemination, with no factors receiving less than 50% support. Taken together, these findings indicate that EBCC may be a useful framework through which an evidence-based treatment for dental fear treatment can be delivered.
Galich, Nikolay E.; Filatov, Michael V.
2008-07-01
Communication contains the description of the immunology experiments and the experimental data treatment. New nonlinear methods of immunofluorescence statistical analysis of peripheral blood neutrophils have been developed. We used technology of respiratory burst reaction of DNA fluorescence in the neutrophils cells nuclei due to oxidative activity. The histograms of photon count statistics the radiant neutrophils populations' in flow cytometry experiments are considered. Distributions of the fluorescence flashes frequency as functions of the fluorescence intensity are analyzed. Statistic peculiarities of histograms set for healthy and unhealthy donors allow dividing all histograms on the three classes. The classification is based on three different types of smoothing and long-range scale averaged immunofluorescence distributions and their bifurcation. Heterogeneity peculiarities of long-range scale immunofluorescence distributions allow dividing all histograms on three groups. First histograms group belongs to healthy donors. Two other groups belong to donors with autoimmune and inflammatory diseases. Some of the illnesses are not diagnosed by standards biochemical methods. Medical standards and statistical data of the immunofluorescence histograms for identifications of health and illnesses are interconnected. Possibilities and alterations of immunofluorescence statistics in registration, diagnostics and monitoring of different diseases in various medical treatments have been demonstrated. Health or illness criteria are connected with statistics features of immunofluorescence histograms. Neutrophils populations' fluorescence presents the sensitive clear indicator of health status.
Directory of Open Access Journals (Sweden)
Pucilowski Sebastian
2017-01-01
Full Text Available In transitive metastable chaotic dynamical systems, there are no invariant neighbourhoods in the phase space. The best that one can do is look for metastable or almost-invariant (AI regions as a means to decompose the system into its basic self-organising building blocks. Here we study the metastable dynamics of a dense granular material embodying strain localization in 3D from the perspective of its conformational landscape: the state space of all observed conformations as defined by the local topology of individual grains relative to their first ring of contacting neighbors. We determine the metastable AI sets that divide this conformational landscape, such that grain rearrangements from one conformation to another conformation in the same AI set occurs with high probability: by contrast, grain rearrangements involving conformational transitions between AI sets are unlikely. The great majority of conformational transitions are identity transitions: grains rearrange and exchange contacts to preserve those topological properties with the greatest influence on cluster stability, namely, the number of contacts and 3-cycles. Force chains show a clear preference for that AI set with the most number of accessible and highly connected conformations. Here force chains continually explore the conformational landscape, wandering from one rarely inhabited conformation to another. As force chains become overloaded and buckle, the energy released enables member grains to overcome the high dynamical barriers that separate metastable regions and subsequently escape one region to enter another in the conformational landscape. Thus, compared to grains locked in stable force chains, those in buckling force chains, confined to the shear band, show a greater propensity for not only non-identity transitions within each metastable region but also inter-transitions between metastable regions.
DEFF Research Database (Denmark)
True, Hans
2011-01-01
In recent years several authors have proposed, "easier" numerical methods' to find the critical speed in railway dynamical problems. Actually the methods do function in some cases, but in most cases it is really a gamble. In this presentation the methods will be discussed and the pros and contras...
Serrao, Mariano; Chini, Giorgia; Iosa, Marco; Casali, Carlo; Morone, Giovanni; Conte, Carmela; Bini, Fabiano; Marinozzi, Franco; Coppola, Gianluca; Pierelli, Francesco; Draicchio, Francesco; Ranavolo, Alberto
2017-10-01
The harmony of the human gait was recently found to be related to the golden ratio value (ϕ). The ratio between the duration of the stance and that of the swing phases of a gait cycle was in fact found to be close to ϕ, which implies that, because of the fractal property of autosimilarity of that number, the gait ratios stride/stance, stance/swing, swing/double support, were not significantly different from one another. We studied a group of patients with cerebellar ataxia to investigate how the differences between their gait ratios and the golden ratio are related to efficiency and stability of their gait, assessed by energy expenditure and stride-to-stride variability, respectively. The gait of 28 patients who were affected by degenerative cerebellar ataxia and of 28 healthy controls was studied using a stereophotogrammetric system. The above mentioned gait ratios, the energy expenditure estimated using the pelvis reconstructed method and the gait variability in terms of the stride length were computed, and their relationships were analyzed. Matching procedures have also been used to avoid multicollinearity biases. The gait ratio values of the patients were farther from the controls (and hence from ϕ), even in speed matched conditions (P=0.011, Cohen's D=0.76), but not when the variability and energy expenditure were matched between the two groups (Cohen's D=0.49). In patients with cerebellar ataxia, the farther the stance-swing ratio was from ϕ, the larger the total mechanical work (R(2)adj=0.64). Further, a significant positive correlation was observed between the difference of the gait ratio from the golden ratio and the severity of the disease (R=0.421, P=0.026). Harmony of gait appears to be a benchmark of physiological gait leading to physiological energy recovery and gait reliability. Neurorehabilitation of patients with ataxia might benefit from the restoration of harmony of their locomotor patterns. Copyright © 2017. Published by Elsevier Ltd.
Kuhl, Julius; Mitina, Olga; Koole, Sander L
2017-10-01
According to the extended trust hypothesis, the ability to cope with negative experiences is grounded in intuitive positive feelings about one's existence (Kuhl, Quirin, & Koole, 2015). In the present study, the authors empirically tested this hypothesis by examining the nonlinear dynamics in a series of day-to-day autoregressive functions of affective states taken from a 30-day daily mood diary study among 40 participants. A parameter (?) related to the asymptotic level of day-to-day changes in implicit positive mood predicted action orientation, a personality variable that relates to coping with negative affect, and psychological symptoms. This effect did not emerge when using a similar parameter l for self-reported positive affect or any linear characteristic (mean or standard deviation) of changes in positive or negative mood. These findings are considered within the broader framework of Personality Systems Interaction theory (PSI theory) that interprets l, under specified conditions, as a form of basic trust that enables people to confront negative affect and permit self-growth through self-confrontational rather than defensive coping.
1987-09-30
Balto County Albuquerque, NM 87196 Columbia, MD 21044 22. Colette Eluhu 30. Carlos Handy Mathematics Department Physics Department Iloward University...University Univ of MD - Balto County Durham, NC 27706 Catonsville, MD 21228 53. Simeon Reich 61. George Sell Mathematics Department Mathematics Department
Topological analysis of chaotic solution of three-element memristive circuit
Ginoux, Jean-Marc; Letellier, Christophe; Chua, Leon
2010-01-01
International audience; The simplest electronic circuit with a memristor was recently proposed. Chaotic attractors solution to this memristive circuit are topologically characterized and compared to Rossler-like attractors.
Misra, Aalok
2008-01-01
We consider issues of moduli stabilization and "area codes" for type II flux compactifications, and the "Inverse Problem" and "Fake Superpotentials" for extremal (non)supersymmetric black holes in type II compactifications on (orientifold of) a compact two-parameter Calabi-Yau expressed as a degree-18 hypersurface in WCP^4[1,1,1,6,9] which has multiple singular loci in its moduli space. We argue the existence of extended "area codes" [1] wherein for the same set of large NS-NS and RR fluxes, one can stabilize all the complex structure moduli and the axion-dilaton modulus (to different sets of values) for points in the moduli space away as well as near the different singular conifold loci leading to the existence of domain walls. By including non-perturbative alpha' and instanton corrections in the Kaehler potential and superpotential [2], we show the possibility of getting a large-volume non-supersymmetric (A)dS minimum. Further, using techniques of [3] we explicitly show that given a set of moduli and choice...
Directory of Open Access Journals (Sweden)
Marcelo Paes Gomes
2001-09-01
Full Text Available Artificial reefs have become an important and popular resource enhancement technique by concentrating fishes and by increasing natural production of biological resources. In order to increase the necto-benthic colonization potencial, an artificial reef was installed on the northern coast of Rio de Janeiro (21º27'S, 41ºOO'W, an area with typically low relief bottom. Measuring nearly 1500 m², the reef consisted of four sets of different materials randomly disposed: concrete pipes (N = 12; tires structures (N = 20; and cement tanks (N = 7 and pre-made blocks (N = 4. ln order to determine the artificial reef effects on the teleost community, trammel nets were used for monthly sampling the reef site (RA and on a control area (AC with sandy bottom. During the 23-month survey from April/96 to March/98, were recorded: a Chaetodipterus faber (Broussonet, 1782 and Haemulon aurolieatum (Cuvier, 1829 as exclusive species of the RA; b higher values of species richness and abundance on the RA, at least in 5 of 8 periods; c increase on the fish abundance on summer months. Correlation analysis indicated that salinity and precipitation were the most significant environmental factors correlated with the temporal fish community variation. This results highlight the importance of rainfall periodicity and the influence of Paraíba do Sul River on the nekton assemblage distribution. It is suggested that the functional role of the artificial reef might be related to higher availability of local shelter and food resources.
Do multiple hydrological steady states exist and emerge under stochastic daily forcing?
Peterson, T. J.; Western, A. W.; Argent, R. M.
2012-12-01
Recent work has shown that including positive feedbacks in hydrological models can result in complex behavior with multiple steady states (henceforth attractors) and a finite resilience from a single parameter set. More generally, this is typical of systems with positive feedbacks. However, a limitation of past studies is that multiple attractors were identified using mean annual or monthly forcing. Considering that most hydrological fluxes do not operate at such large time scales, it remains an open question whether multiple hydrological attractors can exist when a catchment is subject to stochastic daily forcing. To explore this question, this paper summarizes three recently submitted WRR papers (Peterson et al. 2012a, 2012b, 2012c) to ask if multiple hydrological attractors can emerge under stochastic daily forcing; and if they emerge, can daily forcing cause a catchment to switch between them. Using a hill-slope Boussinesq-vadose zone semi-distributed model, the attractors were quantified using a new limit-cycle continuation technique (LCC) that up-scaled climate forcing from daily to monthly (model and limit-cycle code is freely available). Multiple attractors were found to exist; but over a narrower range of parameter values compared with that using monthly mean forcing. This suggested that multiple attractors may exist in fewer catchments. To explore if stochastic daily forcing can switch a catchment to both attractors, time-integration simulations under daily stochastic forcing where conducted at a range of saturated lateral conductivity values. Somewhat surprisingly, the emergence (under stochastic forcing) of attractors differed significantly from the attractors that existed (from LCC). Specifically, attractors were found to exist but never emerge; both attractors may exist and both may emerge; and only one attractor may exist and a second temporary attractor may emerge only during certain periods of stochastic forcing. The latter indicates that more
Variations of Boundary Surface in Chua’s Circuit
Directory of Open Access Journals (Sweden)
M. Guzan
2015-09-01
Full Text Available The paper compares the boundary surfaces with help of cross-sections in three projection planes, for the four changes of Chua’s circuit parameters. It is known that due to changing the parameters, the Chua’s circuit can be characterized in addition to a stable limit cycle also by one double scroll chaotic attractor, two single scroll chaotic attractors or other two stable limit cycles. Chua’s circuit can even start working as a binary memory. It is not known yet, how changes in parameters and conseqently in attractors in the circuit will affect the morphology of the boundary surface. The boundary surface separates the double scroll chaotic attractor from the stable limit cycle. In a variation of the parameters presented in this paper the boundary surface will separate even single scroll chaotic attractors from each other. Dividing the state space into regions of attractivity for different attractors, however, remains fundamentally the same.
Aggregation algorithm towards large-scale Boolean network analysis
Zhao, Y.; Kim, J.; Filippone, M.
2013-01-01
The analysis of large-scale Boolean network dynamics is of great importance in understanding complex phenomena where systems are characterized by a large number of components. The computational cost to reveal the number of attractors and the period of each attractor increases exponentially as the number of nodes in the networks increases. This paper presents an efficient algorithm to find attractors for medium to large-scale networks. This is achieved by analyzing subnetworks within the netwo...
Processus fractals et réaction chimique en milieux turbulents
Nicolleau, Franck,
1994-01-01
Fractal sets were first related to the behaviour of dynamicalsystems with dissipation. Their evolutions are generally very sensitiveto initial and boundary conditionsand they have subsets of "state space" called "attractors". Representation pointslocated inside the domain of attraction are drawn towards an attractor. The pointrepresenting the system is free towander around the attractor at large times, consequently the ultimate behaviour ofthe system can be characterised by their study. The s...
Hyperchaotic Chameleon: Fractional Order FPGA Implementation
Directory of Open Access Journals (Sweden)
Karthikeyan Rajagopal
2017-01-01
Full Text Available There are many recent investigations on chaotic hidden attractors although hyperchaotic hidden attractor systems and their relationships have been less investigated. In this paper, we introduce a hyperchaotic system which can change between hidden attractor and self-excited attractor depending on the values of parameters. Dynamic properties of these systems are investigated. Fractional order models of these systems are derived and their bifurcation with fractional orders is discussed. Field programmable gate array (FPGA implementations of the systems with their power and resource utilization are presented.
Chaos as a part of logical structure in neurodynamics
Zak, Michail
1989-01-01
It is proposed that chaotic attractors incorporated in neural net models can represent classes of patterns in the same way in which a set of static attractors represent unrelated patterns. Therefore, chaotic states of neuron activity are associated with higher level cognitive processes such as generalization and abstraction.
Statistical dynamics of parametrically perturbed sine-square map
Indian Academy of Sciences (India)
Home; Journals; Pramana – Journal of Physics; Volume 75; Issue 3. Statistical ... Keywords. Transient; critical attractor; power-law; scaling exponent; weak and strong chaos; probability distribution. ... We show that the emergence of new attractors is responsible for transients in many trajectories obeying power-law decay.
Modeling Change in Project Duration and Completion
DEFF Research Database (Denmark)
Wiltshire, Travis; Butner, Jonathan E.; Pirtle, Zachary
2017-01-01
simultaneous change in percent complete and estimated duration for a given project as they were included in monthly reports over time. In short, we utilized latent change score mixture modeling to extract the attractor dynamics within the scheduling data. We found three primarily patterns: an attractor at low...
The problem of colliding networks and its relation to cell fusion and cancer.
Koulakov, Alexei A; Lazebnik, Yuri
2012-11-07
Cell fusion, a process that merges two or more cells into one, is required for normal development and has been explored as a tool for stem cell therapy. It has also been proposed that cell fusion causes cancer and contributes to its progression. These functions rely on a poorly understood ability of cell fusion to create new cell types. We suggest that this ability can be understood by considering cells as attractor networks whose basic property is to adopt a set of distinct, stable, self-maintaining states called attractors. According to this view, fusion of two cell types is a collision of two networks that have adopted distinct attractors. To learn how these networks reach a consensus, we model cell fusion computationally. To do so, we simulate patterns of gene activities using a formalism developed to simulate patterns of memory in neural networks. We find that the hybrid networks can assume attractors that are unrelated to parental attractors, implying that cell fusion can create new cell types by nearly instantaneously moving cells between attractors. We also show that hybrid networks are prone to assume spurious attractors, which are emergent and sporadic network states. This finding means that cell fusion can produce abnormal cell types, including cancerous types, by placing cells into normally inaccessible spurious states. Finally, we suggest that the problem of colliding networks has general significance in many processes represented by attractor networks, including biological, social, and political phenomena. Copyright © 2012 Biophysical Society. Published by Elsevier Inc. All rights reserved.
Analysis of stochastic effects in Kaldor-type business cycle discrete model
Bashkirtseva, Irina; Ryashko, Lev; Sysolyatina, Anna
2016-07-01
We study nonlinear stochastic phenomena in the discrete Kaldor model of business cycles. A numerical parametric analysis of stochastically forced attractors (equilibria, closed invariant curves, discrete cycles) of this model is performed using the stochastic sensitivity functions technique. A spatial arrangement of random states in stochastic attractors is modeled by confidence domains. The phenomenon of noise-induced transitions ;chaos-order; is discussed.
Fractal snapshot components in chaos induced by strong noise.
Bódai, Tamás; Károlyi, György; Tél, Tamás
2011-04-01
In systems exhibiting transient chaos in coexistence with periodic attractors, the inclusion of weak noise might give rise to noise-induced chaotic attractors. When the noise amplitude exceeds a critical value, an extended attractor appears along the fractal unstable manifold of the underlying nonattracting chaotic set. A further increase of noise leads to a fuzzy nonfractal pattern. By means of the concept of snapshot attractors and random maps, we point out that the fuzzy pattern can be decomposed into well-defined fractal components, the snapshot attractors belonging to a given realization of the noise and generated by following an ensemble of noisy trajectories. The pattern of the snapshot attractor and its characteristic numbers, such as the finite time Lyapunov exponents and numerically evaluated fractal dimensions, change continuously in time. We find that this temporal fluctuation is a robust property of the system which hardly changes with increasing ensemble size. The validity of the Kaplan-Yorke formula is also investigated. A superposition of about 100 snapshot attractors provides a good approximant to the fuzzy noise-induced attractor at the same noise strength.
Multistability in Chua's circuit with two stable node-foci
Energy Technology Data Exchange (ETDEWEB)
Bao, B. C.; Wang, N.; Xu, Q. [School of Information Science and Engineering, Changzhou University, Changzhou 213164 (China); Li, Q. D. [Research Center of Analysis and Control for Complex Systems, Chongqing University of Posts and Telecommunications, Chongqing 400065 (China)
2016-04-15
Only using one-stage op-amp based negative impedance converter realization, a simplified Chua's diode with positive outer segment slope is introduced, based on which an improved Chua's circuit realization with more simpler circuit structure is designed. The improved Chua's circuit has identical mathematical model but completely different nonlinearity to the classical Chua's circuit, from which multiple attractors including coexisting point attractors, limit cycle, double-scroll chaotic attractor, or coexisting chaotic spiral attractors are numerically simulated and experimentally captured. Furthermore, with dimensionless Chua's equations, the dynamical properties of the Chua's system are studied including equilibrium and stability, phase portrait, bifurcation diagram, Lyapunov exponent spectrum, and attraction basin. The results indicate that the system has two symmetric stable nonzero node-foci in global adjusting parameter regions and exhibits the unusual and striking dynamical behavior of multiple attractors with multistability.
The error of representation: basic understanding
Directory of Open Access Journals (Sweden)
Daniel Hodyss
2015-01-01
Full Text Available Representation error arises from the inability of the forecast model to accurately simulate the climatology of the truth. We present a rigorous framework for understanding this kind of error of representation. This framework shows that the lack of an inverse in the relationship between the true climatology (true attractor and the forecast climatology (forecast attractor leads to the error of representation. A new gain matrix for the data assimilation problem is derived that illustrates the proper approaches one may take to perform Bayesian data assimilation when the observations are of states on one attractor but the forecast model resides on another. This new data assimilation algorithm is the optimal scheme for the situation where the distributions on the true attractor and the forecast attractors are separately Gaussian, and there exists a linear map between them. The results of this theory are illustrated in a simple Gaussian multivariate model.
A Cayley Tree Immune Network Model with Antibody Dynamics
Anderson, R W; Perelson, A S; Anderson, Russell W.; Neumann, Avidan U.; Perelson, Alan S.
1993-01-01
Abstract: A Cayley tree model of idiotypic networks that includes both B cell and antibody dynamics is formulated and analyzed. As in models with B cells only, localized states exist in the network with limited numbers of activated clones surrounded by virgin or near-virgin clones. The existence and stability of these localized network states are explored as a function of model parameters. As in previous models that have included antibody, the stability of immune and tolerant localized states are shown to depend on the ratio of antibody to B cell lifetimes as well as the rate of antibody complex removal. As model parameters are varied, localized steady-states can break down via two routes: dynamically, into chaotic attractors, or structurally into percolation attractors. For a given set of parameters, percolation and chaotic attractors can coexist with localized attractors, and thus there do not exist clear cut boundaries in parameter space that separate regions of localized attractors from regions of percola...
Extreme multistability in a memristor-based multi-scroll hyper-chaotic system
Energy Technology Data Exchange (ETDEWEB)
Yuan, Fang, E-mail: yf210yf@163.com; Wang, Guangyi, E-mail: wanggyi@163.com [Institute of Modern Circuits and Intelligent Information, Hangzhou Dianzi University, Hangzhou 310018 (China); Wang, Xiaowei [Department of Automation, Shanghai University, Shanghai 200072 (China)
2016-07-15
In this paper, a new memristor-based multi-scroll hyper-chaotic system is designed. The proposed memristor-based system possesses multiple complex dynamic behaviors compared with other chaotic systems. Various coexisting attractors and hidden coexisting attractors are observed in this system, which means extreme multistability arises. Besides, by adjusting parameters of the system, this chaotic system can perform single-scroll attractors, double-scroll attractors, and four-scroll attractors. Basic dynamic characteristics of the system are investigated, including equilibrium points and stability, bifurcation diagrams, Lyapunov exponents, and so on. In addition, the presented system is also realized by an analog circuit to confirm the correction of the numerical simulations.
Energy Technology Data Exchange (ETDEWEB)
Saiki, Yoshitaka, E-mail: yoshi.saiki@r.hit-u.ac.jp [Graduate School of Commerce and Management, Hitotsubashi University, Tokyo 186-8601 (Japan); Yamada, Michio [Research Institute for Mathematical Sciences (RIMS), Kyoto University, Kyoto 606-8502 (Japan); Chian, Abraham C.-L. [Paris Observatory, LESIA, CNRS, 92195 Meudon (France); National Institute for Space Research (INPE), P.O. Box 515, São José dos Campos, São Paulo 12227-010 (Brazil); Institute of Aeronautical Technology (ITA) and World Institute for Space Environment Research (WISER), São José dos Campos, São Paulo 12228-900 (Brazil); School of Mathematical Sciences, University of Adelaide, Adelaide SA 5005 (Australia); Department of Biomedical Engineering, George Washington University, Washington, DC 20052 (United States); Miranda, Rodrigo A. [Faculty UnB-Gama, and Plasma Physics Laboratory, Institute of Physics, University of Brasília (UnB), Brasília DF 70910-900 (Brazil); Rempel, Erico L. [Institute of Aeronautical Technology (ITA) and World Institute for Space Environment Research (WISER), São José dos Campos, São Paulo 12228-900 (Brazil)
2015-10-15
The unstable periodic orbits (UPOs) embedded in a chaotic attractor after an attractor merging crisis (MC) are classified into three subsets, and employed to reconstruct chaotic saddles in the Kuramoto-Sivashinsky equation. It is shown that in the post-MC regime, the two chaotic saddles evolved from the two coexisting chaotic attractors before crisis can be reconstructed from the UPOs embedded in the pre-MC chaotic attractors. The reconstruction also involves the detection of the mediating UPO responsible for the crisis, and the UPOs created after crisis that fill the gap regions of the chaotic saddles. We show that the gap UPOs originate from saddle-node, period-doubling, and pitchfork bifurcations inside the periodic windows in the post-MC chaotic region of the bifurcation diagram. The chaotic attractor in the post-MC regime is found to be the closure of gap UPOs.
Real time unsupervised learning of visual stimuli in neuromorphic VLSI systems
Giulioni, Massimiliano; Corradi, Federico; Dante, Vittorio; Del Giudice, Paolo
2015-10-01
Neuromorphic chips embody computational principles operating in the nervous system, into microelectronic devices. In this domain it is important to identify computational primitives that theory and experiments suggest as generic and reusable cognitive elements. One such element is provided by attractor dynamics in recurrent networks. Point attractors are equilibrium states of the dynamics (up to fluctuations), determined by the synaptic structure of the network; a ‘basin’ of attraction comprises all initial states leading to a given attractor upon relaxation, hence making attractor dynamics suitable to implement robust associative memory. The initial network state is dictated by the stimulus, and relaxation to the attractor state implements the retrieval of the corresponding memorized prototypical pattern. In a previous work we demonstrated that a neuromorphic recurrent network of spiking neurons and suitably chosen, fixed synapses supports attractor dynamics. Here we focus on learning: activating on-chip synaptic plasticity and using a theory-driven strategy for choosing network parameters, we show that autonomous learning, following repeated presentation of simple visual stimuli, shapes a synaptic connectivity supporting stimulus-selective attractors. Associative memory develops on chip as the result of the coupled stimulus-driven neural activity and ensuing synaptic dynamics, with no artificial separation between learning and retrieval phases.
Bistability in Coupled Oscillators Exhibiting Synchronized Dynamics
Olusola, O. I.; Vincent, U. E.; Njah, A. N.; Olowofela, J. A.
2010-05-01
We report some new results associated with the synchronization behavior of two coupled double-well Duffing oscillators (DDOs). Some sufficient algebraic criteria for global chaos synchronization of the drive and response DDOs via linear state error feedback control are obtained by means of Lyapunov stability theory. The synchronization is achieved through a bistable state in which a periodic attractor co-exists with a chaotic attractor. Using the linear perturbation analysis, the prevalence of attractors in parameter space and the associated bifurcations are examined. Subcritical and supercritical Hopf bifurcations and abundance of Arnold tongues — a signature of mode locking phenomenon are found.
Chaotic itinerancy and its roles in cognitive neurodynamics.
Tsuda, Ichiro
2015-04-01
Chaotic itinerancy is an autonomously excited trajectory through high-dimensional state space of cortical neural activity that causes the appearance of a temporal sequence of quasi-attractors. A quasi-attractor is a local region of weakly convergent flows that represent ordered activity, yet connected to divergent flows representing disordered, chaotic activity between the regions. In a cognitive neurodynamic aspect, quasi-attractors represent perceptions, thoughts and memories, chaotic trajectories between them with intelligent searches, such as history-dependent trial-and-error via exploration, and itinerancy with history-dependent sequences in thinking, speaking and writing. Copyright © 2014 Elsevier Ltd. All rights reserved.
Dynamic analysis of a buckled asymmetric piezoelectric beam for energy harvesting
Energy Technology Data Exchange (ETDEWEB)
Van Blarigan, Louis, E-mail: louis01@umail.ucsb.edu; Moehlis, Jeff [Department of Mechanical Engineering, University of California, Santa Barbara, California 93106 (United States)
2016-03-15
A model of a buckled beam energy harvester is analyzed to determine the phenomena behind the transition between high and low power output levels. It is shown that the presence of a chaotic attractor is a sufficient condition to predict high power output, though there are relatively small areas where high output is achieved without a chaotic attractor. The chaotic attractor appears as a product of a period doubling cascade or a boundary crisis. Bifurcation diagrams provide insight into the development of the chaotic region as the input power level is varied, as well as the intermixed periodic windows.
Global dynamics of a reaction-diffusion system
Directory of Open Access Journals (Sweden)
Yuncheng You
2011-02-01
Full Text Available In this work the existence of a global attractor for the semiflow of weak solutions of a two-cell Brusselator system is proved. The method of grouping estimation is exploited to deal with the challenge in proving the absorbing property and the asymptotic compactness of this type of coupled reaction-diffusion systems with cubic autocatalytic nonlinearity and linear coupling. It is proved that the Hausdorff dimension and the fractal dimension of the global attractor are finite. Moreover, the existence of an exponential attractor for this solution semiflow is shown.
On the Dynamics of Abstract Retarded Evolution Equations
Directory of Open Access Journals (Sweden)
Desheng Li
2013-01-01
where is a self-adjoint positive-definite operator with compact resolvent and is a locally Lipschitz continuous mapping. The dissipativity and pullback attractors are investigated, and the existence of locally almost periodic solutions is established.
Energy Technology Data Exchange (ETDEWEB)
Nicolis, John S. E-mail: lalnicol-archgist@tee.gr
2007-08-15
We propose a common formalism concerning the non-linear filtering abilities of brains and enzymes via the study of the unevenness of the invariant measures of the multifractal attractors involved (classical and quantum respectively)
An algorithm for engineering regime shifts in one-dimensional dynamical systems
Tan, James P. L.
2018-01-01
Regime shifts are discontinuous transitions between stable attractors hosting a system. They can occur as a result of a loss of stability in an attractor as a bifurcation is approached. In this work, we consider one-dimensional dynamical systems where attractors are stable equilibrium points. Relying on critical slowing down signals related to the stability of an equilibrium point, we present an algorithm for engineering regime shifts such that a system may escape an undesirable attractor into a desirable one. We test the algorithm on synthetic data from a one-dimensional dynamical system with a multitude of stable equilibrium points and also on a model of the population dynamics of spruce budworms in a forest. The algorithm and other ideas discussed here contribute to an important part of the literature on exercising greater control over the sometimes unpredictable nature of nonlinear systems.
Integer and Fractional General T-System and Its Application to Control Chaos and Synchronization
National Research Council Canada - National Science Library
Mihaela Neamtu; Anamaria Litoiu; Petru C. Strain
2015-01-01
.... Also, the fractional order general T-system is proposed and analyzed. We provide some numerical simulations, where the chaos attractor and the dynamics of the Lyapunov coefficients are taken into consideration...
Crisis-induced intermittency in two coupled chaotic maps: towards understanding chaotic itinerancy.
Tanaka, G; Sanjuán, M A F; Aihara, K
2005-01-01
The present paper considers crisis-induced intermittency in a system composed of two coupled logistic maps. Its purpose is to clarify a bifurcation scenario generating such intermittent behaviors that can be regarded as a simple example of chaotic itinerancy. The intermittent dynamics appears immediately after an attractor-merging crisis of two off-diagonal chaotic attractors in a symmetrically coupled system. The scenario for the crisis is investigated through analyses of sequential bifurcations leading to the two chaotic attractors and successive changes in basin structures with variation of a system parameter. The successive changes of the basins are also characterized by variation of a dimension of a fractal basin boundary. A numerical analysis shows that simultaneous contacts between the attractors and the fractal basin boundary bring about the crisis and a snap-back repeller generated at the crisis produces the intermittent transitions. Furthermore, a modified scenario for intermittent behaviors in an asymmetrically coupled system is also discussed.
Directory of Open Access Journals (Sweden)
Hanfeng Kuang
2013-01-01
mean-square ultimate boundedness, the existence of an attractor, and the mean-square exponential stability are established. A numerical example is provided to illustrate the effectiveness of the proposed results.
Absence of chaos in digital memcomputing machines with solutions
Di Ventra, Massimiliano; Traversa, Fabio L.
2017-10-01
Digital memcomputing machines (DMMs) are non-linear dynamical systems designed so that their equilibrium points are solutions of the Boolean problem they solve. In a previous work [Chaos 27 (2017) 023107] it was argued that when DMMs support solutions of the associated Boolean problem then strange attractors cannot coexist with such equilibria. In this work, we demonstrate such conjecture. In particular, we show that both topological transitivity, and the strongest property of topological mixing, are inconsistent with the point dissipative property of DMMs when equilibrium points are present. This is true for both the whole phase space and the global attractor. Absence of topological transitivity is enough to imply absence of chaotic behavior. In a similar vein, we prove that if DMMs do not have equilibrium points, the only attractors present are invariant tori/periodic orbits with periods that may possibly increase with system size (quasi-attractors).
Hyperbolic Chaos A Physicist’s View
Kuznetsov, Sergey P
2012-01-01
"Hyperbolic Chaos: A Physicist’s View” presents recent progress on uniformly hyperbolic attractors in dynamical systems from a physical rather than mathematical perspective (e.g. the Plykin attractor, the Smale – Williams solenoid). The structurally stable attractors manifest strong stochastic properties, but are insensitive to variation of functions and parameters in the dynamical systems. Based on these characteristics of hyperbolic chaos, this monograph shows how to find hyperbolic chaotic attractors in physical systems and how to design a physical systems that possess hyperbolic chaos. This book is designed as a reference work for university professors and researchers in the fields of physics, mechanics, and engineering. Dr. Sergey P. Kuznetsov is a professor at the Department of Nonlinear Processes, Saratov State University, Russia.
2010-04-01
University campuses are considered major trip attractors. This intense level of activity generates significant : congestion levels within the campuses and in their vicinity, particularly in urban campus settings. With : university enrollment trends e...
Visually Evoked Spiking Evolves While Spontaneous Ongoing Dynamics Persist
DEFF Research Database (Denmark)
Huys, Raoul; Jirsa, Viktor K; Darokhan, Ziauddin
2016-01-01
attractor. Its existence guarantees that evoked spiking return to the spontaneous state. However, the spontaneous ongoing spiking state and the visual evoked spiking states are qualitatively different and are separated by a threshold (separatrix). The functional advantage of this organization...
(Re)Sources of opportunities – The Role of Spatial Context for Entrepreneurship
DEFF Research Database (Denmark)
Müller, Sabine; Korsgaard, Steffen
2014-01-01
contexts and results in four entrepreneurial types called Attractors, Valorisers, Artisans, and Entrepreneurs in the rural. The typology highlights the diversity of rural entrepreneurs and surfaces the distinguishing characteristics of rural ventures. This brings about the opportunity to identify...
Persistent activity in neural networks with dynamic synapses.
Directory of Open Access Journals (Sweden)
Omri Barak
2007-02-01
Full Text Available Persistent activity states (attractors, observed in several neocortical areas after the removal of a sensory stimulus, are believed to be the neuronal basis of working memory. One of the possible mechanisms that can underlie persistent activity is recurrent excitation mediated by intracortical synaptic connections. A recent experimental study revealed that connections between pyramidal cells in prefrontal cortex exhibit various degrees of synaptic depression and facilitation. Here we analyze the effect of synaptic dynamics on the emergence and persistence of attractor states in interconnected neural networks. We show that different combinations of synaptic depression and facilitation result in qualitatively different network dynamics with respect to the emergence of the attractor states. This analysis raises the possibility that the framework of attractor neural networks can be extended to represent time-dependent stimuli.
Hypogenetic chaotic jerk flows
Energy Technology Data Exchange (ETDEWEB)
Li, Chunbiao, E-mail: goontry@126.com [Jiangsu Key Laboratory of Meteorological Observation and Information Processing, Nanjing University of Information Science & Technology, Nanjing 210044 (China); School of Electronic & Information Engineering, Nanjing University of Information Science & Technology, Nanjing 210044 (China); Sprott, Julien Clinton [Department of Physics, University of Wisconsin–Madison, Madison, WI 53706 (United States); Xing, Hongyan [Jiangsu Key Laboratory of Meteorological Observation and Information Processing, Nanjing University of Information Science & Technology, Nanjing 210044 (China); School of Electronic & Information Engineering, Nanjing University of Information Science & Technology, Nanjing 210044 (China)
2016-03-11
Removing the amplitude or polarity information in the feedback loop of a jerk structure shows that special nonlinearities with partial information in the variable can also lead to chaos. Some striking properties are found for this kind of hypogenetic chaotic jerk flow, including multistability of symmetric coexisting attractors from an asymmetric structure, hidden attractors with respect to equilibria but with global attraction, easy amplitude control, and phase reversal which is convenient for chaos applications. - Highlights: • Hypogenetic chaotic jerk flows with incomplete feedback of amplitude or polarity are obtained. • Multistability of symmetric coexisting attractors from an asymmetric structure is found. • Some jerk systems have hidden attractors with respect to equilibria but have global attraction. • These chaotic jerk flows have the properties of amplitude control and phase reversal.
Prediction of walk-to-run transition using stride frequency
DEFF Research Database (Denmark)
Hansen, Ernst Albin; Nielsen, Andreas Møller; Kristensen, Lasse Andreas Risgaard
2018-01-01
The transition from walking to running has previously been predicted to occur at a point where the stride frequency starts getting closer to the running attractor than to the walking attractor. The two behavioural attractors were considered to be represented by the freely chosen stride frequencies...... during unrestricted treadmill walking and running. The aim of the present study was to determine the relative and absolute test-retest reliability of the predicted walk-to-run transition stride frequency. Healthy individuals (n=25) performed walking and running on a treadmill in a day-to-day test......-retest design. The two behavioral attractors were determined during walking and running at freely chosen velocities and stride frequencies. Subsequently, the walk-to-run transition stride frequency was predicted using camera recordings and a previously reported equation for prediction. The walk...
The phase-space analysis of scalar fields with non-minimally derivative coupling
Energy Technology Data Exchange (ETDEWEB)
Huang, Yumei [Beijing Normal University, Department of Astronomy, Beijing (China); Gao, Qing; Gong, Yungui [Huazhong University of Science and Technology, MOE Key Laboratory of Fundamental Quantities Measurement, School of Physics, Wuhan, Hubei (China)
2015-04-01
We perform a dynamical analysis for the exponential scalar field with non-minimally derivative coupling. For the quintessence case, the stable fixed points are the same with and without the non-minimally derivative coupling. For the phantom case, the attractor with dark energy domination exists for the minimal coupling only. For the non-minimally derivative coupling without the standard canonical kinetic term, only the de Sitter attractor exists, and the dark matter solution is unstable. (orig.)
Chan, H B; Stambaugh, C
2007-08-10
We explore fluctuation-induced switching in parametrically driven micromechanical torsional oscillators. The oscillators possess one, two, or three stable attractors depending on the modulation frequency. Noise induces transitions between the coexisting attractors. Near the bifurcation points, the activation barriers are found to have a power law dependence on frequency detuning with critical exponents that are in agreement with predicted universal scaling relationships. At large detuning, we observe a crossover to a different power law dependence with an exponent that is device specific.
Locus of boundary crisis: expect infinitely many gaps.
Osinga, Hinke M
2006-09-01
Boundary crisis is a mechanism for destroying a chaotic attractor when one parameter is varied. In a two-parameter setting the locus of the boundary crisis is associated with curves of homoclinic or heteroclinic bifurcations of periodic saddle points. It is known that this locus has nondifferentiable points. We show here that the locus of boundary crisis is far more complicated than previously reported. It actually contains infinitely many gaps, corresponding to regions (of positive measure) where attractors exist.
Applications of chaotic neurodynamics in pattern recognition
Baird, Bill; Freeman, Walter J.; Eeckman, Frank H.; Yao, Yong
1991-08-01
Network algorithms and architectures for pattern recognition derived from neural models of the olfactory system are reviewed. These span a range from highly abstract to physiologically detailed, and employ the kind of dynamical complexity observed in olfactory cortex, ranging from oscillation to chaos. A simple architecture and algorithm for analytically guaranteed associative memory storage of analog patterns, continuous sequences, and chaotic attractors in the same network is described. A matrix inversion determines network weights, given prototype patterns to be stored. There are N units of capacity in an N node network with 3N2 weights. It costs one unit per static attractor, two per Fourier component of each sequence, and three to four per chaotic attractor. There are no spurious attractors, and for sequences there is a Liapunov function in a special coordinate system which governs the approach of transient states to stored trajectories. Unsupervised or supervised incremental learning algorithms for pattern classification, such as competitive learning or bootstrap Widrow-Hoff can easily be implemented. The architecture can be ''folded'' into a recurrent network with higher order weights that can be used as a model of cortex that stores oscillatory and chaotic attractors by a Hebb rule. Network performance is demonstrated by application to the problem of real-time handwritten digit recognition. An effective system with on-line learning has been written by Eeckman and Baird for the Macintosh. It utilizes static, oscillatory, and/or chaotic attractors of two kinds--Lorenze attractors, or attractors resulting from chaotically interacting oscillatory modes. The successful application to an industrial pattern recognition problem of a network architecture of considerable physiological and dynamical complexity, developed by Freeman and Yao, is described. The data sets of the problem come in three classes of difficulty, and performance of the biological network is
Two Invariants of Human-Swarm Interaction
2018-01-16
often have formal attractors such as nest selection (Nevai & Passino, 2010) and many of the collective animal behaviors described by Sumpter (Sumpter...can be used to design swarm systems with desired fan-outs and workloads in mind . The key reason this is possible is that we are managing attractors...E., Giardina, I., et al. (2008). Interaction ruling animal collective behavior depends on topological rather than metric distance: Evidence from a
Kinetics for Reduction of Iron Ore Based on the Phase Space Reconstruction
Guo-Feng Fan; Li-Ling Peng; Wei-Chiang Hong; Fan Sun
2014-01-01
A series of smelting reduction experiments has been carried out with high-phosphorus iron ore of the different bases and heating rates by thermogravimetric analyzer. The derivative thermo gravimetric (DTG) data have been obtained from the experiments. After analyzing its phase space reconstruction, it is found that DTG phase portrait contains with a clear double “ $\\infty $ ” attractor characteristic by one-order delay. The statistical properties of the attractor inside and outside the double...
Moisés Damián Perales Escudero
2013-01-01
Previous L1 and L2 research on inferential comprehension has tended to follow a quantitative orientation. By contrast, L2 research on critical reading is qualitative and tends to ignore inferences. This paper presents a qualitative, design-based study of a critical reading intervention focused on promoting generative rhetorical inferences and investigating co-adaptation and emergence of new meaning-making capacities. Complexity theory (CT) constructs were used to research processes of co-adap...
Modeling and controlling the two-phase dynamics of the p53 network: a Boolean network approach
Lin, Guo-Qiang; Ao, Bin; Chen, Jia-Wei; Wang, Wen-Xu; Di, Zeng-Ru
2014-12-01
Although much empirical evidence has demonstrated that p53 plays a key role in tumor suppression, the dynamics and function of the regulatory network centered on p53 have not yet been fully understood. Here, we develop a Boolean network model to reproduce the two-phase dynamics of the p53 network in response to DNA damage. In particular, we map the fates of cells into two types of Boolean attractors, and we find that the apoptosis attractor does not exist for minor DNA damage, reflecting that the cell is reparable. As the amount of DNA damage increases, the basin of the repair attractor shrinks, accompanied by the rising of the apoptosis attractor and the expansion of its basin, indicating that the cell becomes more irreparable with more DNA damage. For severe DNA damage, the repair attractor vanishes, and the apoptosis attractor dominates the state space, accounting for the exclusive fate of death. Based on the Boolean network model, we explore the significance of links, in terms of the sensitivity of the two-phase dynamics, to perturbing the weights of links and removing them. We find that the links are either critical or ordinary, rather than redundant. This implies that the p53 network is irreducible, but tolerant of small mutations at some ordinary links, and this can be interpreted with evolutionary theory. We further devised practical control schemes for steering the system into the apoptosis attractor in the presence of DNA damage by pinning the state of a single node or perturbing the weight of a single link. Our approach offers insights into understanding and controlling the p53 network, which is of paramount importance for medical treatment and genetic engineering.
PENGARUH ILUMINASI ATRAKTOR CAHAYA TERHADAP HASIL TANGKAPAN IKAN PADA BAGAN APUNG PELABUHAN RATU
Directory of Open Access Journals (Sweden)
Regi Fiji Anggawangsa
2016-04-01
Full Text Available Atraktor cahaya sebagai alat bantu penangkapan banyak digunakan untuk mengumpulkan ikan pada alat tangkap bagan apung. Tiga macam atraktor cahaya, yaitu petromaks minyak tanah (dengan iluminasi maksimal 80 lux, petromaks gas (dengan iluminasi maksimal 60 lux, dan lampu genset (dengan iluminasi maksimal 500 lux digunakan pada bagan apung di Palabuhanratu. Penelitian ini bertujuan untuk mengetahui pengaruh perbedaan iluminasi cahaya pada ketiga macam sumber cahaya tersebut terhadap hasil tangkapan bagan apung. Metode yang digunakan adalah eksperimen penangkapan ikan dengan menggunakan tiga jenis atraktor cahaya pada bagan apung. Hasil penelitian menunjukkan perbedaan iluminasi atraktor cahaya pada bagan apung berpengaruh terhadap komposisi hasil tangkapan. Hasil tangkapan bagan pada saat menggunakan atraktor cahaya petromaks minyak tanah (80 lux didominasi oleh ikan layur (Trichiurus spp. yang mencapai lebih dari 50%, petromaks gas (60 lux didominasi oleh ikan layur (Trichiurus spp. dan cumi-cumi (Loligo spp. sedangkan untuk atraktor lampu genset (500 lux didominasi oleh layur dan cumi-cumi. Light attractor has been used as a fishing device to gather fish schooling on lift net. There are three types of light attractors i.e. kerosene pressure lamp, gas pressure lamp and genset lamp used by Palabuhanratu’s lift net. The aim of this research is to investigate the effect of those light attractors on the lift net catches. The experimental fishing method was used. The results show that illumination produced by genset lamp was higher (500 lux than the two other light attractors at all observation positions with maximum illumination obtained of 80 lux for kerosene pressure lamp and 60 lux for gas pressure lamp. Catch of lift net when using kerosene pressure lamp attractor (80 lux was dominated by hairtail fish (Trichiurus spp. that reaches more than 50%, gas kerosene lamps attractor (60 lux was dominated by fish Layur (Trichiurus spp. and squid
Hidden hyperchaos and electronic circuit application in a 5D self-exciting homopolar disc dynamo.
Wei, Zhouchao; Moroz, Irene; Sprott, J C; Akgul, Akif; Zhang, Wei
2017-03-01
We report on the finding of hidden hyperchaos in a 5D extension to a known 3D self-exciting homopolar disc dynamo. The hidden hyperchaos is identified through three positive Lyapunov exponents under the condition that the proposed model has just two stable equilibrium states in certain regions of parameter space. The new 5D hyperchaotic self-exciting homopolar disc dynamo has multiple attractors including point attractors, limit cycles, quasi-periodic dynamics, hidden chaos or hyperchaos, as well as coexisting attractors. We use numerical integrations to create the phase plane trajectories, produce bifurcation diagram, and compute Lyapunov exponents to verify the hidden attractors. Because no unstable equilibria exist in two parameter regions, the system has a multistability and six kinds of complex dynamic behaviors. To the best of our knowledge, this feature has not been previously reported in any other high-dimensional system. Moreover, the 5D hyperchaotic system has been simulated using a specially designed electronic circuit and viewed on an oscilloscope, thereby confirming the results of the numerical integrations. Both Matlab and the oscilloscope outputs produce similar phase portraits. Such implementations in real time represent a new type of hidden attractor with important consequences for engineering applications.
Boundary crisis and transient in a dissipative relativistic standard map
Energy Technology Data Exchange (ETDEWEB)
Oliveira, Diego F.M., E-mail: diegofregolente@gmail.com [CAMTP, Center for Applied Mathematics and Theoretical Physics, University of Maribor, Krekova 2, SI-2000, Maribor (Slovenia); Leonel, Edson D., E-mail: edleonel@rc.unesp.br [Departamento de Estatistica, Matematica Aplicada e Computacao, UNESP, Univ. Estadual Paulista, Av. 24A, 1515, Bela Vista, 13506-900, Rio Claro, SP (Brazil); Robnik, Marko, E-mail: robnik@uni-mb.si [CAMTP, Center for Applied Mathematics and Theoretical Physics, University of Maribor, Krekova 2, SI-2000, Maribor (Slovenia)
2011-09-05
Some dynamical properties for a problem concerning the acceleration of particles in a wave packet are studied. The model is described in terms of a two-dimensional nonlinear map obtained from a Hamiltonian which describes the motion of a relativistic standard map. The phase space is mixed in the sense that there are regular and chaotic regions coexisting. When dissipation is introduced, the property of area preservation is broken and attractors emerge. We have shown that a tiny increase of the dissipation causes a change in the phase space. A chaotic attractor as well as its basin of attraction are destroyed thereby leading the system to experience a boundary crisis. We have characterized such a boundary crisis via a collision of the chaotic attractor with the stable manifold of a saddle fixed point. Once the chaotic attractor is destroyed, a chaotic transient described by a power law with exponent -1 is observed. -- Highlights: → A problem concerning the acceleration of particles. Dissipation is introduced. → The property of area preservation is broken and attractors emerge. → After a tiny increase of the dissipation the system experience a boundary crisis. → The chaotic transient is described by a power law with exponent -1.
Directory of Open Access Journals (Sweden)
Carolina Ospina-Aguirre
2008-12-01
Full Text Available In order to characterize physiological signals, which may have highly nonlinear structures, it’s common to use methodologies derived from fractal techniques that make part of complexity analysis. This work proposes is proposed an evaluation function based on measuring the capacity of prediction of a neural network trained with Kalman filter to predict points in a reconstructed state space attractor, so measuring the quality of the attractor from a onedimensional signal. We propose use of statistic measures such as Kullback –Leibler, Kolmogorov-Smirnov and Hellinger to determine difference between the embedded statistic structure in the predicted points and the original signal points. Results were obtained on attractor reconstruction from ECG signals of MIT-BIH database and EEG signals obtained from Clinic for Epileptologie Epileptologie Bonn University database. In this way, it was possible to evaluate the prediction capacity corresponding to reconstruct attractors from records, from which we concluded that an attractor with high capacity of time series prediction implies good embedding properties in state space.
The mathematical cell model reconstructed from interference microscopy data
Rogotnev, A. A.; Nikitiuk, A. S.; Naimark, O. B.; Nebogatikov, V. O.; Grishko, V. V.
2017-09-01
The mathematical model of cell dynamics is developed to link the dynamics of the phase cell thickness with the signs of the oncological pathology. The measurements of irregular oscillations of cancer cells phase thickness were made with laser interference microscope MIM-340 in order to substantiate this model. These data related to the dynamics of phase thickness for different cross-sections of cells (nuclei, nucleolus, and cytoplasm) allow the reconstruction of the attractor of dynamic system. The attractor can be associated with specific types of collective modes of phase thickness responsible for the normal and cancerous cell dynamics. Specific type of evolution operator was determined using an algorithm of designing of the mathematical cell model and temporal phase thickness data for cancerous and normal cells. Qualitative correspondence of attractor types to the cell states was analyzed in terms of morphological signs associated with maximum value of mean square irregular oscillations of phase thickness dynamics.
NARX prediction of some rare chaotic flows: Recurrent fuzzy functions approach
Energy Technology Data Exchange (ETDEWEB)
Goudarzi, Sobhan [Biomedical Engineering Department, Amirkabir University of Technology, Tehran 15875-4413 (Iran, Islamic Republic of); Jafari, Sajad, E-mail: sajadjafari@aut.ac.ir [Biomedical Engineering Department, Amirkabir University of Technology, Tehran 15875-4413 (Iran, Islamic Republic of); Moradi, Mohammad Hassan [Biomedical Engineering Department, Amirkabir University of Technology, Tehran 15875-4413 (Iran, Islamic Republic of); Sprott, J.C. [Department of Physics, University of Wisconsin–Madison, Madison, WI 53706 (United States)
2016-02-15
The nonlinear and dynamic accommodating capability of time domain models makes them a useful representation of chaotic time series for analysis, modeling and prediction. This paper is devoted to the modeling and prediction of chaotic time series with hidden attractors using a nonlinear autoregressive model with exogenous inputs (NARX) based on a novel recurrent fuzzy functions (RFFs) approach. Case studies of recently introduced chaotic systems with hidden attractors plus classical chaotic systems demonstrate that the proposed modeling methodology exhibits better prediction performance from different viewpoints (short term and long term) compared to some other existing methods. - Highlights: • A new method is proposed for prediction of chaotic time series. • This method is based on novel recurrent fuzzy functions (RFFs) approach. • Some rare chaotic flows are used as test systems. • The new method shows proper performance in short-term prediction. • It also shows proper performance in prediction of attractor's topology.
Directory of Open Access Journals (Sweden)
Ian Bickerton
2017-11-01
Full Text Available Experiments have been conducted on a dual electric grid thermionic device to investigate an alternative method of space charge mitigation in a thermionic energy convertor (TEC. Two electric grids, the attractor and deflector grids, provide opposing electric fields to overcome space charge while minimizing power losses to the attractor grid. Electron beams are formed in the electrode gap providing a more efficient electron transport from hot cathode to collector. The attractor gird can be run in DC or pulse mode which usefully supports transformer coupling for the energy convertor output. This is a simple low cost inter-electrode space charge solution running at low voltage which has the potential to improve TEC efficiency, increase reliability, and reduce the cost of manufacture.
Pascal (Yang Hui) triangles and power laws in the logistic map
Velarde, Carlos; Robledo, Alberto
2015-04-01
We point out the joint occurrence of Pascal triangle patterns and power-law scaling in the standard logistic map, or more generally, in unimodal maps. It is known that these features are present in its two types of bifurcation cascades: period and chaotic-band doubling of attractors. Approximate Pascal triangles are exhibited by the sets of lengths of supercycle diameters and by the sets of widths of opening bands. Additionally, power-law scaling manifests along periodic attractor supercycle positions and chaotic band splitting points. Consequently, the attractor at the mutual accumulation point of the doubling cascades, the onset of chaos, displays both Gaussian and power-law distributions. Their combined existence implies both ordinary and exceptional statistical-mechanical descriptions of dynamical properties.
Basins of Attraction for Generative Justice
Eglash, Ron; Garvey, Colin
It has long been known that dynamic systems typically tend towards some state - an "attractor" - into which they finally settle. The introduction of chaos theory has modified our understanding of these attractors: we no longer think of the final "resting state" as necessarily being at rest. In this essay we consider the attractors of social ecologies: the networks of people, technologies and natural resources that makeup our built environments. Following the work of "communitarians" we posit that basins of attraction could be created for social ecologies that foster both environmental sustainability and social justice. We refer to this confluence as "generative justice"; a phrase which references both the "bottom-up", self-generating source of its adaptive meta stability, as well as its grounding in the ethics of egalitarian political theory.
Global dynamics of a PDE model for aedes aegypti mosquitoe incorporating female sexual preference
Parshad, Rana
2011-01-01
In this paper we study the long time dynamics of a reaction diffusion system, describing the spread of Aedes aegypti mosquitoes, which are the primary cause of dengue infection. The system incorporates a control attempt via the sterile insect technique. The model incorporates female mosquitoes sexual preference for wild males over sterile males. We show global existence of strong solution for the system. We then derive uniform estimates to prove the existence of a global attractor in L-2(Omega), for the system. The attractor is shown to be L-infinity(Omega) regular and posess state of extinction, if the injection of sterile males is large enough. We also provide upper bounds on the Hausdorff and fractal dimensions of the attractor.
Stochastic Chaos in a Turbulent Swirling Flow
Faranda, D.; Sato, Y.; Saint-Michel, B.; Wiertel, C.; Padilla, V.; Dubrulle, B.; Daviaud, F.
2017-07-01
We report the experimental evidence of the existence of a random attractor in a fully developed turbulent swirling flow. By defining a global observable which tracks the asymmetry in the flux of angular momentum imparted to the flow, we can first reconstruct the associated turbulent attractor and then follow its route towards chaos. We further show that the experimental attractor can be modeled by stochastic Duffing equations, that match the quantitative properties of the experimental flow, namely, the number of quasistationary states and transition rates among them, the effective dimensions, and the continuity of the first Lyapunov exponents. Such properties can be recovered neither using deterministic models nor using stochastic differential equations based on effective potentials obtained by inverting the probability distributions of the experimental global observables. Our findings open the way to low-dimensional modeling of systems featuring a large number of degrees of freedom and multiple quasistationary states.
Crisis bifurcations in plane Poiseuille flow.
Zammert, Stefan; Eckhardt, Bruno
2015-04-01
Many shear flows follow a route to turbulence that has striking similarities to bifurcation scenarios in low-dimensional dynamical systems. Among the bifurcations that appear, crisis bifurcations are important because they cause global transitions between open and closed attractors, or indicate drastic increases in the range of the state space that is covered by the dynamics. We here study exterior and interior crisis bifurcations in direct numerical simulations of transitional plane Poiseuille flow in a mirror-symmetric subspace. We trace the state space dynamics from the appearance of the first three-dimensional exact coherent structures to the transition from an attractor to a chaotic saddle in an exterior crisis. For intermediate Reynolds numbers, the attractor undergoes several interior crises, in which new states appear and intermittent behavior can be observed. The bifurcations contribute to increasing the complexity of the dynamics and to a more dense coverage of state space.
How Anatomy Shapes Dynamics: A Semi-Analytical Study of the Brain at Rest by a Simple Spin Model
Directory of Open Access Journals (Sweden)
Gustavo eDeco
2012-09-01
Full Text Available Resting state networks show a surprisingly coherent and robust spatiotemporal organization. Previous theoretical studies demonstrated that these patterns can be understood as emergent on the basis of the underlying neuroanatomical connectivity skeleton. Integrating the biologically realistic DTI/DSI based neuroanatomical connectivity into a brain model of Ising spin dynamics, we found the presence of latent ghost multi-stable attractors, which can be studied analytically. The multistable attractor landscape defines a functionally meaningful dynamic repertoire of the brain network that is inherently present in the neuroanatomical connectivity. We demonstrate that the more entropy of attractors exists, the richer is the dynamical repertoire and consequently the brain network displays more capabilities of computation. We hypothesize therefore that human brain connectivity developed a scale free type of architecture in order to be able to store a large number of different and flexibly accessible brain functions
How anatomy shapes dynamics: a semi-analytical study of the brain at rest by a simple spin model.
Deco, Gustavo; Senden, Mario; Jirsa, Viktor
2012-01-01
Resting state networks (RSNs) show a surprisingly coherent and robust spatiotemporal organization. Previous theoretical studies demonstrated that these patterns can be understood as emergent on the basis of the underlying neuroanatomical connectivity skeleton. Integrating the biologically realistic DTI/DSI-(Diffusion Tensor Imaging/Diffusion Spectrum Imaging)based neuroanatomical connectivity into a brain model of Ising spin dynamics, we found a system with multiple attractors, which can be studied analytically. The multistable attractor landscape thus defines a functionally meaningful dynamic repertoire of the brain network that is inherently present in the neuroanatomical connectivity. We demonstrate that the more entropy of attractors exists, the richer is the dynamical repertoire and consequently the brain network displays more capabilities of computation. We hypothesize therefore that human brain connectivity developed a scale free type of architecture in order to be able to store a large number of different and flexibly accessible brain functions.
Turing patterns and long-time behavior in a three-species food-chain model
Parshad, Rana D.
2014-08-01
We consider a spatially explicit three-species food chain model, describing generalist top predator-specialist middle predator-prey dynamics. We investigate the long-time dynamics of the model and show the existence of a finite dimensional global attractor in the product space, L2(Ω). We perform linear stability analysis and show that the model exhibits the phenomenon of Turing instability, as well as diffusion induced chaos. Various Turing patterns such as stripe patterns, mesh patterns, spot patterns, labyrinth patterns and weaving patterns are obtained, via numerical simulations in 1d as well as in 2d. The Turing and non-Turing space, in terms of model parameters, is also explored. Finally, we use methods from nonlinear time series analysis to reconstruct a low dimensional chaotic attractor of the model, and estimate its fractal dimension. This provides a lower bound, for the fractal dimension of the attractor, of the spatially explicit model. © 2014 Elsevier Inc.
Nonlinear Stochastic stability analysis of Wind Turbine Wings by Monte Carlo Simulations
DEFF Research Database (Denmark)
Larsen, Jesper Winther; Iwankiewiczb, R.; Nielsen, Søren R.K.
2007-01-01
Wind turbines are increasing in magnitude without a proportional increase of stiffness, for which reason geometrical nonlinearities become increasingly important. In this paper the nonlinear equations of motion are analysed of a rotating Bernoulli-Euler beam including nonlinear geometrical and in...... under narrow-banded excitation, and it is shown that the qualitative behaviour of the strange attractor is very similar for the periodic and almost periodic responses, whereas the strange attractor for the chaotic case loses structure as the excitation becomes narrow-banded. Furthermore......, the characteristic behaviour of the strange attractor is shown to be identifiable by the so-called information dimension. Due to the complexity of the coupled nonlinear structural system all analyses are carried out via Monte Carlo simulations....
Dynamics of logistic equations with non-autonomous bounded coefficients
Directory of Open Access Journals (Sweden)
. N. Nkashama
2000-01-01
Full Text Available We prove that the Verhulst logistic equation with positive non-autonomous bounded coefficients has exactly one bounded solution that is positive, and that does not approach the zero-solution in the past and in the future. We also show that this solution is an attractor for all positive solutions, some of which are shown to blow-up in finite time backward. Since the zero-solution is shown to be a repeller for all solutions that remain below the afore-mentioned one, we obtain an attractor-repeller pair, and hence (connecting heteroclinic orbits. The almost-periodic attractor case is also discussed. Our techniques apply to the critical threshold-level equation as well.
A Memristive Hyperchaotic Multiscroll Jerk System with Controllable Scroll Numbers
Wang, Chunhua; Xia, Hu; Zhou, Ling
2017-06-01
A memristor is the fourth circuit element, which has wide applications in chaos generation. In this paper, a four-dimensional hyperchaotic jerk system based on a memristor is proposed, where the scroll number of the memristive jerk system is controllable. The new system is constructed by introducing one extra flux-controlled memristor into three-dimensional multiscroll jerk system. We can get different scroll attractors by varying the strength of memristor in this system without changing the circuit structure. Such a method for controlling the scroll number without changing the circuit structure is very important in designing the modern circuits and systems. The new memristive jerk system can exhibit a hyperchaotic attractor, which has more complex dynamic behavior. Furthermore, coexisting attractors are observed in the system. Phase portraits, dissipativity, equilibria, Lyapunov exponents and bifurcation diagrams are analyzed. Finally, the circuit implementation is carried out to verify the new system.
Chaos analysis of EEG during isoflurane-induced loss of righting in rats
Directory of Open Access Journals (Sweden)
Bruce eMaciver
2014-10-01
Full Text Available It has long been known that electroencephalogram (EEG signals generate chaotic strange attractors and the shape of these attractors correlate with depth of anesthesia. We applied chaos analysis to frontal cortical and hippocampal micro-EEG signals from implanted microelectrodes (layer 4 and CA1, respectively. Rats were taken to and from loss of righting reflex (LORR with isoflurane and behavioral measures were compared to attractor shape. Resting EEG signals at LORR differed markedly from awake signals, more similar to slow wave sleep signals, and easily discerned in raw recordings (high amplitude slow waves, and in fast Fourier transform analysis (FFT; increased delta power, in good agreement with previous studies. EEG activation stimulated by turning rats on their side, to test righting, produced signals quite similar to awake resting state EEG signals. That is, the high amplitude slow wave activity changed to low amplitude fast activity that lasted for several seconds, before returning to slow wave activity. This occurred regardless of whether the rat was able to right itself, or not. Testing paw pinch and tail clamp responses produced similar EEG activations, even from deep anesthesia when burst suppression dominated the spontaneous EEG. Chaotic attractor shape was far better at discerning between these awake-like signals, at loss of responses, than was FFT analysis. Comparisons are provided between FFT and chaos analysis of EEG during awake walking, slow wave sleep, and isoflurane-induced effects at several depths of anesthesia. Attractors readily discriminated between natural sleep and isoflurane-induced ‘delta’ activity. Chaotic attractor shapes changed gradually through the transition from awake to LORR, indicating that this was not an on/off like transition, but rather a point along a continuum of brain states.
Breeding novel solutions in the brain: a model of Darwinian neurodynamics.
Szilágyi, András; Zachar, István; Fedor, Anna; de Vladar, Harold P; Szathmáry, Eörs
2016-01-01
Background: The fact that surplus connections and neurons are pruned during development is well established. We complement this selectionist picture by a proof-of-principle model of evolutionary search in the brain, that accounts for new variations in theory space. We present a model for Darwinian evolutionary search for candidate solutions in the brain. Methods: We combine known components of the brain - recurrent neural networks (acting as attractors), the action selection loop and implicit working memory - to provide the appropriate Darwinian architecture. We employ a population of attractor networks with palimpsest memory. The action selection loop is employed with winners-share-all dynamics to select for candidate solutions that are transiently stored in implicit working memory. Results: We document two processes: selection of stored solutions and evolutionary search for novel solutions. During the replication of candidate solutions attractor networks occasionally produce recombinant patterns, increasing variation on which selection can act. Combinatorial search acts on multiplying units (activity patterns) with hereditary variation and novel variants appear due to (i) noisy recall of patterns from the attractor networks, (ii) noise during transmission of candidate solutions as messages between networks, and, (iii) spontaneously generated, untrained patterns in spurious attractors. Conclusions: Attractor dynamics of recurrent neural networks can be used to model Darwinian search. The proposed architecture can be used for fast search among stored solutions (by selection) and for evolutionary search when novel candidate solutions are generated in successive iterations. Since all the suggested components are present in advanced nervous systems, we hypothesize that the brain could implement a truly evolutionary combinatorial search system, capable of generating novel variants.
Applications of nonlinear time-series analysis
Nichols, Jonathan Michael
In this work, new applications in chaos theory and nonlinear time-series analysis are explored. Tools for attractor-based analysis are developed along with a complete description of invariant measures. The focus is on the computation of dimension and Lyapunov spectra from a single time-history for the purposes of system identification. The need for accurate attractor reconstruction is stressed as it may have severe effects on the quality of estimated invariants and of attractor based predictions. These tools are then placed in the context of several different problems of importance to the engineering community. Dimension and Lyaponuv spectra are used to indicate the operating regime of a nonlinear mechanical oscillator. Subtle changes to the way in which the oscillator is forced may give rise to a response with different state space characteristics. These differences are clearly discernible using invariant measures yet are undetectable using linear-based techniques. A state space approach is also used to extract damping estimates from the oscillator by means of the complete Lyapunov spectrum. The sum of the exponents may be thought of as the average divergence of the system which will, for a viscous damping model, provide quantitative information about the coefficient of viscous damping. The notion of chaotic excitation of a linear system is also explored. A linear structure subject to chaotic excitation will effectively act as a filter. The resulting dynamical interaction gives rise to response (filtered) attractors which possess information about the linear system. Differences in the geometric properties of the filtered attractors are used to detect damage in structures. These attractor-based statistics are shown to be more robust indicators of damage than linear-based statistics (e.g. mode shapes, frequencies, etc.). The same procedure is also used to estimate the coefficient of viscous damping for a multi-degree-of-freedom linear structure.
Directory of Open Access Journals (Sweden)
András Szilágyi
2016-09-01
Full Text Available Background: The fact that surplus connections and neurons are pruned during development is well established. We complement this selectionist picture by a proof-of-principle model of evolutionary search in the brain, that accounts for new variations in theory space. We present a model for Darwinian evolutionary search for candidate solutions in the brain. Methods: We combine known components of the brain – recurrent neural networks (acting as attractors, the action selection loop and implicit working memory – to provide the appropriate Darwinian architecture. We employ a population of attractor networks with palimpsest memory. The action selection loop is employed with winners-share-all dynamics to select for candidate solutions that are transiently stored in implicit working memory. Results: We document two processes: selection of stored solutions and evolutionary search for novel solutions. During the replication of candidate solutions attractor networks occasionally produce recombinant patterns, increasing variation on which selection can act. Combinatorial search acts on multiplying units (activity patterns with hereditary variation and novel variants appear due to (i noisy recall of patterns from the attractor networks, (ii noise during transmission of candidate solutions as messages between networks, and, (iii spontaneously generated, untrained patterns in spurious attractors. Conclusions: Attractor dynamics of recurrent neural networks can be used to model Darwinian search. The proposed architecture can be used for fast search among stored solutions (by selection and for evolutionary search when novel candidate solutions are generated in successive iterations. Since all the suggested components are present in advanced nervous systems, we hypothesize that the brain could implement a truly evolutionary combinatorial search system, capable of generating novel variants.
Directory of Open Access Journals (Sweden)
András Szilágyi
2017-06-01
Full Text Available Background: The fact that surplus connections and neurons are pruned during development is well established. We complement this selectionist picture by a proof-of-principle model of evolutionary search in the brain, that accounts for new variations in theory space. We present a model for Darwinian evolutionary search for candidate solutions in the brain. Methods: We combine known components of the brain – recurrent neural networks (acting as attractors, the action selection loop and implicit working memory – to provide the appropriate Darwinian architecture. We employ a population of attractor networks with palimpsest memory. The action selection loop is employed with winners-share-all dynamics to select for candidate solutions that are transiently stored in implicit working memory. Results: We document two processes: selection of stored solutions and evolutionary search for novel solutions. During the replication of candidate solutions attractor networks occasionally produce recombinant patterns, increasing variation on which selection can act. Combinatorial search acts on multiplying units (activity patterns with hereditary variation and novel variants appear due to (i noisy recall of patterns from the attractor networks, (ii noise during transmission of candidate solutions as messages between networks, and, (iii spontaneously generated, untrained patterns in spurious attractors. Conclusions: Attractor dynamics of recurrent neural networks can be used to model Darwinian search. The proposed architecture can be used for fast search among stored solutions (by selection and for evolutionary search when novel candidate solutions are generated in successive iterations. Since all the suggested components are present in advanced nervous systems, we hypothesize that the brain could implement a truly evolutionary combinatorial search system, capable of generating novel variants.
Statistical Properties of Lorenz-like Flows, Recent Developments and Perspectives
Araujo, Vitor; Galatolo, Stefano; Pacifico, Maria José
We comment on the mathematical results about the statistical behavior of Lorenz equations and its attractor, and more generally on the class of singular hyperbolic systems. The mathematical theory of such kind of systems turned out to be surprisingly difficult. It is remarkable that a rigorous proof of the existence of the Lorenz attractor was presented only around the year 2000 with a computer-assisted proof together with an extension of the hyperbolic theory developed to encompass attractors robustly containing equilibria. We present some of the main results on the statistical behavior of such systems. We show that for attractors of three-dimensional flows, robust chaotic behavior is equivalent to the existence of certain hyperbolic structures, known as singular-hyperbolicity. These structures, in turn, are associated with the existence of physical measures: in low dimensions, robust chaotic behavior for flows ensures the existence of a physical measure. We then give more details on recent results on the dynamics of singular-hyperbolic (Lorenz-like) attractors: (1) there exists an invariant foliation whose leaves are forward contracted by the flow (and further properties which are useful to understand the statistical properties of the dynamics); (2) there exists a positive Lyapunov exponent at every orbit; (3) there is a unique physical measure whose support is the whole attractor and which is the equilibrium state with respect to the center-unstable Jacobian; (4) this measure is exact dimensional; (5) the induced measure on a suitable family of cross-sections has exponential decay of correlations for Lipschitz observables with respect to a suitable Poincaré return time map; (6) the hitting time associated to Lorenz-like attractors satisfy a logarithm law; (7) the geometric Lorenz flow satisfies the Almost Sure Invariance Principle (ASIP) and the Central Limit Theorem (CLT); (8) the rate of decay of large deviations for the volume measure on the ergodic basin of
Dynamic complexities in a hyperparasitic system with prolonged diapause for host
Energy Technology Data Exchange (ETDEWEB)
Zhang Limin [School of Mathematics and Information Science, Wenzhou University, Wenzhou, Zhejiang 325035 (China); Zhao Min [School of Life and Environmental Science, Wenzhou University, Wenzhou, Zhejiang 325027 (China)], E-mail: zmcn@tom.com
2009-10-30
In this paper, a hyperparasitic system with prolonged diapause for host is proposed and analyzed. For the biologically reasonable range of parameter values, the global dynamics of the system has been studied numerically. Especially, the effect of prolonged diapause and hyperparasitism on the system is investigated. Many forms of complex dynamics are observed. The complexities include (1) chaotic bands with periodic windows; (2) antimonotonicity; (3) pitchfork and tangent bifurcations; (4) period-doubling cascades; (5) intermittency; (6) supertransients; (7) non-unique dynamic, meaning that several attractors coexist; and (8) attractors crises. Furthermore, the complex dynamic behaviors of the model are confirmed by the largest Lyapunov exponents.
Asymptotic behavior of a system of micropolar equations
Directory of Open Access Journals (Sweden)
Pedro Marin-Rubio
2016-03-01
Full Text Available This work is concerned with three-dimensional micropolar fluids flows in a bounded domain with boundary of class $C^{\\infty}.$ Based on the theory of dissipative systems, we prove the existence of a restricted global attractors for local semiflows on suitable fractional phase spaces $\\mathbf{Z}^{\\alpha}_{p},$ namely for $p\\in (3,+\\infty$ and $\\alpha\\in [1/2,1$. Moreover, we prove that all these attractors are in fact the same set. Previously, it is shown that the Lamé operator is a sectorial operator in each $L_{p}(\\Omega$ with $1
Power-law distributions in noisy dynamical systems
Wilkinson, Michael; Guichardaz, Robin; Pradas, Marc; Pumir, Alain
2015-09-01
We consider a dynamical system which is non-autonomous, has a stable attractor and which is perturbed by an additive noise. We establish that under some quite typical conditions, the intermittent fluctuations from the attractor have a probability distribution with power-law tails. We show that this results from a stochastic cascade of amplification of fluctuations due to transient periods of instability. The exponent of the power-law is interpreted as a negative fractal dimension, and is explicitly determined, using numerics or perturbation expansion, in the case of a model of colloidal particles in one-dimension.
Bellucci, S; Marrani, A; Yeranyan, A
2008-01-01
The general solutions of the radial attractor flow equations for extremal black holes, both for non-BPS with non-vanishing central charge Z and for Z=0, are obtained for the so-called stu model, the minimal rank-3 N=2 symmetric supergravity in d=4 space-time dimensions. Comparisons with previous results, as well as the fake supergravity (first order) formalism and an analysis of the BPS bound all along the non-BPS attractor flows and of the marginal stability of corresponding D-brane configurations, are given.
Bellucci, Stefano; Ferrara, Sergio; Marrani, Alessio; Yeranyan, Armen
2008-12-01
The general solutions of the radial attractor flow equations for extremal black holes, both for non-BPS with non-vanishing central charge Z and for Z = 0, are obtained for the so-called stu model, the minimal rank-3 N = 2 symmetric supergravity in d = 4 space-time dimensions. Comparisons with previous results, as well as the fake supergravity (first order) formalism and an analysis of the BPS bound all along the non-BPS attractor flows and of the marginal stability of corresponding D-brane configurations, are given.
Role of multistability in the transition to chaotic phase synchronization
DEFF Research Database (Denmark)
Postnov, D.E.; Vadivasova, T.E.; Sosnovtseva, Olga
1999-01-01
In this paper we describe the transition to phase synchronization for systems of coupled nonlinear oscillators that individually follow the Feigenbaum route to chaos. A nested structure of phase synchronized regions of different attractor families is observed. With this structure, the transition...... to nonsynchronous behavior is determined by the loss of stability for the most stable synchronous mode. It is shown that the appearance of hyperchaos and the transition from lag synchronization to phase synchronization are related to the merging of chaotic attractors from different families. Numerical examples...
Fractal Image Filters for Specialized Image Recognition Tasks
2010-02-11
parabolas, line segments , triangles, and circles. How do the individual numbers in IFS codes relate to the properties of the attractors that they de...2=3) nf1 (x; y); and f (2n+1) 2 (x; y) = (2=3)nf2(x; y) for all points (x; y) in R2. But fOg is not an attractor for the IFS because (f1 f2)n(x...in R2. Let c denote a point on the line segment AB, let a denote a point on the line segment BC, and let b denote a point on the line segment CA
Dimensions of Fractals Generated by Bi-Lipschitz Maps
Directory of Open Access Journals (Sweden)
Qi-Rong Deng
2014-01-01
Full Text Available On the class of iterated function systems of bi-Lipschitz mappings that are contractions with respect to some metrics, we introduce a logarithmic distortion property, which is weaker than the well-known bounded distortion property. By assuming this property, we prove the equality of the Hausdorff and box dimensions of the attractor. We also obtain a formula for the dimension of the attractor in terms of certain modified topological pressure functions, without imposing any separation condition. As an application, we prove the equality of Hausdorff and box dimensions for certain iterated function systems consisting of affine maps and nonsmooth maps.
Generalizations of SRB Measures to Nonautonomous, Random, and Infinite Dimensional Systems
Young, Lai-Sang
2017-02-01
We review some developments that are direct outgrowths of, or closely related to, the idea of SRB measures as introduced by Sinai, Ruelle and Bowen in the 1970s. These new directions of research include the emergence of strange attractors in periodically forced dynamical systems, random attractors in systems defined by stochastic differential equations, SRB measures for infinite dimensional systems including those defined by large classes of dissipative PDEs, quasi-static distributions for slowly varying time-dependent systems, and surviving distributions in leaky dynamical systems.
Directory of Open Access Journals (Sweden)
Pavlo O. Kasyanov
2012-01-01
Full Text Available We consider autonomous evolution inclusions and hemivariational inequalities with nonsmooth dependence between determinative parameters of a problem. The dynamics of all weak solutions defined on the positive semiaxis of time is studied. We prove the existence of trajectory and global attractors and investigate their structure. New properties of complete trajectories are justified. We study classes of mathematical models for geophysical processes and fields containing the multidimensional “reaction-displacement” law as one of possible application. The pointwise behavior of such problem solutions on attractor is described.
Noise and Dissipation on Coadjoint Orbits
Arnaudon, Alexis; De Castro, Alex L.; Holm, Darryl D.
2018-02-01
We derive and study stochastic dissipative dynamics on coadjoint orbits by incorporating noise and dissipation into mechanical systems arising from the theory of reduction by symmetry, including a semidirect product extension. Random attractors are found for this general class of systems when the Lie algebra is semi-simple, provided the top Lyapunov exponent is positive. We study in details two canonical examples, the free rigid body and the heavy top, whose stochastic integrable reductions are found and numerical simulations of their random attractors are shown.
Thenu, Imanuel M; Puspito, Gondo; Martasuganda, Sulaeman
2013-01-01
Lift net fishermen usually use fluorescent lamp as attractor to lure fish. As price of fuel rise, fishermen are forced to find another option to change their attractor into some much lower cost and more energy-save lamp, or in other words, to change into LED lamp. This research are providing evidence that sunked LED lamps can be utilized as a helper tools, and also determined the best time for catching fish in the lift net. Two lift net used in this research, one of them used sunked LED lamps...
Kashchenko, Serguey
2015-01-01
This monograph examines in detail models of neural systems described by delay-differential equations. Each element of the medium (neuron) is an oscillator that generates, in standalone mode, short impulses also known as spikes. The book discusses models of synaptic interaction between neurons, which lead to complex oscillatory modes in the system. In addition, it presents a solution to the problem of choosing the parameters of interaction in order to obtain attractors with predetermined structure. These attractors are represented as images encoded in the form of autowaves (wave memory). The target audience primarily comprises researchers and experts in the field, but it will also be beneficial for graduate students.
Sinai-Ruelle-Bowen measure for normal form map of grazing bifurcations of impact oscillators
Li, Denghui; Chen, Hebai; Xie, Jianhua; Zhang, Jiye
2017-09-01
Grazing bifurcations are typical non-smooth bifurcations that occur in impact oscillators. They are described by a discrete map with square-root singularities. In this paper we study the structure of a strange attractor which is the closure of the unstable manifold at hyperbolic fixed point of the normal form map for grazing bifurcations of one-degree-of-freedom impact oscillators from the ergodic theoretic point of view. We prove that for some set of values of the parameters this map has an Sinai-Ruelle-Bowen measure which is supported on the strange attractor and is ergodic.
On the strongly damped wave equation and the heat equation with mixed boundary conditions
Directory of Open Access Journals (Sweden)
Aloisio F. Neves
2000-01-01
Full Text Available We study two one-dimensional equations: the strongly damped wave equation and the heat equation, both with mixed boundary conditions. We prove the existence of global strong solutions and the existence of compact global attractors for these equations in two different spaces.
Crisis and unstable dimension variability in the bailout embedding ...
Indian Academy of Sciences (India)
An attractor widening and merging crisis is seen in the phase space in the aerosol case. Crisis-induced intermittency is seen in the time series and the laminar length distribution of times before bursts give rise to a power law with the exponent β = −1/3. The maximum Lyapunov exponent near the crisis fluctuates around zero.
Renewal theory of coupled neuronal pools: stable states and slow trajectories.
Leibold, Christian
2011-09-01
A theory is provided to analyze the dynamics of delay-coupled pools of spiking neurons based on stability analysis of stationary firing. Transitions between stable and unstable regimes can be predicted by bifurcation analysis of the underlying integral dynamics. Close to the bifurcation point the network exhibits slowly changing activities and allows for slow collective phenomena like continuous attractors.
Classifying and quantifying basins of attraction
Energy Technology Data Exchange (ETDEWEB)
Sprott, J. C.; Xiong, Anda [Physics Department, University of Wisconsin-Madison, 1150 University Avenue, Madison, Wisconsin 53706 (United States)
2015-08-15
A scheme is proposed to classify the basins for attractors of dynamical systems in arbitrary dimensions. There are four basic classes depending on their size and extent, and each class can be further quantified to facilitate comparisons. The calculation uses a Monte Carlo method and is applied to numerous common dissipative chaotic maps and flows in various dimensions.
Antisynchronization of a novel hyperchaotic system with parameter ...
Indian Academy of Sciences (India)
College of Information Science and Engineering, Hunan University, Changsha 410082,. People's Republic of China. ∗ ... Introduction. Chaos has attracted wide attention after Lorenz [1] found the first chaotic system dur- ing his studies of the atmospheric convection in 1963. Many new chaotic attractors, such as the Rössler ...
Extracting dynamics from threshold-crossing interspike intervals: possibilities and limitations
DEFF Research Database (Denmark)
Pavlov, A N; Sosnovtseva, Olga; Mosekilde, Erik
2000-01-01
In this paper we estimate dynamical characteristics of chaotic attractors from sequences of threshold-crossing interspike intervals, and study how the choice of the threshold level (which sets the equation of a secant plane) influences the results of the numerical computations. Under quite genera...
Bifurcation Analysis of Gene Propagation Model Governed by Reaction-Diffusion Equations
Directory of Open Access Journals (Sweden)
Guichen Lu
2016-01-01
Full Text Available We present a theoretical analysis of the attractor bifurcation for gene propagation model governed by reaction-diffusion equations. We investigate the dynamical transition problems of the model under the homogeneous boundary conditions. By using the dynamical transition theory, we give a complete characterization of the bifurcated objects in terms of the biological parameters of the problem.
Global chaos synchronization of coupled parametrically excited ...
Indian Academy of Sciences (India)
coupled double-well Duffing oscillators (DDOs) and showed that synchronization was characterized by boundary crisis of the chaotic attractors. In our previous work [23,25], only numerical results were presented. In this paper, we extend our results to parametrically excited systems and in particular obtain sufficient crite-.
Synchronization and basin bifurcations in mutually coupled oscillators
Indian Academy of Sciences (India)
ing the structural changes associated with the basins of attraction of two coexisting resonance attractors in the phase space. 2. The model. Let us consider two identically coupled periodically forced double-well Duffing oscil- lators (DDOs) described by the following second-order nonautonomous differential equations:.
Dynamical hysteresis and spatial synchronization in coupled non ...
Indian Academy of Sciences (India)
... via mutual synchronization indices reveals that one attractor corresponds to spatially synchronized oscillators, while the other corresponds to desynchronized oscillators. Dynamical hysteresis may thus help to understand critical aspects of the dynamical behavior of complex biological systems, e.g. seizures in the epileptic ...
Zak, M.
1998-01-01
Quantum analog computing is based upon similarity between mathematical formalism of quantum mechanics and phenomena to be computed. It exploits a dynamical convergence of several competing phenomena to an attractor which can represent an externum of a function, an image, a solution to a system of ODE, or a stochastic process.
The Butterfly Effect for Physics Laboratories
Claycomb, James R.; Valentine, John H.
2015-01-01
A low-cost chaos dynamics lab is developed for quantitative demonstration of the butterfly effect using a magnetic pendulum. Chaotic motion is explored by recording magnetic time series. Students analyze the data in Excel® to investigate the butterfly effect as well as the reconstruction of the strange attractor using time delay plots. The lab…
Chaos and fractals an elementary introduction
Feldman, David P
2012-01-01
For students with a background in elementary algebra, this text provides a vivid introduction to the key phenomena and ideas of chaos and fractals, including the butterfly effect, strange attractors, fractal dimensions, Julia sets and the Mandelbrot set, power laws, and cellular automata.
Symmetric Spaces in Supergravity
Ferrara, Sergio
2008-01-01
We exploit the relation among irreducible Riemannian globally symmetric spaces (IRGS) and supergravity theories in 3, 4 and 5 space-time dimensions. IRGS appear as scalar manifolds of the theories, as well as moduli spaces of the various classes of solutions to the classical extremal black hole Attractor Equations. Relations with Jordan algebras of degree three and four are also outlined.
SAM Lectures on Extremal Black Holes in d=4 Extended Supergravity
Bellucci, S; Günaydin, M; Marrani, A
2009-01-01
We report on recent results in the study of extremal black hole attractors in N=2, d=4 ungauged Maxwell-Einstein supergravities. For homogeneous symmetric scalar manifolds, the three general classes of attractor solutions with non-vanishing Bekenstein-Hawking entropy are discussed. They correspond to three (inequivalent) classes of orbits of the charge vector, which sits in the relevant symplectic representation R_{V} of the U-duality group. Other than the 1/2-BPS one, there are two other distinct non-BPS classes of charge orbits, one of which has vanishing central charge. The complete classification of the U-duality orbits, as well as of the moduli spaces of non-BPS attractors (spanned by the scalars which are not stabilized at the black hole event horizon), is also reviewed. Finally, we consider the analogous classification for N>2-extended, d=4 ungauged supergravities, in which also the 1/N-BPS attractors yield a related moduli space.
Pramana – Journal of Physics | Indian Academy of Sciences
Indian Academy of Sciences (India)
... provides a clever means to drastically reduce the requirement of storage. It is shown that theoretically this algorithm faces no problem in computing capacity dimension in any dimension of the embedding state space as far as the actual dimension of the attractor is ﬁnite. Unlike the existing algorithms, memory requirement ...
Second Life in the Library: An Empirical Study of New Users' Experiences
Clarke, Christopher Peter
2012-01-01
Purpose: This paper aims to examine the experiences of new users of Second Life in order to identify potential barriers and attractors to the expansion of the userbase and therefore the market for in-world information services. Design/methodology/approach: A multi-faceted methodological approach was taken utilising two questionnaires (pre- and…
Lichtwarck-Aschoff, Anna; van Geert, Paul
2004-01-01
In this article we discussed a dynamic systems view on social behaviour in adolescence. Social behaviour is defined as a self-organizing attractor landscape, based on a network of proximal (i.e., direct) causes. In some cases, social development is disturbed, leading to problematic behaviour in
Page 1 840 V Ajjarapu saddle node transcritical pitchfork ...
Indian Academy of Sciences (India)
features such as strange attractors. The methods and results of bifurcation theory are fundamental to an understanding of nonlinear dynamical systems, and the theory can be potentially applied to any area of nonlinear engineering systems. In power systems this theory received considerable attention especially with respect ...
Study on chaotic behaviors of RCLSJ model Josephson junctions
Energy Technology Data Exchange (ETDEWEB)
Hu, Y-T; Zhou, T-g; Gu, J; Yan, S-l; Fang, L; Zhao, X-J [College of Information Technical Science, Nankai University, Tianjin, 300071 (China)], E-mail: huytnankai@yahoo.com.cn
2008-02-15
Chaotic behaviors of the dc-biased resistively-capacitively-inductively shunted Josephson junctions are studied numerically. The existence of the chaos is proved by the spectrum and strange attractor. We also find out the route to chaos is intermittence. The parameter space in which chaos exits is obtained, and different features of the chaos in different parameter range are also given.
The potential and flux landscape theory of ecology.
Directory of Open Access Journals (Sweden)
Li Xu
Full Text Available The species in ecosystems are mutually interacting and self sustainable stable for a certain period. Stability and dynamics are crucial for understanding the structure and the function of ecosystems. We developed a potential and flux landscape theory of ecosystems to address these issues. We show that the driving force of the ecological dynamics can be decomposed to the gradient of the potential landscape and the curl probability flux measuring the degree of the breaking down of the detailed balance (due to in or out flow of the energy to the ecosystems. We found that the underlying intrinsic potential landscape is a global Lyapunov function monotonically going down in time and the topology of the landscape provides a quantitative measure for the global stability of the ecosystems. We also quantified the intrinsic energy, the entropy, the free energy and constructed the non-equilibrium thermodynamics for the ecosystems. We studied several typical and important ecological systems: the predation, competition, mutualism and a realistic lynx-snowshoe hare model. Single attractor, multiple attractors and limit cycle attractors emerge from these studies. We studied the stability and robustness of the ecosystems against the perturbations in parameters and the environmental fluctuations. We also found that the kinetic paths between the multiple attractors do not follow the gradient paths of the underlying landscape and are irreversible because of the non-zero flux. This theory provides a novel way for exploring the global stability, function and the robustness of ecosystems.
Potentials for sustainable tourism development at Danube in Serbia
Directory of Open Access Journals (Sweden)
Maksin Marija
2012-01-01
Full Text Available The importance of Corridor VII for tourism development in spatial planning and sector planning for tourism has been presented. The key tourism assets, primarily Danube and natural and cultural heritage assets along its coastal area are identified. Based on the FAS methodology (UNWTO the attractiveness of identified key tourism assets is evaluated. The results of this evaluation indicate there is still more factors than attractors, the least developed are the man-made attractors, while the natural attractors are underdeveloped. Based on identified tourism assets and their attractiveness the differentiation of Danube and its coastal area into three highly valuable zones are proposed. Bearing in mind that potential tourism attractiveness of identified factors and attractors has not yet been realized, necessary actions for activating and sustainable development of three proposed tourism zones are suggested. Therefore the criteria for nautical infrastructure prioritization, as well as criteria for urban and rural tourism centers differentiation at Danube coastal area are defined. The paper indicates the priority actions for sustainable tourism development, namely the upgrading of tourist presentation and interpretation in order to achieve the potential attractiveness of tourism assets, supported with their better accessibility, as well as development of tourism products, integration and diversification of tourism offer at Danube and along its coastal area. One of the key problems for achieving sustainable tourism development are insufficient institutional arrangements that need to be changed and improved for Danube primary tourism destination management in Serbia.
A novel four-wing non-equilibrium chaotic system and its circuit ...
Indian Academy of Sciences (India)
In this paper, we construct a novel, 4D smooth autonomous system. Compared to the existing chaotic systems, the most attractive point is that this system does not display any equilibria, but can still exhibit four-wing chaotic attractors. The proposed system is investigated through numerical simulations and analyses including ...
Crises in a driven Josephson junction studied by cell mapping
DEFF Research Database (Denmark)
Sørensen, Mads Peter; Davidson, A.; Pedersen, Niels Falsig
1988-01-01
We use the method of cell-to-cell mapping to locate attractors, basins, and saddle nodes in the phase plane of a driven Josephson junction. The cell-mapping method is discussed in some detail, emphasizing its ability to provide a global view of the phase plane. Our computations confirm the existe...
Homoclinic Bifurcation as a Mechanism of Chaotic Phase Synchronization
DEFF Research Database (Denmark)
Postnov, D.E.; Balanov, A.G.; Janson, N.B.
1999-01-01
This paper demonstrates a mechanism of chaotic phase synchronization in which the transition from asynchronous to synchronous chaos is associated with the collision of the asynchronous chaotic attractor with an unstable periodic orbit. This gives rise to a hysteretic transition with the two chaotic...
Indian Academy of Sciences (India)
and the Causes there of. Ani! P Gore and S A Paranjpe. GENERAL ARTICLES. 19 Crises. Critical Junctures in the life of a Chaotic Attractor. N Ananthakrishnan and Tuhin Sahai. 34 The Mathematics of Error Correcting Quantum Codes. Quantum Probability. K R Parthasarathy. 46 Computer Based Modelling and Simulation.
Applications of non-linear methods in astronomy
Martens, P.C.H.
1984-01-01
In this review I discuss catastrophes, bifurcations and strange attractors in a non-mathematical manner by giving very simple examples that st ill contain the essence of the phenomenon. The salientresults of the applications of these non-linear methods in astrophysics are reviewed and include such
On univoque points for self-similar sets
Baker, Simon; Dajani, Karma; Jiang, Kan
2015-01-01
Let K ⊆ R be the unique attractor of an iterated function system. We consider the case where K is an interval and study those elements of K with a unique coding. We prove under mild conditions that the set of points with a unique coding can be identified with a subshift of finite type. As a
Self-Affine Sets with Positive Lebesgue Measure
Dajani, Karma; Jiang, Kan; Kempton, Tom
2014-01-01
Using techniques introduced by C. G ̈unt ̈urk, we prove that the attractors of a family of overlapping self-affine iterated function systems contain a neighbourhood of zero for all parameters in a certain range. This corresponds to giving conditions under which a single sequence may serve as a
Hervais-Adelman, A.; Legrand, L.B.; Zhan, M.; Tamietto, M.; de Gelder, B.; Pegna, A.J.
2015-01-01
Fast and automatic behavioral responses are required to avoid collision with an approaching stimulus. Accordingly, looming stimuli have been found to be highly salient and efficient attractors of attention due to the implication of potential collision and potential threat. Here, we address the
Fractal basins in an ecological model
Directory of Open Access Journals (Sweden)
I. Djellit
2013-09-01
Full Text Available Complex dynamics is detected in an ecological model of host-parasitoid interaction. It illustrates fractalization of basins with self-similarity and chaotic attractors. This paper describes these dynamic behaviors, bifurcations, and chaos. Fractals basins are displayed by numerical simulations.
Bursztyn, Natalie; Pederson, Joel; Shelton, Brett; Walker, Andrew; Campbell, Todd
2015-01-01
Declining interest and low persistence is well documented among undergraduate students in Science, Technology, Engineering, and Math in the United States. For geoscience, field trips are important attractors to students, however with high enrollment courses and increasing costs they are becoming rare. We propose in this concept paper that the…
On stabilization of small solutions in the nonlinear Dirac equation with a trapping potential
Cuccagna, Scipio; Tarulli, Mirko
2014-01-01
We consider a Dirac operator with short range potential and with eigenvalues. We add a nonlinear term and we show that the small standing waves of the corresponding nonlinear Dirac equation (NLD) are attractors for small solutions of the NLD. This extends to the NLD results already known for the Nonlinear Schr\\"odinger Equation (NLS)
Temporal Structures in Shell Models
Okkels, Fridolin
2000-01-01
The intermittent dynamics of the turbulent GOY shell-model is characterised by a single type of burst-like structure, which moves through the shells like a front. This temporal structure is described by the dynamics of the instantaneous configuration of the shell-amplitudes revealing a approximative chaotic attractor of the dynamics.
Pattern formation in the bistable Gray-Scott model
DEFF Research Database (Denmark)
Mazin, W.; Rasmussen, K.E.; Mosekilde, Erik
1996-01-01
rate are obtained. The distribution in parameter space of a wide variety of different spatio-temporal attractors that can be reached through a strong local perturbation of the linearly stable homogeneous steady state is mapped out. Special emphasis is given to the newly discovered spot multiplication...
Regional Labour Markets and Job Accessibility in City Network Systems in Germany
Reggiani, A.; Bucci, P; Russo, G.; de Haas, A.; Nijkamp, P.
2011-01-01
Spatial labour markets are subjected to the forces of regional economic activity and competing network effects. Commuting is, therefore, an important equilibrating vehicle in a City Network constellation. Cities act as attractors of commuters, as most economic activity occurs in cities, thus
Dynamical networks with topological self-organization
Zak, M.
2001-01-01
Coupled evolution of state and topology of dynamical networks is introduced. Due to the well organized tensor structure, the governing equations are presented in a canonical form, and required attractors as well as their basins can be easily implanted and controlled.
Directory of Open Access Journals (Sweden)
Nobuyuki Kenmochi
1996-01-01
w is constrained to have double obstacles σ*≤w≤σ* (i.e., σ* and σ* are the threshold values of w. The objective of this paper is to discuss the semigroup {S(t} associated with the phase separation model, and construct its global attractor.
An M-estimator for tail dependence in arbitrary dimensions
Einmahl, J.H.J.; Krajina, A.; Segers, J.
2012-01-01
Consider a random sample in the max-domain of attraction of a multivariate extreme value distribution such that the dependence structure of the attractor belongs to a parametric model. A new estimator for the unknown parameter is defined as the value that minimizes the distance between a vector of
Cosmological dynamics in f(R) gravity
Guo, Jun-Qi; Frolov, Andrei V.
2013-12-01
In this paper, we study the cosmological viability conditions, the phase-space dynamics, and the cosmological evolution of f(R) gravity. In contrast to most previous works in the literature, which analyzed the background dynamics of f(R) gravity by means of a dynamical system, we proceed by focusing on the equivalent scalar field description of the theory, which we believe is a more intuitive way of treating the problem. In order to study how the physical solutions evolve in f(R) cosmology, we explore the cosmological dynamics of a range of f(R) models, including models that yield a large hierarchy of scales and are singularity free. We present generic features of the phase-space dynamics in f(R) cosmology. We study the global structure of the phase space in f(R) gravity by compactifying the infinite phase space into a finite space via the Poincaré transformation. On the expansion branch of the phase space, the constraint surface has a repeller and a de Sitter attractor, while on the contraction branch, the constraint surface has an attractor and a de Sitter repeller. Generally, the phase currents originate from the repeller and terminate at the corresponding attractor in each space. The trajectories between the repeller and the attractor in the presence of matter density are different from those in the vacuum case. The phase analysis techniques developed in this paper are very general, and can be applied to other similar dynamical systems.
Implementation of a new memristor-based multiscroll hyperchaotic ...
Indian Academy of Sciences (India)
Keywords. Memristor; hyperchaos; three-scroll chaotic attractor; circuit implementation. ... Phase portraits, Lyapunov exponents, bifurcation diagram, equilibrium points and stability analysis have been used to research the basic dynamics of this chaotic system. The consistency of circuit implementation and numerical ...
Global investigation of the nonlinear dynamics of carbon nanotubes
Xu, Tiantian
2016-11-17
Understanding the complex nonlinear dynamics of carbon nanotubes (CNTs) is essential to enable utilization of these structures in devices and practical applications. We present in this work an investigation of the global nonlinear dynamics of a slacked CNT when actuated by large electrostatic and electrodynamic excitations. The coexistence of several attractors is observed. The CNT is modeled as an Euler–Bernoulli beam. A reduced-order model based on the Galerkin method is developed and utilized to simulate the static and dynamic responses. Critical computational challenges are posed due to the complicated form of the electrostatic force, which describes the interaction between the upper electrode, consisting of the cylindrically shaped CNT, and the lower electrode. Toward this, we approximate the electrostatic force using the Padé expansion. We explore the dynamics near the primary and superharmonic resonances. The nanostructure exhibits several attractors with different characteristics. To achieve deep insight and describe the complexity and richness of the behavior, we analyze the nonlinear response from an attractor-basins point of view. The competition of attractors is highlighted. Compactness and/or fractality of their basins are discussed. Both the effects of varying the excitation frequency and amplitude are examined up to the dynamic pull-in instability.
Affinity Spaces and 21st Century Learning
Gee, James Paul
2017-01-01
This article discusses video games as "attractors" to "affinity spaces." It argues that affinity spaces are key sites today where people teach and learn 21st Century skills. While affinity spaces are proliferating on the Internet as interest-and-passion-driven sites devoted to a common set of endeavors, they are not new, just…
Karachentsev, I. D.; Nasonova, O. G.; Courtois, H. M.
2013-03-01
A nearby friable cloud in Ursa Majoris contains 270 galaxies with radial velocities 500 Z-wave' effect caused by infall towards a massive attractor. This constrains the total amount of dark matter between the UMa groups within the cloud volume.
VizieR Online Data Catalog: Galaxies in the UMa cluster complex (Karachentsev+, 2013)
Karachentsev, I. D.; Nasonova, O. G.; Courtois, H. M.
2015-04-01
A nearby friable cloud in Ursa Majoris contains 270 galaxies with radial velocities 500Z-wave' effect caused by infall towards a massive attractor. This constrains the total amount of dark matter between the UMa groups within the cloud volume. (1 data file).
Page 1 Chaos in plastic flow Appendix The fractal measures of the ...
Indian Academy of Sciences (India)
a small range of r only, due to the fact that we set r = N for numerical stability, where N is the length of the dynamical trajectory. There are alternate numerical techniques introduced for fractal characterization of chaotic strange attractor and we consider below one of them proposed by Paladin and Vulpiani (25). We define the ...
Chaos and Crisis: Propositions for a General Theory of Crisis Communication.
Seeger, Matthew W.
2002-01-01
Presents key concepts of chaos theory (CT) as a general framework for describing organizational crisis and crisis communication. Discusses principles of predictability, sensitive dependence on initial conditions, bifurcation as system breakdown, emergent self-organization, and fractals and strange attractors as principles of organization. Explores…
Visualising Property Crime in Gauteng: Applying GIS to crime ...
African Journals Online (AJOL)
The present study explores the relationship between one of the most frequently reported property crimes (thefts out of motor vehicles) and the environment in which they occur, using Geographic Information Systems (GIS). Utilising the framework of crime pattern theory, crime generators and attractors are visually examined ...
A time-delayed method for controlling chaotic maps
Energy Technology Data Exchange (ETDEWEB)
Chen Maoyin [Department of Automation, Tsinghua University, Beijing 100084 (China)]. E-mail: maoyinchen@163.com; Zhou Donghua [Department of Automation, Tsinghua University, Beijing 100084 (China); Shang Yun [College of Mathematics and Information Science, Shaanxi Normal University, Xi' an 710062 (China)
2005-12-19
Combining the repetitive learning strategy and the optimality principle, this Letter proposes a time-delayed method to control chaotic maps. This method can effectively stabilize unstable periodic orbits within chaotic attractors in the sense of least mean square. Numerical simulations of some chaotic maps verify the effectiveness of this method.
Consistency of the Takens estimator for the correlation dimension
Borovkova, S.; Burton, Robert; Dehling, H.
Motivated by the problem of estimating the fractal dimension of a strange attractor, we prove weak consistency of U-statistics for stationary ergodic and mixing sequences when the kernel function is unbounded, extending by this earlier results of Aaronson, Burton, Dehling, Gilat, Hill and Weiss. We
Indian Academy of Sciences (India)
Home; Journals; Pramana – Journal of Physics. WEIQUAN PAN. Articles written in Pramana – Journal of Physics. Volume 88 Issue 4 April 2017 pp 62 Research Article. Hidden attractors without equilibrium and adaptive reduced-order function projective synchronization from hyperchaotic Rikitake system · YU FENG ...
Primordial perturbations generated by Higgs field and R2 operator
Wang, Yun-Chao; Wang, Tower
2017-12-01
If the very early Universe is dominated by the nonminimally coupled Higgs field and Starobinsky's curvature-squared term together, the potential diagram would mimic the landscape of a valley, serving as a cosmological attractor. The inflationary dynamics along this valley is studied, model parameters are constrained against observational data, and the effect of isocurvature perturbation is estimated.
Wada basin boundaries and basin cells
Nusse, H.E.; Yorke, J.A.
1996-01-01
In dynamical systems examples are common in which two or more attractors coexist, and in such cases the basin boundary is nonempty. We consider a two-dimensional diffeomorphism F (that is, F is an invertible map and both F and its inverse are differentiable with continuous derivatives), which has at
DEFF Research Database (Denmark)
Vester, Steen
2016-01-01
in their own right. In particular, we show that the winning core and the winning region for a player in a parity game are equivalently empty. Moreover, the winning core contains all fatal attractors but is not necessarily a dominion itself. Experimental results are very positive both with respect to quality...
How attractive is a barchan dune?
Energy Technology Data Exchange (ETDEWEB)
Groh, Christopher; Rehberg, Ingo; Kruelle, Christof A [Experimentalphysik V, Universitaet Bayreuth, D-95440 Bayreuth (Germany)], E-mail: Christopher.Groh@uni-bayreuth.de
2009-02-15
The spatio-temporal behaviour of barchan dunes is investigated experimentally with downsized longitudinal barchan dune slices generated in a narrow water flow tube. The development towards a shape attractor is shown on the basis of four different starting configurations in qualitative observation and quantitative analysis.
Jump and pull-in dynamics of an electrically actuated bistable MEMS device
Ruzziconi, Laura
2014-09-01
This study analyzes a theoretical bistable MEMS device, which exhibits a considerable versatility of behavior. After exploring the coexistence of attractors, we focus on each rest position, and investigate the final outcome, when the electrodynamic voltage is suddenly applied. Our aim is to describe the parameter range where each attractor may practically be observed under realistic conditions, when an electric load is suddenly applied. Since disturbances are inevitably encountered in experiments and practice, a dynamical integrity analysis is performed in order to take them into account. We build the integrity charts, which examine the practical vulnerability of each attractor. A small integrity enhances the sensitivity of the system to disturbances, leading in practice either to jump or to dynamic pull-in. Accordingly, the parameter range where the device, subjected to a suddenly applied load, can operate in safe conditions with a certain attractor is smaller, and sometimes considerably smaller, than in the theoretical predictions. While we refer to a particular case-study, the approach is very general.
van Ulzen, Niek R.; Lamoth, Claudine J. C.; Daffertshofer, Andreas; Semin, Guen R.; Beek, Peter J.
2010-01-01
To examine whether the Haken-Kelso-Bunz model for rhythmic interlimb coordination applies to walking side-by-side on a treadmill, we invited six pairs of participants to coordinate their stepping movements at seven prescribed relative phases (between 0 degrees and 180 degrees) to scan the attractor
Pramana – Journal of Physics | Indian Academy of Sciences
Indian Academy of Sciences (India)
A new 4D chaotic system with hidden attractor and its engineering applications: analog circuit design and FPGA implementation. Hamid Reza Abdolmohammadi, Abdul Jalil M. Khalaf, Shirin Panahi, Karthikeyan Rajagopal, Viet-Thanh Pham, Sajad Jafari. P-12800. Applicability of Strange Nonchaotic Wien-Bridge Oscillators ...
We present an experimental circuit realization of a simple jerk ...
Indian Academy of Sciences (India)
IAS Admin
We have also numerically solved equation (4) by using 4th order Runge–Kutta method in QBASIC programming language to observe the cha- otic attractor. In this case we have observed P-1, P-2, P-4, P-8, chaos and P-5 for different values of a as shown in Figure 3. (horizontal axes denote x and vertical axes denote xx ).
Essentially asymptotically stable homoclinic networks
Driesse, R.; Homburg, A.J.
2009-01-01
Melbourne [An example of a nonasymptotically stable attractor, Nonlinearity 4(3) (1991), pp. 835-844] discusses an example of a robust heteroclinic network that is not asymptotically stable but which has the strong attracting property called essential asymptotic stability. We establish that this
Dissipative Quasigeostrophic Motion under Temporally Almost Periodic Forcing
Duan, J; Duan, Jinqiao; Kloeden, Peter E.
1999-01-01
The full nonlinear dissipative quasigeostrophic model is shown to have a unique temporally almost periodic solution when the wind forcing is temporally almost periodic under suitable constraints on the spatial square-integral of the wind forcing and the $\\beta$ parameter, Ekman number, viscosity and the domain size. The proof involves the pullback attractor for the associated nonautonomous dynamical system.
Late-time behaviour of the tilted Bianchi type VIh models
Hervik, S.; van den Hoogen, R. J.; Lim, W. C.; Coley, A. A.
2007-08-01
We study tilted perfect fluid cosmological models with a constant equation of state parameter in spatially homogeneous models of Bianchi type VIh using dynamical systems methods and numerical experimentation, with an emphasis on their future asymptotic evolution. We determine all of the equilibrium points of the type VIh state space (which correspond to exact self-similar solutions of the Einstein equations, some of which are new), and their stability is investigated. We find that there are vacuum plane-wave solutions that act as future attractors. In the parameter space, a 'loophole' is shown to exist in which there are no stable equilibrium points. We then show that a Hopf-bifurcation can occur resulting in a stable closed orbit (which we refer to as the Mussel attractor) corresponding to points both inside the loophole and points just outside the loophole; in the former case the closed curves act as late-time attractors while in the latter case these attracting curves will co-exist with attracting equilibrium points. In the special Bianchi type III case, centre manifold theory is required to determine the future attractors. Comprehensive numerical experiments are carried out to complement and confirm the analytical results presented. We note that the Bianchi type VIh case is of particular interest in that it contains many different subcases which exhibit many of the different possible future asymptotic behaviours of Bianchi cosmological models.
DEFF Research Database (Denmark)
Jensen, Tom Nørgaard; Wisniewski, Rafal
2013-01-01
is extended by showing that an attractor set with a global basin of attraction exists for arbitrary values of positive control gains, given that the upper level of the quantiser is properly designed. Furthermore, the proof is given for general monotone quantisation maps. Since the basin of attraction...
Intermittency at critical transitions and aging dynamics at the onset of ...
Indian Academy of Sciences (India)
We recall that at both the intermittency transitions and the Feigenbaum attractor, in unimodal maps of non-linearity of order > 1, the dynamics rigorously obeys the Tsallis statistics. We account for the -indices and the generalized Lyapunov coefficients that characterize the universality classes of the pitchfork and ...
Pramana – Journal of Physics | Indian Academy of Sciences
Indian Academy of Sciences (India)
Article ID 6 Research Article. Dynamic analyses, FPGA implementation and engineering applications of multi-butterfly chaotic attractors generated from generalised Sprott C system · QIANG LAI XIAO-WEN ZHAO KARTHIKEYAN RAJAGOPAL GUANGHUI XU AKIF AKGUL EMRE GULERYUZ · More Details Abstract Fulltext ...
The Processing of Gender Agreement in L1 and L2 Spanish: Evidence from Reaction Time Data
Alarcon, Irma
2009-01-01
The present study investigates the processing of Spanish gender agreement during an online comprehension task. The linguistic variables examined are the noun class (semantic or non-semantic) and gender (masculine or feminine) of the head and attractor nouns, head noun morphology (overt or non-overt), and noun class and gender congruencies (matched…
Harmonic balance analysis of the generalized chua's circuit
Savacı, Ferit Acar; Günel, Serkan
2006-01-01
In this paper, the harmonic balance analysis of Generalized Chua's circuit exhibiting n-scroll attractors has been accomplished. The dual-input describing functions of the piecewise-linear characteristics of Chua's diode have been obtained and based on the harmonic balance principle, the existence and the locations of the n-scrolls have been verified.
1983-06-01
this experimental framework. An outline of th. biology of the entorhinal cortex to dentate gyrus projection is therefore included at the end of Part IV...equilibria. For aq> aqa they are stable, otherwise they *repel" states. StLablit.L in uaia~ environments Isolated attractors are generally stable in
Affine fractal functions as bases of continuous funtions | Navascues ...
African Journals Online (AJOL)
The objective of the present paper is the study of affine transformations of the plane, which provide self-affine curves as attractors. The properties of these curves depend decisively of the coefficients of the system of affinities involved. The corresponding functions are continuous on a compact interval. If the scale factors are ...
Global Dynamics of Three Anticompetitive Systems of Difference Equations in the Plane
Directory of Open Access Journals (Sweden)
M. DiPippo
2013-01-01
Full Text Available We investigate the global dynamics of several anticompetitive systems of rational difference equations which are special cases of general linear fractional system of the forms ., where all parameters and the initial conditions are arbitrary nonnegative numbers, such that both denominators are positive. We find the basins of attraction of all attractors of these systems.
Dynamic analyses, FPGA implementation and engineering ...
Indian Academy of Sciences (India)
QIANG LAI
2017-12-14
Dec 14, 2017 ... Abstract. This paper considers the generation of multi-butterfly chaotic attractors from a generalised Sprott C system with multiple non-hyperbolic equilibria. The system is constructed by introducing an additional variable whose derivative has a switching function to the Sprott C system. It is numerically found ...
Degenerate Hopf bifurcation in a self-exciting Faraday disc dynamo
Pan, Weiquan; Li, Lijie
2017-06-01
In order to further understand a self-exciting Faraday disc dynamo (Hide et al, in Proc. R. Soc. A 452, 1369 1996), showing chaotic attractors with very complicated topological structures, we present codimension one and two (degenerate) Hopf bifurcations and prove the existence of periodic solutions. In addition, numerical simulations are given for confirming the theoretical results.
Detection of system changes due to damage using a tuned hyperchaotic probe
Torkamani, S.; Butcher, E. A.; Todd, M. D.; Park, G.
2011-02-01
This study explores the use of a hyperchaotic signal as an excitation to probe a system for dynamic changes induced by damage events. In chaotic interrogation a deterministic chaotic input (rather than the more commonly employed stochastic white noise input) is applied to the structure and the dynamic response is mined for features derived from its state space reconstruction. The steady-state chaotic excitation is tuned to excite the structure in a way that optimal sensitivity to dimensionality changes in the response may be observed, resulting in damage-sensitive features extracted from the resulting attractors. The enhanced technique proposed in this paper explores a hyperchaotic excitation, which is fundamentally new in its use as an excitation. Hyperchaotic oscillators have at least two Lyapunov exponents, in contrast to simple chaotic oscillators. By using the Kaplan-Yorke conjecture and performing a parametric investigation, the steady-state hyperchaotic excitation is tuned to excite the structure in such a way that the optimal (as will be defined) dimensionality of the steady-state response is achieved. A feature called the 'average local attractor variance ratio' (ALAVR), which is based on attractor geometry, is used to compare the geometry of a baseline attractor to a test attractor. The enhanced technique is applied to analytically and experimentally analyze the response of an eight-degree-of-freedom system to the hyperchaotic excitation for the purpose of damage assessment. A comparison between the results obtained from current hyperchaotic excitation versus a chaotic excitation highlights the higher damage sensitivity in the system response to the hyperchaotic excitation.
Energy landscapes of resting-state brain networks
Directory of Open Access Journals (Sweden)
Takamitsu eWatanabe
2014-02-01
Full Text Available During rest, the human brain performs essential functions such as memory maintenance, which are associated with resting-state brain networks (RSNs including the default-mode network (DMN and frontoparietal network (FPN. Previous studies based on spiking-neuron network models and their reduced models, as well as those based on imaging data, suggest that resting-state network activity can be captured as attractor dynamics, i.e., dynamics of the brain state toward an attractive state and transitions between different attractors. Here, we analyze the energy landscapes of the RSNs by applying the maximum entropy model, or equivalently the Ising spin model, to human RSN data. We use the previously estimated parameter values to define the energy landscape, and the disconnectivity graph method to estimate the number of local energy minima (equivalent to attractors in attractor dynamics, the basin size, and hierarchical relationships among the different local minima. In both of the DMN and FPN, low-energy local minima tended to have large basins. A majority of the network states belonged to a basin of one of a few local minima. Therefore, a small number of local minima constituted the backbone of each RSN. In the DMN, the energy landscape consisted of two groups of low-energy local minima that are separated by a relatively high energy barrier. Within each group, the activity patterns of the local minima were similar, and different minima were connected by relatively low energy barriers. In the FPN, all dominant energy were separated by relatively low energy barriers such that they formed a single coarse-grained global minimum. Our results indicate that multistable attractor dynamics may underlie the DMN, but not the FPN, and assist memory maintenance with different memory states.
Ferraz-Mello, Sylvio
2015-08-01
This paper deals with the application of the creep tide theory (Ferraz-Mello, Celest Mech Dyn Astron 116:109, 2013a) to the rotation of close-in satellites, Mercury, close-in exoplanets, and their host stars. The solutions show different behaviors with two extreme cases: close-in giant gaseous planets with fast relaxation (low viscosity) and satellites and Earth-like planets with slow relaxation (high viscosity). The rotation of close-in gaseous planets follows the classical Darwinian pattern: it is tidally driven toward a stationary solution that is synchronized with the orbital motion when the orbit is circular, but if the orbit is elliptical, it has a frequency larger than the orbital mean motion. The rotation of rocky bodies, however, may be driven to several attractors whose frequencies are times the mean motion. The number of attractors increases with the viscosity of the body and with the orbital eccentricity. The final stationary state depends on the initial conditions. The classical example is Mercury, whose rotational period is 2/3 of the orbital period (3/2 attractor). The planet behaves as a molten body with a relaxation that allowed it to cross the 2/1 attractor without being trapped but not to escape being trapped in the 3/2 one. In that case, the relaxation is estimated to lie in the interval (equivalent to a quality factor roughly constrained to the interval ). The stars have a relaxation similar to the hot Jupiters, and their rotation is also driven to the only stationary solution existing in these cases. However, solar-type stars may lose angular momentum due to stellar wind, braking the rotation and displacing the attractor toward larger periods. Old, active host stars with big close-in companions generally have rotational periods larger than the orbital periods of the companions. The paper also includes a study of energy dissipation and the evolution of orbital eccentricity.
Energy Technology Data Exchange (ETDEWEB)
Freeman, W.J. [Univ of California, Berkeley, CA (United States)
1996-12-31
There are two main levels of neural function to be modeled with appropriate state variables and operations. Microscopic activity is seen in the fraction of the variance of single neuron pulse trains (>99.9%) that is largely random and uncorrelated with pulse trains of other neurons in the neuropil. Macroscopic activity is revealed in the >0.1% of the total variance of each neuron that is covariant with all other neurons in neuropil comprising a population. It is observed in dendritic potentials recorded as surface EEGs. The {open_quotes}spontaneous{close_quotes} background activity of neuropil at both levels arises from mutual excitation within a population of excitatory neurons. Its governing point attractor is set by the macroscopic state, which acts as an order parameter to regulate the contributing neurons. The point attractor manifests a homogeneous field of white noise, which can be modeled by a continuous time state variable for pulse density. Neuropil comprises both excitatory and inhibitory neurons Their interactions at the macroscopic level give oscillations, manifesting a limit cycle attractor. Multiple areas of neuropil comprising a sensory system interact. Due to their incommensurate characteristic frequencies and the long axonal delays between them, the system maintains a global chaotic attractor having multiple wings, one for each discriminable class of stimuli. Access to each wing is by stimulus- induced state transitions, causing construction of macroscopic chaotic patterns, that are carried to targets of cortical transmission by axon tracts. AM patterns of the carrier are extracted by the targets by spatiotemporal integration, thereby retrieving the covariance comprising the chaotic signal. In digital models, noise serves to stabilize the chaotic attractors. An example will be given of the model operating as an interface between the environment and a pattern classifier, which learns to form its own feature detectors.
An enactive and dynamical systems theory account of dyadic relationships.
Kyselo, Miriam; Tschacher, Wolfgang
2014-01-01
Many social relationships are a locus of struggle and suffering, either at the individual or interactional level. In this paper we explore why this is the case and suggest a modeling approach for dyadic interactions and the well-being of the participants. To this end we bring together an enactive approach to self with dynamical systems theory. Our basic assumption is that the quality of any social interaction or relationship fundamentally depends on the nature and constitution of the individuals engaged in these interactions. From an enactive perspective the self is conceived as an embodied and socially enacted autonomous system striving to maintain an identity. This striving involves a basic two-fold goal: the ability to exist as an individual in one's own right, while also being open to and affected by others. In terms of dynamical systems theory one can thus consider the individual self as a self-other organized system represented by a phase space spanned by the dimensions of distinction and participation, where attractors can be defined. Based on two everyday examples of dyadic relationship we propose a simple model of relationship dynamics, in which struggle or well-being in the dyad is analyzed in terms of movements of dyadic states that are in tension or in harmony with individually developed attractors. Our model predicts that relationships can be sustained when the dyad develops a new joint attractor toward which dyadic states tend to move, and well-being when this attractor is in balance with the individuals' attractors. We outline how this can inspire research on psychotherapy. The psychotherapy process itself provides a setting that supports clients to become aware how they fare with regards to the two-fold norm of distinction and participation and develop, through active engagement between client (or couple) and therapist, strategies to co-negotiate their self-organization.
Inflationary tensor fossils in large-scale structure
Energy Technology Data Exchange (ETDEWEB)
Dimastrogiovanni, Emanuela [School of Physics and Astronomy, University of Minnesota, Minneapolis, MN 55455 (United States); Fasiello, Matteo [Department of Physics, Case Western Reserve University, Cleveland, OH 44106 (United States); Jeong, Donghui [Department of Astronomy and Astrophysics, The Pennsylvania State University, University Park, PA 16802 (United States); Kamionkowski, Marc, E-mail: ema@physics.umn.edu, E-mail: mrf65@case.edu, E-mail: duj13@psu.edu, E-mail: kamion@jhu.edu [Department of Physics and Astronomy, 3400 N. Charles St., Johns Hopkins University, Baltimore, MD 21218 (United States)
2014-12-01
Inflation models make specific predictions for a tensor-scalar-scalar three-point correlation, or bispectrum, between one gravitational-wave (tensor) mode and two density-perturbation (scalar) modes. This tensor-scalar-scalar correlation leads to a local power quadrupole, an apparent departure from statistical isotropy in our Universe, as well as characteristic four-point correlations in the current mass distribution in the Universe. So far, the predictions for these observables have been worked out only for single-clock models in which certain consistency conditions between the tensor-scalar-scalar correlation and tensor and scalar power spectra are satisfied. Here we review the requirements on inflation models for these consistency conditions to be satisfied. We then consider several examples of inflation models, such as non-attractor and solid-inflation models, in which these conditions are put to the test. In solid inflation the simplest consistency conditions are already violated whilst in the non-attractor model we find that, contrary to the standard scenario, the tensor-scalar-scalar correlator probes directly relevant model-dependent information. We work out the predictions for observables in these models. For non-attractor inflation we find an apparent local quadrupolar departure from statistical isotropy in large-scale structure but that this power quadrupole decreases very rapidly at smaller scales. The consistency of the CMB quadrupole with statistical isotropy then constrains the distance scale that corresponds to the transition from the non-attractor to attractor phase of inflation to be larger than the currently observable horizon. Solid inflation predicts clustering fossils signatures in the current galaxy distribution that may be large enough to be detectable with forthcoming, and possibly even current, galaxy surveys.
PyBoolNet: a python package for the generation, analysis and visualization of boolean networks.
Klarner, Hannes; Streck, Adam; Siebert, Heike
2017-03-01
The goal of this project is to provide a simple interface to working with Boolean networks. Emphasis is put on easy access to a large number of common tasks including the generation and manipulation of networks, attractor and basin computation, model checking and trap space computation, execution of established graph algorithms as well as graph drawing and layouts. P y B ool N et is a Python package for working with Boolean networks that supports simple access to model checking via N u SMV, standard graph algorithms via N etwork X and visualization via dot . In addition, state of the art attractor computation exploiting P otassco ASP is implemented. The package is function-based and uses only native Python and N etwork X data types. https://github.com/hklarner/PyBoolNet. hannes.klarner@fu-berlin.de.
Noise-Assisted Concurrent Multipath Traffic Distribution in Ad Hoc Networks
Directory of Open Access Journals (Sweden)
Narun Asvarujanon
2013-01-01
Full Text Available The concept of biologically inspired networking has been introduced to tackle unpredictable and unstable situations in computer networks, especially in wireless ad hoc networks where network conditions are continuously changing, resulting in the need of robustness and adaptability of control methods. Unfortunately, existing methods often rely heavily on the detailed knowledge of each network component and the preconfigured, that is, fine-tuned, parameters. In this paper, we utilize a new concept, called attractor perturbation (AP, which enables controlling the network performance using only end-to-end information. Based on AP, we propose a concurrent multipath traffic distribution method, which aims at lowering the average end-to-end delay by only adjusting the transmission rate on each path. We demonstrate through simulations that, by utilizing the attractor perturbation relationship, the proposed method achieves a lower average end-to-end delay compared to other methods which do not take fluctuations into account.
Global dynamics and asymptotics for monomial scalar field potentials and perfect fluids
Alho, Artur; Uggla, Claes
2015-01-01
We consider a minimally coupled scalar field with a monomial potential and a perfect fluid in flat FLRW cosmology. We apply local and global dynamical systems techniques to a new three-dimensional dynamical systems reformulation of the field equations on a compact state space. This leads to a visual global description of the solution space and asymptotic behavior. At late times we employ averaging techniques to prove statements about how the relationship between the equation of state of the fluid and the monomial exponent of the scalar field affects asymptotic source dominance and asymptotic manifest self-similarity breaking. We also situate the `attractor' solution in the three-dimensional state space and show that it corresponds to the one-dimensional unstable center manifold of a de Sitter fixed point, located on an unphysical boundary associated with the dynamics at early times. By deriving a center manifold expansion we obtain approximate expressions for the attractor solution. We subsequently improve th...
Homoclinic bifurcation in a Hodgkin-Huxley model of thermally sensitive neurons
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Feudel, Ulrike [Department of Physics, University of Potsdam, Potsdam 14415, (Germany); Neiman, Alexander [Center for Neurodynamics, University of Missouri at St. Louis, St. Louis, Missouri 63121 (United States); Pei, Xing [Center for Neurodynamics, University of Missouri at St. Louis, St. Louis, Missouri 63121 (United States); Wojtenek, Winfried [Center for Neurodynamics, University of Missouri at St. Louis, St. Louis, Missouri 63121 (United States); Braun, Hans [Institute of Physiology, University of Marburg, Marburg 35037, (Germany); Huber, Martin [Institute of Physiology, University of Marburg, Marburg 35037, (Germany); Moss, Frank [Center for Neurodynamics, University of Missouri at St. Louis, St. Louis, Missouri 63121 (United States)
2000-03-01
We study global bifurcations of the chaotic attractor in a modified Hodgkin-Huxley model of thermally sensitive neurons. The control parameter for this model is the temperature. The chaotic behavior is realized over a wide range of temperatures and is visualized using interspike intervals. We observe an abrupt increase of the interspike intervals in a certain temperature region. We identify this as a homoclinic bifurcation of a saddle-focus fixed point which is embedded in the chaotic attractors. The transition is accompanied by intermittency, which obeys a universal scaling law for the average length of trajectory segments exhibiting only short interspike intervals with the distance from the onset of intermittency. We also present experimental results of interspike interval measurements taken from the crayfish caudal photoreceptor, which qualitatively demonstrate the same bifurcation structure. (c) 2000 American Institute of Physics.
Computational Approach To Understanding Autism Spectrum Disorders
Directory of Open Access Journals (Sweden)
Włodzisław Duch
2012-01-01
Full Text Available Every year the prevalence of Autism Spectrum of Disorders (ASD is rising. Is there a unifying mechanism of various ASD cases at the genetic, molecular, cellular or systems level? The hypothesis advanced in this paper is focused on neural dysfunctions that lead to problems with attention in autistic people. Simulations of attractor neural networks performing cognitive functions help to assess system long-term neurodynamics. The Fuzzy Symbolic Dynamics (FSD technique is used for the visualization of attractors in the semantic layer of the neural model of reading. Large-scale simulations of brain structures characterized by a high order of complexity requires enormous computational power, especially if biologically motivated neuron models are used to investigate the inﬂuence of cellular structure dysfunctions on the network dynamics. Such simulations have to be implemented on computer clusters in a grid-based architectures
Control and amplification of cortical neurodynamics
Liljenstroem, Hans; Aronsson, P.
1999-03-01
We investigate different mechanisms for the control and amplification of cortical neurodynamics, using a neural network model of a three layered cortical structure. We show that different dynamical states can be obtained by changing a control parameter of the input-output relation, or by changing the noise level. Point attractor, limit cycle, and strange attractor dynamics occur at different values of the control parameter. For certain, optimal noise levels, system performance is maximized, analogous to stochastic resonance phenomena. Noise can also be used to induce different dynamical states. A few noisy network units distributed in a network layer can result in global synchronous oscillations, or waves of activity moving across the network. We further demonstrate that fast synchronization of network activity can be obtained by implementing electromagnetic interactions between network units.
Dynamics of a host-parasitoid model with prolonged diapause for parasitoid
Zhao, Min; Zhang, Limin; Zhu, Jun
2011-01-01
In this paper, a host-parasitoid model with prolonged diapause for parasitoid is proposed and analyzed. The asymptotic stability analysis of the system is performed. For a biologically reasonable range of parameter values, the global dynamics of the system have been studied numerically. In particular, the effect of prolonged diapause and parasitism on the system has been investigated. Many forms of complex dynamics are observed. The complexities include: (1) chaotic bands with periodic windows; (2) pitchfork and tangent bifurcations; (3) period-doubling and period-halving cascades; (4) intermittency; (5) supertransients; (6) non-unique dynamics, meaning that several attractors coexist; and (7) attractor crises. Furthermore, the complex dynamic behaviors of the model are confirmed by the largest Lyapunov exponents.