Bifurcation diagram of a cubic three-parameter autonomous system
Lenka Barakova
2005-07-01
Full Text Available In this paper, we study the cubic three-parameter autonomous planar system $$displaylines{ dot x_1 = k_1 + k_2x_1 - x_1^3 - x_2,cr dot x_2 = k_3 x_1 - x_2, }$$ where $k_2, k_3$ are greater than 0. Our goal is to obtain a bifurcation diagram; i.e., to divide the parameter space into regions within which the system has topologically equivalent phase portraits and to describe how these portraits are transformed at the bifurcation boundaries. Results may be applied to the macroeconomical model IS-LM with Kaldor's assumptions. In this model existence of a stable limit cycles has already been studied (Andronov-Hopf bifurcation. We present the whole bifurcation diagram and among others, we prove existence of more difficult bifurcations and existence of unstable cycles.
Bifurcation diagram features of a dc-dc converter under current-mode control
Ruzbehani, Mohsen; Zhou Luowei; Wang Mingyu
2006-01-01
A common tool for analysis of the systems dynamics when the system has chaotic behaviour is the bifurcation diagram. In this paper, the bifurcation diagram of an ideal model of a dc-dc converter under current-mode control is analysed. Algebraic relations that give the critical points locations and describe the pattern of the bifurcation diagram are derived. It is shown that these simple algebraic and geometrical relations are responsible for the complex pattern of the bifurcation diagrams in such circuits. More explanation about the previously observed properties and introduction of some new ones are exposited. In addition, a new three-dimensional bifurcation diagram that can give better imagination of the parameters role is introduced
Phase diagram of N = 2 superconformal field theories and bifurcation sets in catastrophe theory
Kei Ito.
1989-08-01
Phase diagrams of N=2 superconformal field theories are mapped out. It is shown that they coincide with bifurcation sets in catastrophe theory. The results are applied to the determination of renormalization group flows triggered by a combination of two or more relevant operators. (author). 13 refs, 2 figs
Global Bifurcation of a Novel Computer Virus Propagation Model
Jianguo Ren
2014-01-01
Full Text Available In a recent paper by J. Ren et al. (2012, a novel computer virus propagation model under the effect of the antivirus ability in a real network is established. The analysis there only partially uncovers the dynamics behaviors of virus spread over the network in the case where around bifurcation is local. In the present paper, by mathematical analysis, it is further shown that, under appropriate parameter values, the model may undergo a global B-T bifurcation, and the curves of saddle-node bifurcation, Hopf bifurcation, and homoclinic bifurcation are obtained to illustrate the qualitative behaviors of virus propagation. On this basis, a collection of policies is recommended to prohibit the virus prevalence. To our knowledge, this is the first time the global bifurcation has been explored for the computer virus propagation. Theoretical results and corresponding suggestions may help us suppress or eliminate virus propagation in the network.
Simplest bifurcation diagrams for monotone families of vector fields on a torus
Baesens, C.; MacKay, R. S.
2018-06-01
In part 1, we prove that the bifurcation diagram for a monotone two-parameter family of vector fields on a torus has to be at least as complicated as the conjectured simplest one proposed in Baesens et al (1991 Physica D 49 387–475). To achieve this, we define ‘simplest’ by sequentially minimising the numbers of equilibria, Bogdanov–Takens points, closed curves of centre and of neutral saddle, intersections of curves of centre and neutral saddle, Reeb components, other invariant annuli, arcs of rotational homoclinic bifurcation of horizontal homotopy type, necklace points, contractible periodic orbits, points of neutral horizontal homoclinic bifurcation and half-plane fan points. We obtain two types of simplest case, including that initially proposed. In part 2, we analyse the bifurcation diagram for an explicit monotone family of vector fields on a torus and prove that it has at most two equilibria, precisely four Bogdanov–Takens points, no closed curves of centre nor closed curves of neutral saddle, at most two Reeb components, precisely four arcs of rotational homoclinic connection of ‘horizontal’ homotopy type, eight horizontal saddle-node loop points, two necklace points, four points of neutral horizontal homoclinic connection, and two half-plane fan points, and there is no simultaneous existence of centre and neutral saddle, nor contractible homoclinic connection to a neutral saddle. Furthermore, we prove that all saddle-nodes, Bogdanov–Takens points, non-neutral and neutral horizontal homoclinic bifurcations are non-degenerate and the Hopf condition is satisfied for all centres. We also find it has four points of degenerate Hopf bifurcation. It thus provides an example of a family satisfying all the assumptions of part 1 except the one of at most one contractible periodic orbit.
Bifurcation and phase diagram of turbulence constituted from three different scale-length modes
Itoh, S.-I.; Kitazawa, A.; Yagi, M. [Kyushu Univ., Research Inst. for Applied Mechanics, Kasuga, Fukuoka (Japan); Itoh, K. [National Inst. for Fusion Science, Toki, Gifu (Japan)
2002-04-01
Cases where three kinds of fluctuations having the different typical scale-lengths coexist are analyzed, and the statistical theory of strong turbulence in inhomogeneous plasmas is developed. Statistical nonlinear interactions between fluctuations are kept in the analysis as the renormalized drag, statistical noise and the averaged drive. The nonlinear interplay through them induces a quenching or suppressing effect, even if all the modes are unstable when they are analyzed independently. Variety in mode appearance takes place: one mode quenches the other two modes, or one mode is quenched by the other two modes, etc. The bifurcation of turbulence is analyzed and a phase diagram is drawn. Phase diagrams with cusp type catastrophe and butterfly type catastrophe are obtained. The subcritical bifurcation is possible to occur through the nonlinear interplay, even though each one is supercritical turbulence when analyzed independently. Analysis reveals that the nonlinear stability boundary (marginal point) and the amplitude of each mode may substantially shift from the conventional results of independent analyses. (author)
The integrable case of Adler-van Moerbeke. Discriminant set and bifurcation diagram
Ryabov, Pavel E.; Oshemkov, Andrej A.; Sokolov, Sergei V.
2016-09-01
The Adler-van Moerbeke integrable case of the Euler equations on the Lie algebra so(4) is investigated. For the L- A pair found by Reyman and Semenov-Tian-Shansky for this system, we explicitly present a spectral curve and construct the corresponding discriminant set. The singularities of the Adler-van Moerbeke integrable case and its bifurcation diagram are discussed. We explicitly describe singular points of rank 0, determine their types, and show that the momentum mapping takes them to self-intersection points of the real part of the discriminant set. In particular, the described structure of singularities of the Adler-van Moerbeke integrable case shows that it is topologically different from the other known integrable cases on so(4).
Global bifurcations in a piecewise-smooth Cournot duopoly game
Tramontana, Fabio; Gardini, Laura; Puu, Toenu
2010-01-01
The object of the work is to perform the global analysis of the Cournot duopoly model with isoelastic demand function and unit costs, presented in Puu . The bifurcation of the unique Cournot fixed point is established, which is a resonant case of the Neimark-Sacker bifurcation. New properties associated with the introduction of horizontal branches are evidenced. These properties differ significantly when the constant value is zero or positive and small. The good behavior of the case with positive constant is proved, leading always to positive trajectories. Also when the Cournot fixed point is unstable, stable cycles of any period may exist.
Flow Topology Transition via Global Bifurcation in Thermally Driven Turbulence
Xie, Yi-Chao; Ding, Guang-Yu; Xia, Ke-Qing
2018-05-01
We report an experimental observation of a flow topology transition via global bifurcation in a turbulent Rayleigh-Bénard convection. This transition corresponds to a spontaneous symmetry breaking with the flow becomes more turbulent. Simultaneous measurements of the large-scale flow (LSF) structure and the heat transport show that the LSF bifurcates from a high heat transport efficiency quadrupole state to a less symmetric dipole state with a lower heat transport efficiency. In the transition zone, the system switches spontaneously and stochastically between the two long-lived metastable states.
Hamdipour, Mohammad
2018-04-01
We study an array of coupled Josephson junction of superconductor/insulator/superconductor type (SIS junction) as a model for high temperature superconductors with layered structure. In the current-voltage characteristics of this system there is a breakpoint region in which a net electric charge appear on superconducting layers, S-layers, of junctions which motivate us to study the charge dynamics in this region. In this paper first of all we show a current voltage characteristics (CVC) of Intrinsic Josephson Junctions (IJJs) with N=3 Junctions, then we show the breakpoint region in that CVC, then we try to investigate the chaos in this region. We will see that at the end of the breakpoint region, behavior of the system is chaotic and Lyapunov exponent become positive. We also study the route by which the system become chaotic and will see this route is bifurcation. Next goal of this paper is to show the self similarity in the bifurcation diagram of the system and detailed analysis of bifurcation diagram.
B. Swathi
2009-01-01
Full Text Available Simulation of the Gyorgyi, Rempe and Field eleven variable chaotic model in CSTR [Continuously Stirred Tank Reactor] is performed with respect to the concentrations of malonic acid and [Ce(III]. These simulation studies show steady state, periodic and non-periodic regions. These studies have been presented as two variable bifurcation phase diagrams. We also have observed the bursting phenomenon under different set of constraints. We have given much importance on computer simulation work but not included the experimental methods in this paper.
Global Hopf Bifurcation for a Predator-Prey System with Three Delays
Jiang, Zhichao; Wang, Lin
2017-06-01
In this paper, a delayed predator-prey model is considered. The existence and stability of the positive equilibrium are investigated by choosing the delay τ = τ1 + τ2 as a bifurcation parameter. We see that Hopf bifurcation can occur as τ crosses some critical values. The direction of the Hopf bifurcations and the stability of the bifurcation periodic solutions are also determined by using the center manifold and normal form theory. Furthermore, based on the global Hopf bifurcation theorem for general function differential equations, which was established by J. Wu using fixed point theorem and degree theory methods, the existence of global Hopf bifurcation is investigated. Finally, numerical simulations to support the analytical conclusions are carried out.
Pandey, Vikas; Singh, Suneet, E-mail: suneet.singh@iitb.ac.in
2017-04-15
Highlights: • Non-linear stability analysis of nuclear reactor is carried out. • Global and local stability boundaries are drawn in the parameter space. • Globally stable, bi-stable, and unstable regions have been demarcated. • The identification of the regions is verified by numerical simulations. - Abstract: Nonlinear stability study of the neutron coupled thermal hydraulics instability has been carried out by several researchers for boiling water reactors (BWRs). The focus of these studies has been to identify subcritical and supercritical Hopf bifurcations. Supercritical Hopf bifurcation are soft or safe due to the fact that stable limit cycles arise in linearly unstable region; linear and global stability boundaries are same for this bifurcation. It is well known that the subcritical bifurcations can be considered as hard or dangerous due to the fact that unstable limit cycles (nonlinear phenomena) exist in the (linearly) stable region. The linear stability leads to a stable equilibrium in such regions, only for infinitesimally small perturbations. However, finite perturbations lead to instability due to the presence of unstable limit cycles. Therefore, it is evident that the linear stability analysis is not sufficient to understand the exact stability characteristics of BWRs. However, the effect of these bifurcations on the stability boundaries has been rarely discussed. In the present work, the identification of global stability boundary is demonstrated using simplified models. Here, five different models with different thermal hydraulics feedback have been investigated. In comparison to the earlier works, current models also include the impact of adding the rate of change in temperature on void reactivity as well as effect of void reactivity on rate of change of temperature. Using the bifurcation analysis of these models the globally stable region in the parameter space has been identified. The globally stable region has only stable solutions and
Pandey, Vikas; Singh, Suneet
2017-01-01
Highlights: • Non-linear stability analysis of nuclear reactor is carried out. • Global and local stability boundaries are drawn in the parameter space. • Globally stable, bi-stable, and unstable regions have been demarcated. • The identification of the regions is verified by numerical simulations. - Abstract: Nonlinear stability study of the neutron coupled thermal hydraulics instability has been carried out by several researchers for boiling water reactors (BWRs). The focus of these studies has been to identify subcritical and supercritical Hopf bifurcations. Supercritical Hopf bifurcation are soft or safe due to the fact that stable limit cycles arise in linearly unstable region; linear and global stability boundaries are same for this bifurcation. It is well known that the subcritical bifurcations can be considered as hard or dangerous due to the fact that unstable limit cycles (nonlinear phenomena) exist in the (linearly) stable region. The linear stability leads to a stable equilibrium in such regions, only for infinitesimally small perturbations. However, finite perturbations lead to instability due to the presence of unstable limit cycles. Therefore, it is evident that the linear stability analysis is not sufficient to understand the exact stability characteristics of BWRs. However, the effect of these bifurcations on the stability boundaries has been rarely discussed. In the present work, the identification of global stability boundary is demonstrated using simplified models. Here, five different models with different thermal hydraulics feedback have been investigated. In comparison to the earlier works, current models also include the impact of adding the rate of change in temperature on void reactivity as well as effect of void reactivity on rate of change of temperature. Using the bifurcation analysis of these models the globally stable region in the parameter space has been identified. The globally stable region has only stable solutions and
Global Hopf bifurcation analysis on a BAM neural network with delays
Sun, Chengjun; Han, Maoan; Pang, Xiaoming
2007-01-01
A delayed differential equation that models a bidirectional associative memory (BAM) neural network with four neurons is considered. By using a global Hopf bifurcation theorem for FDE and a Bendixon's criterion for high-dimensional ODE, a group of sufficient conditions for the system to have multiple periodic solutions are obtained when the sum of delays is sufficiently large.
Global Hopf bifurcation analysis on a BAM neural network with delays
Sun Chengjun; Han Maoan; Pang Xiaoming
2007-01-01
A delayed differential equation that models a bidirectional associative memory (BAM) neural network with four neurons is considered. By using a global Hopf bifurcation theorem for FDE and a Bendixon's criterion for high-dimensional ODE, a group of sufficient conditions for the system to have multiple periodic solutions are obtained when the sum of delays is sufficiently large
Huitao Zhao
2013-01-01
Full Text Available A ratio-dependent predator-prey model with two time delays is studied. By means of an iteration technique, sufficient conditions are obtained for the global attractiveness of the positive equilibrium. By comparison arguments, the global stability of the semitrivial equilibrium is addressed. By using the theory of functional equation and Hopf bifurcation, the conditions on which positive equilibrium exists and the quality of Hopf bifurcation are given. Using a global Hopf bifurcation result of Wu (1998 for functional differential equations, the global existence of the periodic solutions is obtained. Finally, an example for numerical simulations is also included.
Local and global Hopf bifurcation analysis in a neutral-type neuron system with two delays
Lv, Qiuyu; Liao, Xiaofeng
2018-03-01
In recent years, neutral-type differential-difference equations have been applied extensively in the field of engineering, and their dynamical behaviors are more complex than that of the delay differential-difference equations. In this paper, the equations used to describe a neutral-type neural network system of differential difference equation with two delays are studied (i.e. neutral-type differential equations). Firstly, by selecting τ1, τ2 respectively as a parameter, we provide an analysis about the local stability of the zero equilibrium point of the equations, and sufficient conditions of asymptotic stability for the system are derived. Secondly, by using the theory of normal form and applying the theorem of center manifold introduced by Hassard et al., the Hopf bifurcation is found and some formulas for deciding the stability of periodic solutions and the direction of Hopf bifurcation are given. Moreover, by applying the theorem of global Hopf bifurcation, the existence of global periodic solution of the system is studied. Finally, an example is given, and some computer numerical simulations are taken to demonstrate and certify the correctness of the presented results.
Global Bifurcation from Intervals for the Monge-Ampère Equations and Its Applications
Wenguo Shen
2018-01-01
Full Text Available We shall establish the global bifurcation results from the trivial solutions axis or from infinity for the Monge-Ampère equations: det(D2u=λm(x-uN+m(xf1(x,-u,-u′,λ+f2(x,-u,-u′,λ, in B, u(x=0, on ∂B, where D2u=(∂2u/∂xi∂xj is the Hessian matrix of u, where B is the unit open ball of RN, m∈C(B¯,[0,+∞ is a radially symmetric weighted function and m(r:=m(x≢0 on any subinterval of [0,1], λ is a positive parameter, and the nonlinear term f1,f2∈C(B¯×R+3,R+, but f1 is not necessarily differentiable at the origin and infinity with respect to u, where R+=[0,+∞. Some applications are given to the Monge-Ampère equations and we use global bifurcation techniques to prove our main results.
A global qualitative view of bifurcations and dynamics in the Roessler system
Genesio, R.; Innocenti, G.; Gualdani, F.
2008-01-01
The aim of the Letter is a global study of the well-known Roessler system to point out the main complex dynamics that it can exhibit. The structural analysis is based on the periodic solutions of the system investigated by a harmonic balance technique. Simplified expressions of such limit cycles are first derived and characterized, then their local bifurcations are denoted, also giving indications to predict possible homoclinic orbits with the same unifying approach. These analytical results give a general picture of the system behaviours in the parameter space and numerical analysis and simulations confirm the qualitative accuracy of the whole. Such predictions have also an important role in applying efficiently the above numerical procedures
Dai, Guowei; Romero, Alfonso; Torres, Pedro J.
2018-06-01
We study the existence of spacelike graphs for the prescribed mean curvature equation in the Friedmann-Lemaître-Robertson-Walker (FLRW) spacetime. By using a conformal change of variable, this problem is translated into an equivalent problem in the Lorentz-Minkowski spacetime. Then, by using Rabinowitz's global bifurcation method, we obtain the existence and multiplicity of positive solutions for this equation with 0-Dirichlet boundary condition on a ball. Moreover, the global structure of the positive solution set is studied.
Local and global bifurcations at infinity in models of glycolytic oscillations
Sturis, Jeppe; Brøns, Morten
1997-01-01
We investigate two models of glycolytic oscillations. Each model consists of two coupled nonlinear ordinary differential equations. Both models are found to have a saddle point at infinity and to exhibit a saddle-node bifurcation at infinity, giving rise to a second saddle and a stable node...... at infinity. Depending on model parameters, a stable limit cycle may blow up to infinite period and amplitude and disappear in the bifurcation, and after the bifurcation, the stable node at infinity then attracts all trajectories. Alternatively, the stable node at infinity may coexist with either a stable...... sink (not at infinity) or a stable limit cycle. This limit cycle may then disappear in a heteroclinic bifurcation at infinity in which the unstable manifold from one saddle at infinity joins the stable manifold of the other saddle at infinity. These results explain prior reports for one of the models...
Liu, Xiaojun [State Key Laboratory for Strength and Vibration of Mechanical Structures, Xi' an Jiaotong University, Xi' an 710049 (China); School of Mathematics and Statistics, Tianshui Normal University, Tianshui 741001 (China); Hong, Ling, E-mail: hongling@mail.xjtu.edu.cn; Jiang, Jun [State Key Laboratory for Strength and Vibration of Mechanical Structures, Xi' an Jiaotong University, Xi' an 710049 (China)
2016-08-15
Global bifurcations include sudden changes in chaotic sets due to crises. There are three types of crises defined by Grebogi et al. [Physica D 7, 181 (1983)]: boundary crisis, interior crisis, and metamorphosis. In this paper, by means of the extended generalized cell mapping (EGCM), boundary and interior crises of a fractional-order Duffing system are studied as one of the system parameters or the fractional derivative order is varied. It is found that a crisis can be generally defined as a collision between a chaotic basic set and a basic set, either periodic or chaotic, to cause a sudden discontinuous change in chaotic sets. Here chaotic sets involve three different kinds: a chaotic attractor, a chaotic saddle on a fractal basin boundary, and a chaotic saddle in the interior of a basin and disjoint from the attractor. A boundary crisis results from the collision of a periodic (or chaotic) attractor with a chaotic (or regular) saddle in the fractal (or smooth) boundary. In such a case, the attractor, together with its basin of attraction, is suddenly destroyed as the control parameter passes through a critical value, leaving behind a chaotic saddle in the place of the original attractor and saddle after the crisis. An interior crisis happens when an unstable chaotic set in the basin of attraction collides with a periodic attractor, which causes the appearance of a new chaotic attractor, while the original attractor and the unstable chaotic set are converted to the part of the chaotic attractor after the crisis. These results further demonstrate that the EGCM is a powerful tool to reveal the mechanism of crises in fractional-order systems.
Global Water Cycle Diagrams Minimize Human Influence and Over-represent Water Security
Abbott, B. W.; Bishop, K.; Zarnetske, J. P.; Minaudo, C.; Chapin, F. S., III; Plont, S.; Marçais, J.; Ellison, D.; Roy Chowdhury, S.; Kolbe, T.; Ursache, O.; Hampton, T. B.; GU, S.; Chapin, M.; Krause, S.; Henderson, K. D.; Hannah, D. M.; Pinay, G.
2017-12-01
The diagram of the global water cycle is the central icon of hydrology, and for many people, the point of entry to thinking about key scientific concepts such as conservation of mass, teleconnections, and human dependence on ecological systems. Because humans now dominate critical components of the hydrosphere, improving our understanding of the global water cycle has graduated from an academic exercise to an urgent priority. To assess how the water cycle is conceptualized by researchers and the general public, we analyzed 455 water cycle diagrams from textbooks, scientific articles, and online image searches performed in different languages. Only 15% of diagrams integrated human activity into the water cycle and 77% showed no sign of humans whatsoever, although representation of humans varied substantially by region (lowest in China, N. America, and Australia; highest in Western Europe). The abundance and accessibility of freshwater resources were overrepresented, with 98% of diagrams omitting water pollution and climate change, and over 90% of diagrams making no distinction for saline groundwater and lakes. Oceanic aspects of the water cycle (i.e. ocean size, circulation, and precipitation) and related teleconnections were nearly always underrepresented. These patterns held across disciplinary boundaries and through time. We explore the historical and contemporary reasons for some of these biases and present a revised version of the global water cycle based on research from natural and social sciences. We conclude that current depictions of the global water cycle convey a false sense of water security and that reintegrating humans into water cycle diagrams is an important first step towards understanding and sustaining the hydrosocial cycle.
Suarez-Antola, Roberto, E-mail: roberto.suarez@miem.gub.u, E-mail: rsuarez@ucu.edu.u [Universidad Catolica del Uruguay, Montevideo (Uruguay). Fac. de Ingenieria y Tecnologias. Dept. de Matematica; Ministerio de Industria, Energia y Mineria, Montevideo (Uruguay). Direccion General de Secretaria
2011-07-01
One of the goals of nuclear power systems design and operation is to restrict the possible states of certain critical subsystems to remain inside a certain bounded set of admissible states and state variations. In the framework of an analytic or numerical modeling process of a BWR power plant, this could imply first to find a suitable approximation to the solution manifold of the differential equations describing the stability behavior, and then a classification of the different solution types concerning their relation with the operational safety of the power plant. Inertial manifold theory gives a foundation for the construction and use of reduced order models (ROM's) of reactor dynamics to discover and characterize meaningful bifurcations that may pass unnoticed during digital simulations done with full scale computer codes of the nuclear power plant. The March-Leuba's BWR ROM is generalized and used to exemplify the analytical approach developed here. A nonlinear integral-differential equation in the logarithmic power is derived. Introducing a KBM Ansatz, a coupled set of two nonlinear ordinary differential equations is obtained. Analytical formulae are derived for the frequency of oscillation and the parameters that determine the stability of the steady states, including sub- and supercritical PAH bifurcations. A Bautin's bifurcation scenario seems possible on the power-flow plane: near the boundary of stability, a region where stable steady states are surrounded by unstable limit cycles surrounded at their turn by stable limit cycles. The analytical results are compared with recent digital simulations and applications of semi-analytical bifurcation theory done with reduced order models of BWR. (author)
Suarez-Antola, Roberto; Ministerio de Industria, Energia y Mineria, Montevideo
2011-01-01
One of the goals of nuclear power systems design and operation is to restrict the possible states of certain critical subsystems to remain inside a certain bounded set of admissible states and state variations. In the framework of an analytic or numerical modeling process of a BWR power plant, this could imply first to find a suitable approximation to the solution manifold of the differential equations describing the stability behavior, and then a classification of the different solution types concerning their relation with the operational safety of the power plant. Inertial manifold theory gives a foundation for the construction and use of reduced order models (ROM's) of reactor dynamics to discover and characterize meaningful bifurcations that may pass unnoticed during digital simulations done with full scale computer codes of the nuclear power plant. The March-Leuba's BWR ROM is generalized and used to exemplify the analytical approach developed here. A nonlinear integral-differential equation in the logarithmic power is derived. Introducing a KBM Ansatz, a coupled set of two nonlinear ordinary differential equations is obtained. Analytical formulae are derived for the frequency of oscillation and the parameters that determine the stability of the steady states, including sub- and supercritical PAH bifurcations. A Bautin's bifurcation scenario seems possible on the power-flow plane: near the boundary of stability, a region where stable steady states are surrounded by unstable limit cycles surrounded at their turn by stable limit cycles. The analytical results are compared with recent digital simulations and applications of semi-analytical bifurcation theory done with reduced order models of BWR. (author)
Global structure of curves from generalized unitarity cut of three-loop diagrams
Hauenstein, Jonathan D.; Huang, Rijun; Mehta, Dhagash; Zhang, Yang
2015-01-01
This paper studies the global structure of algebraic curves defined by generalized unitarity cut of four-dimensional three-loop diagrams with eleven propagators. The global structure is a topological invariant that is characterized by the geometric genus of the algebraic curve. We use the Riemann-Hurwitz formula to compute the geometric genus of algebraic curves with the help of techniques involving convex hull polytopes and numerical algebraic geometry. Some interesting properties of genus for arbitrary loop orders are also explored where computing the genus serves as an initial step for integral or integrand reduction of three-loop amplitudes via an algebraic geometric approach.
Suarez Antola, R.
2011-01-01
One of the goals of nuclear power systems design and operation is to restrict the possible states of certain critical subsystems, during steady operation and during transients, to remain inside a certain bounded set of admissible states and state variations. Also, during transients, certain restrictions must be imposed on the time scale of evolution of the critical subsystem's state. A classification of the different solution types concerning their relation with the operational safety of the power plant is done by distributing the different solution types in relation with the exclusion region of the power-flow map. In the framework of an analytic or numerical modeling process of a boiling water reactor (BWR) power plant, this could imply first to find an suitable approximation to the solution manifold of the differential equations describing the stability behavior of this nonlinear system, and then a classification of the different solution types concerning their relation with the operational safety of the power plant, by distributing the different solution types in relation with the exclusion region of the power-flow map. Inertial manifold theory gives a foundation for the construction and use of reduced order models (ROM's) of reactor dynamics to discover and characterize meaningful bifurcations that may pass unnoticed during digital simulations done with full scale computer codes of the nuclear power plant. The March-Leuba's BWR ROM is used to exemplify the analytical approach developed here. The equation for excess void reactivity of this ROM is generalized. A nonlinear integral-differential equation in the logarithmic power is derived, including the generalized thermal-hydraulics feedback on the reactivity. Introducing a Krilov- Bogoliubov-Mitropolsky (KBM) ansatz with both amplitude and phase being slowly varying functions of time relative to the center period of oscillation, a coupled set of nonlinear ordinary differential equations for amplitude and phase
A Genealogy of Convex Solids Via Local and Global Bifurcations of Gradient Vector Fields
Domokos, Gábor; Holmes, Philip; Lángi, Zsolt
2016-12-01
Three-dimensional convex bodies can be classified in terms of the number and stability types of critical points on which they can balance at rest on a horizontal plane. For typical bodies, these are non-degenerate maxima, minima, and saddle points, the numbers of which provide a primary classification. Secondary and tertiary classifications use graphs to describe orbits connecting these critical points in the gradient vector field associated with each body. In previous work, it was shown that these classifications are complete in that no class is empty. Here, we construct 1- and 2-parameter families of convex bodies connecting members of adjacent primary and secondary classes and show that transitions between them can be realized by codimension 1 saddle-node and saddle-saddle (heteroclinic) bifurcations in the gradient vector fields. Our results indicate that all combinatorially possible transitions can be realized in physical shape evolution processes, e.g., by abrasion of sedimentary particles.
A global genetic interaction network maps a wiring diagram of cellular function.
Costanzo, Michael; VanderSluis, Benjamin; Koch, Elizabeth N; Baryshnikova, Anastasia; Pons, Carles; Tan, Guihong; Wang, Wen; Usaj, Matej; Hanchard, Julia; Lee, Susan D; Pelechano, Vicent; Styles, Erin B; Billmann, Maximilian; van Leeuwen, Jolanda; van Dyk, Nydia; Lin, Zhen-Yuan; Kuzmin, Elena; Nelson, Justin; Piotrowski, Jeff S; Srikumar, Tharan; Bahr, Sondra; Chen, Yiqun; Deshpande, Raamesh; Kurat, Christoph F; Li, Sheena C; Li, Zhijian; Usaj, Mojca Mattiazzi; Okada, Hiroki; Pascoe, Natasha; San Luis, Bryan-Joseph; Sharifpoor, Sara; Shuteriqi, Emira; Simpkins, Scott W; Snider, Jamie; Suresh, Harsha Garadi; Tan, Yizhao; Zhu, Hongwei; Malod-Dognin, Noel; Janjic, Vuk; Przulj, Natasa; Troyanskaya, Olga G; Stagljar, Igor; Xia, Tian; Ohya, Yoshikazu; Gingras, Anne-Claude; Raught, Brian; Boutros, Michael; Steinmetz, Lars M; Moore, Claire L; Rosebrock, Adam P; Caudy, Amy A; Myers, Chad L; Andrews, Brenda; Boone, Charles
2016-09-23
We generated a global genetic interaction network for Saccharomyces cerevisiae, constructing more than 23 million double mutants, identifying about 550,000 negative and about 350,000 positive genetic interactions. This comprehensive network maps genetic interactions for essential gene pairs, highlighting essential genes as densely connected hubs. Genetic interaction profiles enabled assembly of a hierarchical model of cell function, including modules corresponding to protein complexes and pathways, biological processes, and cellular compartments. Negative interactions connected functionally related genes, mapped core bioprocesses, and identified pleiotropic genes, whereas positive interactions often mapped general regulatory connections among gene pairs, rather than shared functionality. The global network illustrates how coherent sets of genetic interactions connect protein complex and pathway modules to map a functional wiring diagram of the cell. Copyright © 2016, American Association for the Advancement of Science.
A global interaction network maps a wiring diagram of cellular function
Costanzo, Michael; VanderSluis, Benjamin; Koch, Elizabeth N.; Baryshnikova, Anastasia; Pons, Carles; Tan, Guihong; Wang, Wen; Usaj, Matej; Hanchard, Julia; Lee, Susan D.; Pelechano, Vicent; Styles, Erin B.; Billmann, Maximilian; van Leeuwen, Jolanda; van Dyk, Nydia; Lin, Zhen-Yuan; Kuzmin, Elena; Nelson, Justin; Piotrowski, Jeff S.; Srikumar, Tharan; Bahr, Sondra; Chen, Yiqun; Deshpande, Raamesh; Kurat, Christoph F.; Li, Sheena C.; Li, Zhijian; Usaj, Mojca Mattiazzi; Okada, Hiroki; Pascoe, Natasha; Luis, Bryan-Joseph San; Sharifpoor, Sara; Shuteriqi, Emira; Simpkins, Scott W.; Snider, Jamie; Suresh, Harsha Garadi; Tan, Yizhao; Zhu, Hongwei; Malod-Dognin, Noel; Janjic, Vuk; Przulj, Natasa; Troyanskaya, Olga G.; Stagljar, Igor; Xia, Tian; Ohya, Yoshikazu; Gingras, Anne-Claude; Raught, Brian; Boutros, Michael; Steinmetz, Lars M.; Moore, Claire L.; Rosebrock, Adam P.; Caudy, Amy A.; Myers, Chad L.; Andrews, Brenda; Boone, Charles
2017-01-01
We generated a global genetic interaction network for Saccharomyces cerevisiae, constructing over 23 million double mutants, identifying ~550,000 negative and ~350,000 positive genetic interactions. This comprehensive network maps genetic interactions for essential gene pairs, highlighting essential genes as densely connected hubs. Genetic interaction profiles enabled assembly of a hierarchical model of cell function, including modules corresponding to protein complexes and pathways, biological processes, and cellular compartments. Negative interactions connected functionally related genes, mapped core bioprocesses, and identified pleiotropic genes, whereas positive interactions often mapped general regulatory connections among gene pairs, rather than shared functionality. The global network illustrates how coherent sets of genetic interactions connect protein complex and pathway modules to map a functional wiring diagram of the cell. PMID:27708008
Global soil-climate-biome diagram: linking soil properties to climate and biota
Zhao, X.; Yang, Y.; Fang, J.
2017-12-01
As a critical component of the Earth system, soils interact strongly with both climate and biota and provide fundamental ecosystem services that maintain food, climate, and human security. Despite significant progress in digital soil mapping techniques and the rapidly growing quantity of observed soil information, quantitative linkages between soil properties, climate and biota at the global scale remain unclear. By compiling a large global soil database, we mapped seven major soil properties (bulk density [BD]; sand, silt and clay fractions; soil pH; soil organic carbon [SOC] density [SOCD]; and soil total nitrogen [STN] density [STND]) based on machine learning algorithms (regional random forest [RF] model) and quantitatively assessed the linkage between soil properties, climate and biota at the global scale. Our results demonstrated a global soil-climate-biome diagram, which improves our understanding of the strong correspondence between soils, climate and biomes. Soil pH decreased with greater mean annual precipitation (MAP) and lower mean annual temperature (MAT), and the critical MAP for the transition from alkaline to acidic soil pH decreased with decreasing MAT. Specifically, the critical MAP ranged from 400-500 mm when the MAT exceeded 10 °C but could decrease to 50-100 mm when the MAT was approximately 0 °C. SOCD and STND were tightly linked; both increased in accordance with lower MAT and higher MAP across terrestrial biomes. Global stocks of SOC and STN were estimated to be 788 ± 39.4 Pg (1015 g, or billion tons) and 63 ± 3.3 Pg in the upper 30-cm soil layer, respectively, but these values increased to 1654 ± 94.5 Pg and 133 ± 7.8 Pg in the upper 100-cm soil layer, respectively. These results reveal quantitative linkages between soil properties, climate and biota at the global scale, suggesting co-evolution of the soil, climate and biota under conditions of global environmental change.
Codimension-2 bifurcations of the Kaldor model of business cycle
Wu, Xiaoqin P.
2011-01-01
Research highlights: → The conditions are given such that the characteristic equation may have purely imaginary roots and double zero roots. → Purely imaginary roots lead us to study Hopf and Bautin bifurcations and to calculate the first and second Lyapunov coefficients. → Double zero roots lead us to study Bogdanov-Takens (BT) bifurcation. → Bifurcation diagrams for Bautin and BT bifurcations are obtained by using the normal form theory. - Abstract: In this paper, complete analysis is presented to study codimension-2 bifurcations for the nonlinear Kaldor model of business cycle. Sufficient conditions are given for the model to demonstrate Bautin and Bogdanov-Takens (BT) bifurcations. By computing the first and second Lyapunov coefficients and performing nonlinear transformation, the normal forms are derived to obtain the bifurcation diagrams such as Hopf, homoclinic and double limit cycle bifurcations. Some examples are given to confirm the theoretical results.
Suarez Antola, R.
2009-01-01
In the framework of an analytic or numerical model of a BWR power plant, this could imply first to find an suitable approximation to the solution manifold of the differential equations describing the stability behaviour of this nonlinear system, and then a classification of the different solution types concerning their relation with the operational safety of the power plant, by distributing the different solution types in relation with the exclusion region of the power-flow map. Then the goal is to obtain the best attainable qualitative and quantitative global picture of plant dynamics. To do this, the construction and the analysis of the so called reduced order models (Rom) seems a necessary step. A reduced order model results after the full system of coupled nonlinear partial differential equations of the plant is reduced to a system of coupled nonlinear ordinary differential equations
1991-01-01
Dynamical Bifurcation Theory is concerned with the phenomena that occur in one parameter families of dynamical systems (usually ordinary differential equations), when the parameter is a slowly varying function of time. During the last decade these phenomena were observed and studied by many mathematicians, both pure and applied, from eastern and western countries, using classical and nonstandard analysis. It is the purpose of this book to give an account of these developments. The first paper, by C. Lobry, is an introduction: the reader will find here an explanation of the problems and some easy examples; this paper also explains the role of each of the other paper within the volume and their relationship to one another. CONTENTS: C. Lobry: Dynamic Bifurcations.- T. Erneux, E.L. Reiss, L.J. Holden, M. Georgiou: Slow Passage through Bifurcation and Limit Points. Asymptotic Theory and Applications.- M. Canalis-Durand: Formal Expansion of van der Pol Equation Canard Solutions are Gevrey.- V. Gautheron, E. Isambe...
Sushko, Iryna; Agliari, Anna; Gardini, Laura
2006-01-01
We study the structure of the 2D bifurcation diagram for a two-parameter family of piecewise smooth unimodal maps f with one break point. Analysing the parameters of the normal form for the border-collision bifurcation of an attracting n-cycle of the map f, we describe the possible kinds of dynamics associated with such a bifurcation. Emergence and role of border-collision bifurcation curves in the 2D bifurcation plane are studied. Particular attention is paid also to the curves of homoclinic bifurcations giving rise to the band merging of pieces of cyclic chaotic intervals
Emergence of the bifurcation structure of a Langmuir–Blodgett transfer model
Köpf, Michael H
2014-10-07
© 2014 IOP Publishing Ltd & London Mathematical Society. We explore the bifurcation structure of a modified Cahn-Hilliard equation that describes a system that may undergo a first-order phase transition and is kept permanently out of equilibrium by a lateral driving. This forms a simple model, e.g., for the deposition of stripe patterns of different phases of surfactant molecules through Langmuir-Blodgett transfer. Employing continuation techniques the bifurcation structure is numerically investigated using the non-dimensional transfer velocity as the main control parameter. It is found that the snaking structure of steady front states is intertwined with a large number of branches of time-periodic solutions that emerge from Hopf or period-doubling bifurcations and end in global bifurcations (sniper and homoclinic). Overall the bifurcation diagram has a harp-like appearance. This is complemented by a two-parameter study in non-dimensional transfer velocity and domain size (as a measure of the distance to the phase transition threshold) that elucidates through which local and global codimension 2 bifurcations the entire harp-like structure emerges.
Bifurcations of Fibonacci generating functions
Ozer, Mehmet [Istanbul Kultur University, E5 Karayolu Uzeri Sirinevler, 34191 Istanbul (Turkey) and Semiconductor Physics Institute, LT-01108 and Vilnius Gediminas Technical University, Sauletekio 11, LT-10223 (Lithuania)]. E-mail: m.ozer@iku.edu.tr; Cenys, Antanas [Semiconductor Physics Institute, LT-01108 and Vilnius Gediminas Technical University, Sauletekio 11, LT-10223 (Lithuania); Polatoglu, Yasar [Istanbul Kultur University, E5 Karayolu Uzeri Sirinevler, 34191 Istanbul (Turkey); Hacibekiroglu, Guersel [Istanbul Kultur University, E5 Karayolu Uzeri Sirinevler, 34191 Istanbul (Turkey); Akat, Ercument [Yeditepe University, 26 Agustos Campus Kayisdagi Street, Kayisdagi 81120, Istanbul (Turkey); Valaristos, A. [Aristotle University of Thessaloniki, GR-54124, Thessaloniki (Greece); Anagnostopoulos, A.N. [Aristotle University of Thessaloniki, GR-54124, Thessaloniki (Greece)
2007-08-15
In this work the dynamic behaviour of the one-dimensional family of maps F{sub p,q}(x) = 1/(1 - px - qx {sup 2}) is examined, for specific values of the control parameters p and q. Lyapunov exponents and bifurcation diagrams are numerically calculated. Consequently, a transition from periodic to chaotic regions is observed at values of p and q, where the related maps correspond to Fibonacci generating functions associated with the golden-, the silver- and the bronze mean.
Bifurcations of Fibonacci generating functions
Ozer, Mehmet; Cenys, Antanas; Polatoglu, Yasar; Hacibekiroglu, Guersel; Akat, Ercument; Valaristos, A.; Anagnostopoulos, A.N.
2007-01-01
In this work the dynamic behaviour of the one-dimensional family of maps F p,q (x) = 1/(1 - px - qx 2 ) is examined, for specific values of the control parameters p and q. Lyapunov exponents and bifurcation diagrams are numerically calculated. Consequently, a transition from periodic to chaotic regions is observed at values of p and q, where the related maps correspond to Fibonacci generating functions associated with the golden-, the silver- and the bronze mean
Bifurcations in a discrete time model composed of Beverton-Holt function and Ricker function.
Shang, Jin; Li, Bingtuan; Barnard, Michael R
2015-05-01
We provide rigorous analysis for a discrete-time model composed of the Ricker function and Beverton-Holt function. This model was proposed by Lewis and Li [Bull. Math. Biol. 74 (2012) 2383-2402] in the study of a population in which reproduction occurs at a discrete instant of time whereas death and competition take place continuously during the season. We show analytically that there exists a period-doubling bifurcation curve in the model. The bifurcation curve divides the parameter space into the region of stability and the region of instability. We demonstrate through numerical bifurcation diagrams that the regions of periodic cycles are intermixed with the regions of chaos. We also study the global stability of the model. Copyright © 2015 Elsevier Inc. All rights reserved.
Gul, R; Bernhard, S
2015-11-01
In computational cardiovascular models, parameters are one of major sources of uncertainty, which make the models unreliable and less predictive. In order to achieve predictive models that allow the investigation of the cardiovascular diseases, sensitivity analysis (SA) can be used to quantify and reduce the uncertainty in outputs (pressure and flow) caused by input (electrical and structural) model parameters. In the current study, three variance based global sensitivity analysis (GSA) methods; Sobol, FAST and a sparse grid stochastic collocation technique based on the Smolyak algorithm were applied on a lumped parameter model of carotid bifurcation. Sensitivity analysis was carried out to identify and rank most sensitive parameters as well as to fix less sensitive parameters at their nominal values (factor fixing). In this context, network location and temporal dependent sensitivities were also discussed to identify optimal measurement locations in carotid bifurcation and optimal temporal regions for each parameter in the pressure and flow waves, respectively. Results show that, for both pressure and flow, flow resistance (R), diameter (d) and length of the vessel (l) are sensitive within right common carotid (RCC), right internal carotid (RIC) and right external carotid (REC) arteries, while compliance of the vessels (C) and blood inertia (L) are sensitive only at RCC. Moreover, Young's modulus (E) and wall thickness (h) exhibit less sensitivities on pressure and flow at all locations of carotid bifurcation. Results of network location and temporal variabilities revealed that most of sensitivity was found in common time regions i.e. early systole, peak systole and end systole. Copyright © 2015 Elsevier Inc. All rights reserved.
Numerical bifurcation analysis of a class of nonlinear renewal equations
Breda, Dimitri; Diekmann, Odo; Liessi, Davide; Scarabel, Francesca
2016-01-01
We show, by way of an example, that numerical bifurcation tools for ODE yield reliable bifurcation diagrams when applied to the pseudospectral approximation of a one-parameter family of nonlinear renewal equations. The example resembles logistic-and Ricker-type population equations and exhibits
Bifurcations of optimal vector fields: an overview
Kiseleva, T.; Wagener, F.; Rodellar, J.; Reithmeier, E.
2009-01-01
We develop a bifurcation theory for the solution structure of infinite horizon optimal control problems with one state variable. It turns out that qualitative changes of this structure are connected to local and global bifurcations in the state-costate system. We apply the theory to investigate an
Stochastic bifurcation in a model of love with colored noise
Yue, Xiaokui; Dai, Honghua; Yuan, Jianping
2015-07-01
In this paper, we wish to examine the stochastic bifurcation induced by multiplicative Gaussian colored noise in a dynamical model of love where the random factor is used to describe the complexity and unpredictability of psychological systems. First, the dynamics in deterministic love-triangle model are considered briefly including equilibrium points and their stability, chaotic behaviors and chaotic attractors. Then, the influences of Gaussian colored noise with different parameters are explored such as the phase plots, top Lyapunov exponents, stationary probability density function (PDF) and stochastic bifurcation. The stochastic P-bifurcation through a qualitative change of the stationary PDF will be observed and bifurcation diagram on parameter plane of correlation time and noise intensity is presented to find the bifurcation behaviors in detail. Finally, the top Lyapunov exponent is computed to determine the D-bifurcation when the noise intensity achieves to a critical value. By comparison, we find there is no connection between two kinds of stochastic bifurcation.
Stability diagram for the forced Kuramoto model.
Childs, Lauren M; Strogatz, Steven H
2008-12-01
We analyze the periodically forced Kuramoto model. This system consists of an infinite population of phase oscillators with random intrinsic frequencies, global sinusoidal coupling, and external sinusoidal forcing. It represents an idealization of many phenomena in physics, chemistry, and biology in which mutual synchronization competes with forced synchronization. In other words, the oscillators in the population try to synchronize with one another while also trying to lock onto an external drive. Previous work on the forced Kuramoto model uncovered two main types of attractors, called forced entrainment and mutual entrainment, but the details of the bifurcations between them were unclear. Here we present a complete bifurcation analysis of the model for a special case in which the infinite-dimensional dynamics collapse to a two-dimensional system. Exact results are obtained for the locations of Hopf, saddle-node, and Takens-Bogdanov bifurcations. The resulting stability diagram bears a striking resemblance to that for the weakly nonlinear forced van der Pol oscillator.
Bifurcation and chaos in neural excitable system
Jing Zhujun; Yang Jianping; Feng Wei
2006-01-01
In this paper, we investigate the dynamical behaviors of neural excitable system without periodic external current (proposed by Chialvo [Generic excitable dynamics on a two-dimensional map. Chaos, Solitons and Fractals 1995;5(3-4):461-79] and with periodic external current as system's parameters vary. The existence and stability of three fixed points, bifurcation of fixed points, the conditions of existences of fold bifurcation, flip bifurcation and Hopf bifurcation are derived by using bifurcation theory and center manifold theorem. The chaotic existence in the sense of Marotto's definition of chaos is proved. We then give the numerical simulated results (using bifurcation diagrams, computations of Maximum Lyapunov exponent and phase portraits), which not only show the consistence with the analytic results but also display new and interesting dynamical behaviors, including the complete period-doubling and inverse period-doubling bifurcation, symmetry period-doubling bifurcations of period-3 orbit, simultaneous occurrence of two different routes (invariant cycle and period-doubling bifurcations) to chaos for a given bifurcation parameter, sudden disappearance of chaos at one critical point, a great abundance of period windows (period 2 to 10, 12, 19, 20 orbits, and so on) in transient chaotic regions with interior crises, strange chaotic attractors and strange non-chaotic attractor. In particular, the parameter k plays a important role in the system, which can leave the chaotic behavior or the quasi-periodic behavior to period-1 orbit as k varies, and it can be considered as an control strategy of chaos by adjusting the parameter k. Combining the existing results in [Generic excitable dynamics on a two-dimensional map. Chaos, Solitons and Fractals 1995;5(3-4):461-79] with the new results reported in this paper, a more complete description of the system is now obtained
Bifurcation and instability problems in vortex wakes
Aref, Hassan; Brøns, Morten; Stremler, Mark A.
2007-01-01
A number of instability and bifurcation problems related to the dynamics of vortex wake flows are addressed using various analytical tools and approaches. We discuss the bifurcations of the streamline pattern behind a bluff body as a vortex wake is produced, a theory of the universal Strouhal......-Reynolds number relation for vortex wakes, the bifurcation diagram for "exotic" wake patterns behind an oscillating cylinder first determined experimentally by Williamson & Roshko, and the bifurcations in topology of the streamlines pattern in point vortex streets. The Hamiltonian dynamics of point vortices...... in a periodic strip is considered. The classical results of von Kármán concerning the structure of the vortex street follow from the two-vortices-in-a-strip problem, while the stability results follow largely from a four-vortices-in-a-strip analysis. The three-vortices-in-a-strip problem is argued...
Bifurcation of the spin-wave equations
Cascon, A.; Koiller, J.; Rezende, S.M.
1990-01-01
We study the bifurcations of the spin-wave equations that describe the parametric pumping of collective modes in magnetic media. Mechanisms describing the following dynamical phenomena are proposed: (i) sequential excitation of modes via zero eigenvalue bifurcations; (ii) Hopf bifurcations followed (or not) by Feingenbaum cascades of period doubling; (iii) local and global homoclinic phenomena. Two new organizing center for routes to chaos are identified; in the classification given by Guckenheimer and Holmes [GH], one is a codimension-two local bifurcation, with one pair of imaginary eigenvalues and a zero eigenvalue, to which many dynamical consequences are known; secondly, global homoclinic bifurcations associated to splitting of separatrices, in the limit where the system can be considered a Hamiltonian subjected to weak dissipation and forcing. We outline what further numerical and algebraic work is necessary for the detailed study following this program. (author)
Nonlinear stability control and λ-bifurcation
Erneux, T.; Reiss, E.L.; Magnan, J.F.; Jayakumar, P.K.
1987-01-01
Passive techniques for nonlinear stability control are presented for a model of fluidelastic instability. They employ the phenomena of λ-bifurcation and a generalization of it. λ-bifurcation occurs when a branch of flutter solutions bifurcates supercritically from a basic solution and terminates with an infinite period orbit at a branch of divergence solutions which bifurcates subcritically from the basic solution. The shape of the bifurcation diagram then resembles the greek letter λ. When the system parameters are in the range where flutter occurs by λ-bifurcation, then as the flow velocity increase the flutter amplitude also increases, but the frequencies of the oscillations decrease to zero. This diminishes the damaging effects of structural fatigue by flutter, and permits the flow speed to exceed the critical flutter speed. If generalized λ-bifurcation occurs, then there is a jump transition from the flutter states to a divergence state with a substantially smaller amplitude, when the flow speed is sufficiently larger than the critical flutter speed
Bifurcations of a periodically forced microbial continuous culture model with restrained growth rate
Ren, Jingli; Yuan, Qigang
2017-08-01
A three dimensional microbial continuous culture model with a restrained microbial growth rate is studied in this paper. Two types of dilution rates are considered to investigate the dynamic behaviors of the model. For the unforced system, fold bifurcation and Hopf bifurcation are detected, and numerical simulations reveal that the system undergoes degenerate Hopf bifurcation. When the system is periodically forced, bifurcation diagrams for periodic solutions of period-one and period-two are given by researching the Poincaré map, corresponding to different bifurcation cases in the unforced system. Stable and unstable quasiperiodic solutions are obtained by Neimark-Sacker bifurcation with different parameter values. Periodic solutions of various periods can occur or disappear and even change their stability, when the Poincaré map of the forced system undergoes Neimark-Sacker bifurcation, flip bifurcation, and fold bifurcation. Chaotic attractors generated by a cascade of period doublings and some phase portraits are given at last.
Bifurcation study of phase oscillator systems with attractive and repulsive interaction
Burylko, Oleksandr; Kazanovich, Yakov; Borisyuk, Roman
2014-08-01
We study a model of globally coupled phase oscillators that contains two groups of oscillators with positive (synchronizing) and negative (desynchronizing) incoming connections for the first and second groups, respectively. This model was previously studied by Hong and Strogatz (the Hong-Strogatz model) in the case of a large number of oscillators. We consider a generalized Hong-Strogatz model with a constant phase shift in coupling. Our approach is based on the study of invariant manifolds and bifurcation analysis of the system. In the case of zero phase shift, various invariant manifolds are analytically described and a new dynamical mode is found. In the case of a nonzero phase shift we obtained a set of bifurcation diagrams for various systems with three or four oscillators. It is shown that in these cases system dynamics can be complex enough and include multistability and chaotic oscillations.
A numerical study of crack initiation in a bcc iron system based on dynamic bifurcation theory
Li, Xiantao
2014-01-01
Crack initiation under dynamic loading conditions is studied under the framework of dynamic bifurcation theory. An atomistic model for BCC iron is considered to explicitly take into account the detailed molecular interactions. To understand the strain-rate dependence of the crack initiation process, we first obtain the bifurcation diagram from a computational procedure using continuation methods. The stability transition associated with a crack initiation, as well as the connection to the bifurcation diagram, is studied by comparing direct numerical results to the dynamic bifurcation theory [R. Haberman, SIAM J. Appl. Math. 37, 69–106 (1979)].
Ward, Robin E.; Wandersee, James
2000-01-01
Students must understand key concepts through reasoning, searching out related concepts, and making connections within multiple systems to learn science. The Roundhouse diagram was developed to be a concise, holistic, graphic representation of a science topic, process, or activity. Includes sample Roundhouse diagrams, a diagram checklist, and…
Unfolding the Riddling Bifurcation
Maistrenko, Yu.; Popovych, O.; Mosekilde, Erik
1999-01-01
We present analytical conditions for the riddling bifurcation in a system of two symmetrically coupled, identical, smooth one-dimensional maps to be soft or hard and describe a generic scenario for the transformations of the basin of attraction following a soft riddling bifurcation.......We present analytical conditions for the riddling bifurcation in a system of two symmetrically coupled, identical, smooth one-dimensional maps to be soft or hard and describe a generic scenario for the transformations of the basin of attraction following a soft riddling bifurcation....
Hopf bifurcation analysis of Chen circuit with direct time delay feedback
Hai-Peng, Ren; Wen-Chao, Li; Ding, Liu
2010-01-01
Direct time delay feedback can make non-chaotic Chen circuit chaotic. The chaotic Chen circuit with direct time delay feedback possesses rich and complex dynamical behaviours. To reach a deep and clear understanding of the dynamics of such circuits described by delay differential equations, Hopf bifurcation in the circuit is analysed using the Hopf bifurcation theory and the central manifold theorem in this paper. Bifurcation points and bifurcation directions are derived in detail, which prove to be consistent with the previous bifurcation diagram. Numerical simulations and experimental results are given to verify the theoretical analysis. Hopf bifurcation analysis can explain and predict the periodical orbit (oscillation) in Chen circuit with direct time delay feedback. Bifurcation boundaries are derived using the Hopf bifurcation analysis, which will be helpful for determining the parameters in the stabilisation of the originally chaotic circuit
FFT Bifurcation Analysis of Routes to Chaos via Quasiperiodic Solutions
L. Borkowski
2015-01-01
Full Text Available The dynamics of a ring of seven unidirectionally coupled nonlinear Duffing oscillators is studied. We show that the FFT analysis presented in form of a bifurcation graph, that is, frequency distribution versus a control parameter, can provide a valuable and helpful complement to the corresponding typical bifurcation diagram and the course of Lyapunov exponents, especially in context of detailed identification of the observed attractors. As an example, bifurcation analysis of routes to chaos via 2-frequency and 3-frequency quasiperiodicity is demonstrated.
Travelling waves and their bifurcations in the Lorenz-96 model
van Kekem, Dirk L.; Sterk, Alef E.
2018-03-01
In this paper we study the dynamics of the monoscale Lorenz-96 model using both analytical and numerical means. The bifurcations for positive forcing parameter F are investigated. The main analytical result is the existence of Hopf or Hopf-Hopf bifurcations in any dimension n ≥ 4. Exploiting the circulant structure of the Jacobian matrix enables us to reduce the first Lyapunov coefficient to an explicit formula from which it can be determined when the Hopf bifurcation is sub- or supercritical. The first Hopf bifurcation for F > 0 is always supercritical and the periodic orbit born at this bifurcation has the physical interpretation of a travelling wave. Furthermore, by unfolding the codimension two Hopf-Hopf bifurcation it is shown to act as an organising centre, explaining dynamics such as quasi-periodic attractors and multistability, which are observed in the original Lorenz-96 model. Finally, the region of parameter values beyond the first Hopf bifurcation value is investigated numerically and routes to chaos are described using bifurcation diagrams and Lyapunov exponents. The observed routes to chaos are various but without clear pattern as n → ∞.
Stamatiou, George; Ghikas, Demetris P.K.
2007-01-01
Properties related to entanglement in quantum systems, are known to be associated with distinct properties of the corresponding classical systems, as for example stability, integrability and chaos. This means that the detailed topology, both local and global, of the classical phase space may reveal, or influence, the entangling power of the quantum system. As it has been shown in the literature, the bifurcation points, in autonomous dynamical systems, play a crucial role for the onset of entanglement. Similarly, the existence of scars among the quantum states seems to be a factor in the dynamics of entanglement. Here we study these issues for a non-autonomous system, the quantum kicked top, as a collective model of a multi-qubit system. Using the bifurcation diagram of the corresponding classical limit (the classical kicked top), we analyzed the pair-wise and the bi-partite entanglement of the qubits and their relation to scars, as a function of the critical parameter of the system. We found that the pair-wise entanglement and pair-wise negativity show a strong maximum precisely at the bifurcation points, while the bi-partite entanglement changes slope at these points. We have also investigated the connection between entanglement and the fixed points on the branch of the bifurcation diagram between the two first bifurcation points and we found that the entanglement measures take their extreme values precisely on these points. We conjecture that our results on this behavior of entanglement is generic for many quantum systems with a nonlinear classical analogue
Global mean-field phase diagram of the spin-1 Ising ferromagnet in a random crystal field
Borelli, M. E. S.; Carneiro, C. E. I.
1996-02-01
We study the phase diagram of the mean-field spin-1 Ising ferromagnet in a uniform magnetic field H and a random crystal field Δi, with probability distribution P( Δi) = pδ( Δi - Δ) + (1 - p) δ( Δi). We analyse the effects of randomness on the first-order surfaces of the Δ- T- H phase diagram for different values of the concentration p and show how these surfaces are affected by the dilution of the crystal field.
Hopf bifurcation for tumor-immune competition systems with delay
Ping Bi
2014-01-01
Full Text Available In this article, a immune response system with delay is considered, which consists of two-dimensional nonlinear differential equations. The main purpose of this paper is to explore the Hopf bifurcation of a immune response system with delay. The general formula of the direction, the estimation formula of period and stability of bifurcated periodic solution are also given. Especially, the conditions of the global existence of periodic solutions bifurcating from Hopf bifurcations are given. Numerical simulations are carried out to illustrate the the theoretical analysis and the obtained results.
Relative Lyapunov Center Bifurcations
Wulff, Claudia; Schilder, Frank
2014-01-01
Relative equilibria (REs) and relative periodic orbits (RPOs) are ubiquitous in symmetric Hamiltonian systems and occur, for example, in celestial mechanics, molecular dynamics, and rigid body motion. REs are equilibria, and RPOs are periodic orbits of the symmetry reduced system. Relative Lyapunov...... center bifurcations are bifurcations of RPOs from REs corresponding to Lyapunov center bifurcations of the symmetry reduced dynamics. In this paper we first prove a relative Lyapunov center theorem by combining recent results on the persistence of RPOs in Hamiltonian systems with a symmetric Lyapunov...... center theorem of Montaldi, Roberts, and Stewart. We then develop numerical methods for the detection of relative Lyapunov center bifurcations along branches of RPOs and for their computation. We apply our methods to Lagrangian REs of the N-body problem....
Colwell, Morris A
1976-01-01
Electronic Diagrams is a ready reference and general guide to systems and circuit planning and in the preparation of diagrams for both newcomers and the more experienced. This book presents guidelines and logical procedures that the reader can follow and then be equipped to tackle large complex diagrams by recognition of characteristic 'building blocks' or 'black boxes'. The goal is to break down many of the barriers that often seem to deter students and laymen in learning the art of electronics, especially when they take up electronics as a spare time occupation. This text is comprised of nin
Bifurcations of transition states: Morse bifurcations
MacKay, R S; Strub, D C
2014-01-01
A transition state for a Hamiltonian system is a closed, invariant, oriented, codimension-2 submanifold of an energy level that can be spanned by two compact codimension-1 surfaces of unidirectional flux whose union, called a dividing surface, locally separates the energy level into two components and has no local recrossings. For this to happen robustly to all smooth perturbations, the transition state must be normally hyperbolic. The dividing surface then has locally minimal geometric flux through it, giving an upper bound on the rate of transport in either direction. Transition states diffeomorphic to S 2m−3 are known to exist for energies just above any index-1 critical point of a Hamiltonian of m degrees of freedom, with dividing surfaces S 2m−2 . The question addressed here is what qualitative changes in the transition state, and consequently the dividing surface, may occur as the energy or other parameters are varied? We find that there is a class of systems for which the transition state becomes singular and then regains normal hyperbolicity with a change in diffeomorphism class. These are Morse bifurcations. Various examples are considered. Firstly, some simple examples in which transition states connect or disconnect, and the dividing surface may become a torus or other. Then, we show how sequences of Morse bifurcations producing various interesting forms of transition state and dividing surface are present in reacting systems, by considering a hypothetical class of bimolecular reactions in gas phase. (paper)
Olmstead, W.E.; Davis, S.H.; Rosenblat, S.; Kath, W.L.
1986-01-01
A model equation containing a memory integral is posed. The extent of the memory, the relaxation time lambda, controls the bifurcation behavior as the control parameter R is increased. Small (large) lambda gives steady (periodic) bifurcation. There is a double eigenvalue at lambda = lambda 1 , separating purely steady (lambda 1 ) from combined steady/T-periodic (lambda > lambda 1 ) states with T → infinity as lambda → lambda + 1 . Analysis leads to the co-existence of stable steady/periodic states and as R is increased, the periodic states give way to the steady states. Numerical solutions show that this behavior persists away from lambda = lambda 1
Oostrom, V. van
2004-01-01
We introduce the unifying notion of delimiting diagram. Hitherto unrelated results such as: Minimality of the internal needed strategy for orthogonal first-order term rewriting systems, maximality of the limit strategy for orthogonal higher-order pattern rewrite systems (with maximality of the
Magneto-elastic dynamics and bifurcation of rotating annular plate*
Hu Yu-Da; Piao Jiang-Min; Li Wen-Qiang
2017-01-01
In this paper, magneto-elastic dynamic behavior, bifurcation, and chaos of a rotating annular thin plate with various boundary conditions are investigated. Based on the thin plate theory and the Maxwell equations, the magneto-elastic dynamic equations of rotating annular plate are derived by means of Hamilton’s principle. Bessel function as a mode shape function and the Galerkin method are used to achieve the transverse vibration differential equation of the rotating annular plate with different boundary conditions. By numerical analysis, the bifurcation diagrams with magnetic induction, amplitude and frequency of transverse excitation force as the control parameters are respectively plotted under different boundary conditions such as clamped supported sides, simply supported sides, and clamped-one-side combined with simply-anotherside. Poincaré maps, time history charts, power spectrum charts, and phase diagrams are obtained under certain conditions, and the influence of the bifurcation parameters on the bifurcation and chaos of the system is discussed. The results show that the motion of the system is a complicated and repeated process from multi-periodic motion to quasi-period motion to chaotic motion, which is accompanied by intermittent chaos, when the bifurcation parameters change. If the amplitude of transverse excitation force is bigger or magnetic induction intensity is smaller or boundary constraints level is lower, the system can be more prone to chaos. (paper)
Energetics and monsoon bifurcations
Seshadri, Ashwin K.
2017-01-01
Monsoons involve increases in dry static energy (DSE), with primary contributions from increased shortwave radiation and condensation of water vapor, compensated by DSE export via horizontal fluxes in monsoonal circulations. We introduce a simple box-model characterizing evolution of the DSE budget to study nonlinear dynamics of steady-state monsoons. Horizontal fluxes of DSE are stabilizing during monsoons, exporting DSE and hence weakening the monsoonal circulation. By contrast latent heat addition (LHA) due to condensation of water vapor destabilizes, by increasing the DSE budget. These two factors, horizontal DSE fluxes and LHA, are most strongly dependent on the contrast in tropospheric mean temperature between land and ocean. For the steady-state DSE in the box-model to be stable, the DSE flux should depend more strongly on the temperature contrast than LHA; stronger circulation then reduces DSE and thereby restores equilibrium. We present conditions for this to occur. The main focus of the paper is describing conditions for bifurcation behavior of simple models. Previous authors presented a minimal model of abrupt monsoon transitions and argued that such behavior can be related to a positive feedback called the `moisture advection feedback'. However, by accounting for the effect of vertical lapse rate of temperature on the DSE flux, we show that bifurcations are not a generic property of such models despite these fluxes being nonlinear in the temperature contrast. We explain the origin of this behavior and describe conditions for a bifurcation to occur. This is illustrated for the case of the July-mean monsoon over India. The default model with mean parameter estimates does not contain a bifurcation, but the model admits bifurcation as parameters are varied.
Spijkerboer, T.P.
2017-01-01
The externalization of European migration policy has resulted in a bifurcation of global human mobility, which is divided along a North/South axis. In two judgments, the EU Court of Justice was confronted with cases challenging the exclusion of Syrian refugees from Europe. These cases concern core
Ajith Ananthakrishna Pillai
2012-03-01
Full Text Available Bifurcation percutaneous coronary intervention (PCI is still a difficult call for the interventionist despite advancements in the instrumentation, technical skill and the imaging modalities. With major cardiac events relate to the side-branch (SB compromise, the concept and practice of dedicated bifurcation stents seems exciting. Several designs of such dedicated stents are currently undergoing trials. This novel concept and pristine technology offers new hope notwithstanding the fact that we need to go a long way in widespread acceptance and practice of these gadgets. Some of these designs even though looks enterprising, the mere complex delivering technique and the demanding knowledge of the exact coronary anatomy makes their routine use challenging.
Bifurcation and Nonlinear Oscillations.
1980-09-28
Structural stability and bifurcation theory. pp. 549-560 in Dinamical Systems (Ed. MI. Peixoto), Academic Press, 1973. [211 J. Sotomayor, Generic one...Dynamical Systems Brown University ELECTP" 71, Providence, R. I. 02912 1EC 2 4 1980j //C -*)’ Septabe-4., 1980 / -A + This research was supported in...problems are discussed. The first one deals with the characterization of the flow for a periodic planar system which is the perturbation of an autonomous
Numerical analysis of bifurcations
Guckenheimer, J.
1996-01-01
This paper is a brief survey of numerical methods for computing bifurcations of generic families of dynamical systems. Emphasis is placed upon algorithms that reflect the structure of the underlying mathematical theory while retaining numerical efficiency. Significant improvements in the computational analysis of dynamical systems are to be expected from more reliance of geometric insight coming from dynamical systems theory. copyright 1996 American Institute of Physics
Bifurcation of solutions to Hamiltonian boundary value problems
McLachlan, R. I.; Offen, C.
2018-06-01
A bifurcation is a qualitative change in a family of solutions to an equation produced by varying parameters. In contrast to the local bifurcations of dynamical systems that are often related to a change in the number or stability of equilibria, bifurcations of boundary value problems are global in nature and may not be related to any obvious change in dynamical behaviour. Catastrophe theory is a well-developed framework which studies the bifurcations of critical points of functions. In this paper we study the bifurcations of solutions of boundary-value problems for symplectic maps, using the language of (finite-dimensional) singularity theory. We associate certain such problems with a geometric picture involving the intersection of Lagrangian submanifolds, and hence with the critical points of a suitable generating function. Within this framework, we then study the effect of three special cases: (i) some common boundary conditions, such as Dirichlet boundary conditions for second-order systems, restrict the possible types of bifurcations (for example, in generic planar systems only the A-series beginning with folds and cusps can occur); (ii) integrable systems, such as planar Hamiltonian systems, can exhibit a novel periodic pitchfork bifurcation; and (iii) systems with Hamiltonian symmetries or reversing symmetries can exhibit restricted bifurcations associated with the symmetry. This approach offers an alternative to the analysis of critical points in function spaces, typically used in the study of bifurcation of variational problems, and opens the way to the detection of more exotic bifurcations than the simple folds and cusps that are often found in examples.
Hopf bifurcation of the stochastic model on business cycle
Xu, J; Wang, H; Ge, G
2008-01-01
A stochastic model on business cycle was presented in thas paper. Simplifying the model through the quasi Hamiltonian theory, the Ito diffusion process was obtained. According to Oseledec multiplicative ergodic theory and singular boundary theory, the conditions of local and global stability were acquired. Solving the stationary FPK equation and analyzing the stationary probability density, the stochastic Hopf bifurcation was explained. The result indicated that the change of parameter awas the key factor to the appearance of the stochastic Hopf bifurcation
Experimental Investigation of Bifurcations in a Thermoacoustic Engine
Vishnu R. Unni
2015-06-01
Full Text Available In this study, variation in the characteristics of the pressure oscillations in a thermoacoustic engine is explored as the input heat flux is varied. A bifurcation diagram is plotted to study the variation in the qualitative behavior of the acoustic oscillations as the input heat flux changes. At a critical input heat flux (60 Watt, the engine begins to produce acoustic oscillations in its fundamental longitudinal mode. As the input heat flux is increased, incommensurate frequencies appear in the power spectrum. The simultaneous presence of incommensurate frequencies results in quasiperiodic oscillations. On further increase of heat flux, the fundamental mode disappears and second mode oscillations are observed. These bifurcations in the characteristics of the pressure oscillations are the result of nonlinear interaction between multiple modes present in the thermoacoustic engine. Hysteresis in the bifurcation diagram suggests that the bifurcation is subcritical. Further, the qualitative analysis of different dynamic regimes is performed using nonlinear time series analysis. The physical reason for the observed nonlinear behavior is discussed. Suggestions to avert the variations in qualitative behavior of the pressure oscillations in thermoacoustic engines are also provided.
Bradford, R.A.W.; Tipping, D.J.
2015-01-01
The ratchet and shakedown boundaries are derived analytically for a thin cylinder composed of elastic-perfectly plastic Tresca material subject to constant internal pressure with capped ends, plus an additional constant axial load, F, and a cycling secondary global bending load. The analytic solution is in good agreement with solutions found using the linear matching method. When F is tensile, ratcheting can occur for sufficiently large cyclic bending loads in which the pipe gets longer and thinner but its diameter remains the same. When F is compressive, ratcheting can occur in which the pipe diameter increases and the pipe gets shorter, but its wall thickness remains the same. When subject to internal pressure and cyclic bending alone (F = 0), no ratcheting is possible, even for arbitrarily large bending loads, despite the presence of the axial pressure load. The reason is that the case with a primary axial membrane stress exactly equal to half the primary hoop membrane stress is equipoised between tensile and compressive axial ratcheting, and hence does not ratchet at all. This remarkable result appears to have escaped previous attention. - Highlights: • A thin cylinder is subject to pressure and cyclic global bending and additional axial load. • Ratchet and shakedown boundaries are derived analytically and using LMM. • Good agreement is found. • No ratcheting occurs for zero additional axial load.
Bifurcation and stability analysis of a nonlinear milling process
Weremczuk, Andrzej; Rusinek, Rafal; Warminski, Jerzy
2018-01-01
Numerical investigations of milling operations dynamics are presented in this paper. A two degree of freedom nonlinear model is used to study workpiece-tool vibrations. The analyzed model takes into account both flexibility of the tool and the workpiece. The dynamics of the milling process is described by the discontinuous ordinary differential equation with time delay, which can cause process instability. First, stability lobes diagrams are created on the basis of the parameters determined in impact test of an end mill and workpiece. Next, the bifurcations diagrams are performed for different values of rotational speeds.
Experimental Investigation of Bifurcations in a Thermoacoustic Engine
Vishnu R. Unni; Yogesh M. S. Prasaad; N. T. Ravi; S. Md Iqbal; Bala Pesala; R. I. Sujith
2015-01-01
In this study, variation in the characteristics of the pressure oscillations in a thermoacoustic engine is explored as the input heat flux is varied. A bifurcation diagram is plotted to study the variation in the qualitative behavior of the acoustic oscillations as the input heat flux changes. At a critical input heat flux (60 Watt), the engine begins to produce acoustic oscillations in its fundamental longitudinal mode. As the input heat flux is increased, incommensurate frequencies appear i...
Li, Chengyuan; Deng, Licai; de Grijs, Richard; Jiang, Dengkai; Xin, Yu
2018-01-01
Bifurcated patterns of blue straggler stars in their color--magnitude diagrams have atracted significant attention. This type of special (but rare) pattern of two distinct blue straggler sequences is commonly interpreted as evidence of cluster core-collapse-driven stellar collisions as an efficient formation mechanism. Here, we report the detection of a bifurcated blue straggler distribution in a young Large MagellanicCloud cluster, NGC 2173. Because of the cluster's low central stellar numbe...
Evidence for bifurcation and universal chaotic behavior in nonlinear semiconducting devices
Testa, J.; Perez, J.; Jeffries, C.
1982-01-01
Bifurcations, chaos, and extensive periodic windows in the chaotic regime are observed for a driven LRC circuit, the capacitive element being a nonlinear varactor diode. Measurements include power spectral analysis; real time amplitude data; phase portraits; and a bifurcation diagram, obtained by sampling methods. The effects of added external noise are studied. These data yield experimental determinations of several of the universal numbers predicted to characterize nonlinear systems having this route to chaos
Inverse bifurcation analysis: application to simple gene systems
Schuster Peter
2006-07-01
Full Text Available Abstract Background Bifurcation analysis has proven to be a powerful method for understanding the qualitative behavior of gene regulatory networks. In addition to the more traditional forward problem of determining the mapping from parameter space to the space of model behavior, the inverse problem of determining model parameters to result in certain desired properties of the bifurcation diagram provides an attractive methodology for addressing important biological problems. These include understanding how the robustness of qualitative behavior arises from system design as well as providing a way to engineer biological networks with qualitative properties. Results We demonstrate that certain inverse bifurcation problems of biological interest may be cast as optimization problems involving minimal distances of reference parameter sets to bifurcation manifolds. This formulation allows for an iterative solution procedure based on performing a sequence of eigen-system computations and one-parameter continuations of solutions, the latter being a standard capability in existing numerical bifurcation software. As applications of the proposed method, we show that the problem of maximizing regions of a given qualitative behavior as well as the reverse engineering of bistable gene switches can be modelled and efficiently solved.
Bifurcation and chaos in a Tessiet type food chain chemostat with pulsed input and washout
Wang Fengyan; Hao Chunping; Chen Lansun
2007-01-01
In this paper, we introduce and study a model of a Tessiet type food chain chemostat with pulsed input and washout. We investigate the subsystem with substrate and prey and study the stability of the periodic solutions, which are the boundary periodic solutions of the system. The stability analysis of the boundary periodic solution yields an invasion threshold. By use of standard techniques of bifurcation theory, we prove that above this threshold there are periodic oscillations in substrate, prey and predator. Simple cycles may give way to chaos in a cascade of period-doubling bifurcations. Furthermore, by comparing bifurcation diagrams with different bifurcation parameters, we can see that the impulsive system shows two kinds of bifurcations, whose are period doubling and period halving
Bubble transport in bifurcations
Bull, Joseph; Qamar, Adnan
2017-11-01
Motivated by a developmental gas embolotherapy technique for cancer treatment, we examine the transport of bubbles entrained in liquid. In gas embolotherapy, infarction of tumors is induced by selectively formed vascular gas bubbles that originate from acoustic vaporization of vascular droplets. In the case of non-functionalized droplets with the objective of vessel occlusion, the bubbles are transported by flow through vessel bifurcations, where they may split prior to eventually reach vessels small enough that they become lodged. This splitting behavior affects the distribution of bubbles and the efficacy of flow occlusion and the treatment. In these studies, we investigated bubble transport in bifurcations using computational and theoretical modeling. The model reproduces the variety of experimentally observed splitting behaviors. Splitting homogeneity and maximum shear stress along the vessel walls is predicted over a variety of physical parameters. Maximum shear stresses were found to decrease with increasing Reynolds number. The initial bubble length was found to affect the splitting behavior in the presence of gravitational asymmetry. This work was supported by NIH Grant R01EB006476.
From State Diagram to Class Diagram
Borch, Ole; Madsen, Per Printz
2009-01-01
UML class diagram and Java source code are interrelated and Java code is a kind of interchange format. Working with UML state diagram in CASE tools, a corresponding xml file is maintained. Designing state diagrams is mostly performed manually using design patterns and coding templates - a time...... consuming process. This article demonstrates how to compile such a diagram into Java code and later, by reverse engineering, produce a class diagram. The process from state diagram via intermediate SAX parsed xml file to Apache Velocity generated Java code is described. The result is a fast reproducible...
Gritli, Hassène; Belghith, Safya
2017-01-01
Highlights: • We study the passive walking dynamics of the compass-gait model under OGY-based state-feedback control. • We analyze local bifurcations via a hybrid Poincaré map. • We show exhibition of the super(sub)-critical flip bifurcation, the saddle-node(saddle) bifurcation and a saddle-flip bifurcation. • An analysis via a two-parameter bifurcation diagram is presented. • Some new hidden attractors in the controlled passive walking dynamics are displayed. - Abstract: In our previous work, we have analyzed the passive dynamic walking of the compass-gait biped model under the OGY-based state-feedback control using the impulsive hybrid nonlinear dynamics. Such study was carried out through bifurcation diagrams. It was shown that the controlled bipedal gait exhibits attractive nonlinear phenomena such as the cyclic-fold (saddle-node) bifurcation, the period-doubling (flip) bifurcation and chaos. Moreover, we revealed that, using the controlled continuous-time dynamics, we encountered a problem in finding, identifying and hence following branches of (un)stable solutions in order to characterize local bifurcations. The present paper solves such problem and then provides a further investigation of the controlled bipedal walking dynamics using the developed analytical expression of the controlled hybrid Poincaré map. Thus, we show that analysis via such Poincaré map allows to follow branches of both stable and unstable fixed points in bifurcation diagrams and hence to explore the complete dynamics of the controlled compass-gait biped model. We demonstrate the generation, other than the conventional local bifurcations in bipedal walking, i.e. the flip bifurcation and the saddle-node bifurcation, of a saddle-saddle bifurcation, a subcritical flip bifurcation and a new type of a local bifurcation, the saddle-flip bifurcation. In addition, to further understand the occurrence of the local bifurcations, we present an analysis with a two-parameter bifurcation
Kalkofen, W.
1985-01-01
The assumptions of Ayres' model of the upper solar atmosphere are examined. It is found that the bistable character of his model is postulated - through the assumptions concerning the opacity sources and the effect of mechanical waves, which are allowed to destroy the CO molecules but not to heat the gas. The neglect of cooling by metal lines is based on their reduced local cooling rate, but it ignores the increased depth over which this cooling occurs. Thus, the bifurcated model of the upper solar atmosphere consists of two models, one cold at the temperature minimum, with a kinetic temperature of 2900 K, and the other hot, with a temperature of 4900 K. 8 references
Bifurcations sights, sounds, and mathematics
Matsumoto, Takashi; Kokubu, Hiroshi; Tokunaga, Ryuji
1993-01-01
Bifurcation originally meant "splitting into two parts. " Namely, a system under goes a bifurcation when there is a qualitative change in the behavior of the sys tem. Bifurcation in the context of dynamical systems, where the time evolution of systems are involved, has been the subject of research for many scientists and engineers for the past hundred years simply because bifurcations are interesting. A very good way of understanding bifurcations would be to see them first and study theories second. Another way would be to first comprehend the basic concepts and theories and then see what they look like. In any event, it is best to both observe experiments and understand the theories of bifurcations. This book attempts to provide a general audience with both avenues toward understanding bifurcations. Specifically, (1) A variety of concrete experimental results obtained from electronic circuits are given in Chapter 1. All the circuits are very simple, which is crucial in any experiment. The circuits, howev...
Viral pathogenesis in diagrams
Tremblay, Michel; Berthiaume, Laurent; Ackermann, Hans-Wolfgang
2001-01-01
.... The 268 diagrams in Viral Pathogenesis in Diagrams were selected from over 800 diagrams of English and French virological literature, including one derived from a famous drawing by Leonardo da Vinci...
Stability and bifurcation analysis in a kind of business cycle model with delay
Zhang Chunrui; Wei Junjie
2004-01-01
A kind of business cycle model with delay is considered. Firstly, the linear stability of the model is studied and bifurcation set is drawn in the appropriate parameter plane. It is found that there exist Hopf bifurcations when the delay passes a sequence of critical values. Then the explicit algorithm for determining the direction of the Hopf bifurcations and the stability of the bifurcating periodic solutions are derived, using the normal form method and center manifold theorem. Finally, a group conditions to guarantee the global existence of periodic solutions is given, and numerical simulations are performed to illustrate the analytical results found
Bifurcation analysis of a discrete SIS model with bilinear incidence depending on new infection.
Cao, Hui; Zhou, Yicang; Ma, Zhien
2013-01-01
A discrete SIS epidemic model with the bilinear incidence depending on the new infection is formulated and studied. The condition for the global stability of the disease free equilibrium is obtained. The existence of the endemic equilibrium and its stability are investigated. More attention is paid to the existence of the saddle-node bifurcation, the flip bifurcation, and the Hopf bifurcation. Sufficient conditions for those bifurcations have been obtained. Numerical simulations are conducted to demonstrate our theoretical results and the complexity of the model.
Analysis of stability and Hopf bifurcation for a delayed logistic equation
Sun Chengjun; Han Maoan; Lin Yiping
2007-01-01
The dynamics of a logistic equation with discrete delay are investigated, together with the local and global stability of the equilibria. In particular, the conditions under which a sequence of Hopf bifurcations occur at the positive equilibrium are obtained. Explicit algorithm for determining the stability of the bifurcating periodic solutions and the direction of the Hopf bifurcation are derived by using the theory of normal form and center manifold [Hassard B, Kazarino D, Wan Y. Theory and applications of Hopf bifurcation. Cambridge: Cambridge University Press; 1981.]. Global existence of periodic solutions is also established by using a global Hopf bifurcation result of Wu [Symmetric functional differential equations and neural networks with memory. Trans Amer Math Soc 350:1998;4799-38.
Codimension-Two Bifurcation Analysis in DC Microgrids Under Droop Control
Lenz, Eduardo; Pagano, Daniel J.; Tahim, André P. N.
This paper addresses local and global bifurcations that may appear in electrical power systems, such as DC microgrids, which recently has attracted interest from the electrical engineering society. Most sources in these networks are voltage-type and operate in parallel. In such configuration, the basic technique for stabilizing the bus voltage is the so-called droop control. The main contribution of this work is a codimension-two bifurcation analysis of a small DC microgrid considering the droop control gain and the power processed by the load as bifurcation parameters. The codimension-two bifurcation set leads to practical rules for achieving a robust droop control design. Moreover, the bifurcation analysis also offers a better understanding of the dynamics involved in the problem and how to avoid possible instabilities. Simulation results are presented in order to illustrate the bifurcation analysis.
Riddling bifurcation and interstellar journeys
Kapitaniak, Tomasz
2005-01-01
We show that riddling bifurcation which is characteristic for low-dimensional attractors embedded in higher-dimensional phase space can give physical mechanism explaining interstellar journeys described in science-fiction literature
Dynamic bifurcations on financial markets
Kozłowska, M.; Denys, M.; Wiliński, M.; Link, G.; Gubiec, T.; Werner, T.R.; Kutner, R.; Struzik, Z.R.
2016-01-01
We provide evidence that catastrophic bifurcation breakdowns or transitions, preceded by early warning signs such as flickering phenomena, are present on notoriously unpredictable financial markets. For this we construct robust indicators of catastrophic dynamical slowing down and apply these to identify hallmarks of dynamical catastrophic bifurcation transitions. This is done using daily closing index records for the representative examples of financial markets of small and mid to large capitalisations experiencing a speculative bubble induced by the worldwide financial crisis of 2007-08.
Bifurcation and synchronization of synaptically coupled FHN models with time delay
Wang Qingyun; Lu Qishao; Chen Guanrong; Feng Zhaosheng; Duan Lixia
2009-01-01
This paper presents an investigation of dynamics of the coupled nonidentical FHN models with synaptic connection, which can exhibit rich bifurcation behavior with variation of the coupling strength. With the time delay being introduced, the coupled neurons may display a transition from the original chaotic motions to periodic ones, which is accompanied by complex bifurcation scenario. At the same time, synchronization of the coupled neurons is studied in terms of their mean frequencies. We also find that the small time delay can induce new period windows with the coupling strength increasing. Moreover, it is found that synchronization of the coupled neurons can be achieved in some parameter ranges and related to their bifurcation transition. Bifurcation diagrams are obtained numerically or analytically from the mathematical model and the parameter regions of different behavior are clarified.
Bifurcation and chaos of an axially accelerating viscoelastic beam
Yang Xiaodong; Chen Liqun
2005-01-01
This paper investigates bifurcation and chaos of an axially accelerating viscoelastic beam. The Kelvin-Voigt model is adopted to constitute the material of the beam. Lagrangian strain is used to account for the beam's geometric nonlinearity. The nonlinear partial-differential equation governing transverse motion of the beam is derived from the Newton second law. The Galerkin method is applied to truncate the governing equation into a set of ordinary differential equations. By use of the Poincare map, the dynamical behavior is identified based on the numerical solutions of the ordinary differential equations. The bifurcation diagrams are presented in the case that the mean axial speed, the amplitude of speed fluctuation and the dynamic viscoelasticity is respectively varied while other parameters are fixed. The Lyapunov exponent is calculated to identify chaos. From numerical simulations, it is indicated that the periodic, quasi-periodic and chaotic motions occur in the transverse vibrations of the axially accelerating viscoelastic beam
Synchronization of diffusively coupled oscillators near the homoclinic bifurcation
Postnov, D.; Han, Seung Kee; Kook, Hyungtae
1998-09-01
It has been known that a diffusive coupling between two limit cycle oscillations typically leads to the inphase synchronization and also that it is the only stable state in the weak coupling limit. Recently, however, it has been shown that the coupling of the same nature can result in the distinctive dephased synchronization when the limit cycles are close to the homoclinic bifurcation, which often occurs especially for the neuronal oscillators. In this paper we propose a simple physical model using the modified van der Pol equation, which unfolds the generic synchronization behaviors of the latter kind and in which one may readily observe changes in the synchronization behaviors between the distinctive regimes as well. The dephasing mechanism is analyzed both qualitatively and quantitatively in the weak coupling limit. A general form of coupling is introduced and the synchronization behaviors over a wide range of the coupling parameters are explored to construct the phase diagram using the bifurcation analysis. (author)
Bifurcation theory applied to buckling states of a cylindrical shell
Chaskalovic, J.; Naili, S.
1995-01-01
Veins, bronchii, and many other vessels in the human body are flexible enough to be capable of collapse if submitted to suitable applied external and internal loads. One way to describe this phenomenon is to consider an inextensible elastic and infinite tube, with a circular cross section in the reference configuration, subjected to a uniform external pressure. In this paper, we establish that the nonlinear equilibrium equation for this model has nontrivial solutions which appear for critical values of the pressure. To this end, the tools we use are the Liapunov-Schmidt decomposition and the bifurcation theorem for simple multiplicity. We conclude with the bifurcation diagram, showing the dependence between the cross-sectional area and the pressure.
Hopf-pitchfork bifurcation and periodic phenomena in nonlinear financial system with delay
Ding Yuting; Jiang Weihua; Wang Hongbin
2012-01-01
Highlights: ► We derive the unfolding of a financial system with Hopf-pitchfork bifurcation. ► We show the coexistence of a pair of stable small amplitudes periodic solutions. ► At the same time, also there is a pair of stable large amplitudes periodic solutions. ► Chaos can appear by period-doubling bifurcation far away from Hopf-pitchfork value. ► The study will be useful for interpreting economics phenomena in theory. - Abstract: In this paper, we identify the critical point for a Hopf-pitchfork bifurcation in a nonlinear financial system with delay, and derive the normal form up to third order with their unfolding in original system parameters near the bifurcation point by normal form method and center manifold theory. Furthermore, we analyze its local dynamical behaviors, and show the coexistence of a pair of stable periodic solutions. We also show that there coexist a pair of stable small-amplitude periodic solutions and a pair of stable large-amplitude periodic solutions for different initial values. Finally, we give the bifurcation diagram with numerical illustration, showing that the pair of stable small-amplitude periodic solutions can also exist in a large region of unfolding parameters, and the financial system with delay can exhibit chaos via period-doubling bifurcations as the unfolding parameter values are far away from the critical point of the Hopf-pitchfork bifurcation.
Three dimensional nilpotent singularity and Sil'nikov bifurcation
Li Xindan; Liu Haifei
2007-01-01
In this paper, by using the normal form, blow-up theory and the technique of global bifurcations, we study the singularity at the origin with threefold zero eigenvalue for nonsymmetric vector fields with nilpotent linear part and 4-jet C ∼ -equivalent toy-bar -bar x+z-bar -bar y+ax 3 y-bar -bar z,with a 0, and analytically prove the existence of Sil'nikov bifurcation, and then of the strange attractor for certain subfamilies of the nonsymmetric versal unfoldings of this singularity under some conditions
Quantitative angiography methods for bifurcation lesions
Collet, Carlos; Onuma, Yoshinobu; Cavalcante, Rafael
2017-01-01
Bifurcation lesions represent one of the most challenging lesion subsets in interventional cardiology. The European Bifurcation Club (EBC) is an academic consortium whose goal has been to assess and recommend the appropriate strategies to manage bifurcation lesions. The quantitative coronary...... angiography (QCA) methods for the evaluation of bifurcation lesions have been subject to extensive research. Single-vessel QCA has been shown to be inaccurate for the assessment of bifurcation lesion dimensions. For this reason, dedicated bifurcation software has been developed and validated. These software...
Stochastic stability and bifurcation in a macroeconomic model
Li Wei; Xu Wei; Zhao Junfeng; Jin Yanfei
2007-01-01
On the basis of the work of Goodwin and Puu, a new business cycle model subject to a stochastically parametric excitation is derived in this paper. At first, we reduce the model to a one-dimensional diffusion process by applying the stochastic averaging method of quasi-nonintegrable Hamiltonian system. Secondly, we utilize the methods of Lyapunov exponent and boundary classification associated with diffusion process respectively to analyze the stochastic stability of the trivial solution of system. The numerical results obtained illustrate that the trivial solution of system must be globally stable if it is locally stable in the state space. Thirdly, we explore the stochastic Hopf bifurcation of the business cycle model according to the qualitative changes in stationary probability density of system response. It is concluded that the stochastic Hopf bifurcation occurs at two critical parametric values. Finally, some explanations are given in a simply way on the potential applications of stochastic stability and bifurcation analysis
Duijm, Nijs Jan
2008-01-01
Safety-barrier diagrams and the related so-called 'bow-tie' diagrams have become popular methods in risk analysis. This paper describes the syntax and principles for constructing consistent and valid safety-barrier diagrams. The relation of safety-barrier diagrams to other methods such as fault...... trees and Bayesian networks is discussed. A simple method for quantification of safety-barrier diagrams is proposed. It is concluded that safety-barrier diagrams provide a useful framework for an electronic data structure that integrates information from risk analysis with operational safety management....
Pierce instability and bifurcating equilibria
Godfrey, B.B.
1981-01-01
The report investigates the connection between equilibrium bifurcations and occurrence of the Pierce instability. Electrons flowing from one ground plane to a second through an ion background possess a countable infinity of static equilibria, of which only one is uniform and force-free. Degeneracy of the uniform and simplest non-uniform equilibria at a certain ground plan separation marks the onset of the Pierce instability, based on a newly derived dispersion relation appropriate to all the equilibria. For large ground plane separations the uniform equilibrium is unstable and the non-uniform equilibrium is stable, the reverse of their stability properties at small separations. Onset of the Pierce instability at the first bifurcation of equilibria persists in more complicated geometries, providing a general criterion for marginal stability. It seems probable that bifurcation analysis can be a useful tool in the overall study of stable beam generation in diodes and transport in finite cavities
Introduction to Feynman diagrams
Bilenky, Samoil Mikhelevich
1974-01-01
Introduction to Feynman Diagrams provides Feynman diagram techniques and methods for calculating quantities measured experimentally. The book discusses topics Feynman diagrams intended for experimental physicists. Topics presented include methods for calculating the matrix elements (by perturbation theory) and the basic rules for constructing Feynman diagrams; techniques for calculating cross sections and polarizations; processes in which both leptons and hadrons take part; and the electromagnetic and weak form factors of nucleons. Experimental physicists and graduate students of physics will
Homoclinic bifurcation in Chua's circuit
spiking and bursting behaviors of neurons. Recent experiments ... a limit cycle increases in a wiggle with alternate sequences of stable and unstable orbits via ... further changes in parameter, the system shows period-adding bifurcation when .... [21–23] transition from limit cycle to single scroll chaos via PD and then to alter-.
Bifurcation scenarios for bubbling transition.
Zimin, Aleksey V; Hunt, Brian R; Ott, Edward
2003-01-01
Dynamical systems with chaos on an invariant submanifold can exhibit a type of behavior called bubbling, whereby a small random or fixed perturbation to the system induces intermittent bursting. The bifurcation to bubbling occurs when a periodic orbit embedded in the chaotic attractor in the invariant manifold becomes unstable to perturbations transverse to the invariant manifold. Generically the periodic orbit can become transversely unstable through a pitchfork, transcritical, period-doubling, or Hopf bifurcation. In this paper a unified treatment of the four types of bubbling bifurcation is presented. Conditions are obtained determining whether the transition to bubbling is soft or hard; that is, whether the maximum burst amplitude varies continuously or discontinuously with variation of the parameter through its critical value. For soft bubbling transitions, the scaling of the maximum burst amplitude with the parameter is derived. For both hard and soft transitions the scaling of the average interburst time with the bifurcation parameter is deduced. Both random (noise) and fixed (mismatch) perturbations are considered. Results of numerical experiments testing our theoretical predictions are presented.
Bifurcation of steady tearing states
Saramito, B.; Maschke, E.K.
1985-10-01
We apply the bifurcation theory for compact operators to the problem of the nonlinear solutions of the 3-dimensional incompressible visco-resistive MHD equations. For the plane plasma slab model we compute branches of nonlinear tearing modes, which are stationary for the range of parameters investigated up to now
Bifurcation theory of ac electric arcing
Christen, Thomas; Peinke, Emanuel
2012-01-01
The performance of alternating current (ac) electric arcing devices is related to arc extinction or its re-ignition at zero crossings of the current (so-called ‘current zero’, CZ). Theoretical investigations thus usually focus on the transient behaviour of arcs near CZ, e.g. by solving the modelling differential equations in the vicinity of CZ. This paper proposes as an alternative approach to investigate global mathematical properties of the underlying periodically driven dynamic system describing the electric circuit containing the arcing device. For instance, the uniqueness of the trivial solution associated with the insulating state indicates the extinction of any arc. The existence of non-trivial attractors (typically a time-periodic state) points to a re-ignition of certain arcs. The performance regions of arcing devices, such as circuit breakers and arc torches, can thus be identified with the regions of absence and existence, respectively, of non-trivial attractors. Most important for applications, the boundary of a performance region in the model parameter space is then associated with the bifurcation of the non-trivial attractors. The concept is illustrated for simple black-box arc models, such as the Mayr and the Cassie model, by calculating for various cases the performance boundaries associated with the bifurcation of ac arcs. (paper)
Bifurcation structures of a cobweb model with memory and competing technologies
Agliari, Anna; Naimzada, Ahmad; Pecora, Nicolò
2018-05-01
In this paper we study a simple model based on the cobweb demand-supply framework with costly innovators and free imitators. The evolutionary selection between technologies depends on a performance measure which is related to the degree of memory. The resulting dynamics is described by a two-dimensional map. The map has a fixed point which may lose stability either via supercritical Neimark-Sacker bifurcation or flip bifurcation and several multistability situations exist. We describe some sequences of global bifurcations involving attracting and repelling closed invariant curves. These bifurcations, characterized by the creation of homoclinic connections or homoclinic tangles, are described through several numerical simulations. Particular bifurcation phenomena are also observed when the parameters are selected inside a periodicity region.
Duijm, Nijs Jan
2007-01-01
Safety-barrier diagrams and the related so-called "bow-tie" diagrams have become popular methods in risk analysis. This paper describes the syntax and principles for constructing consistent and valid safety-barrier diagrams. The relation with other methods such as fault trees and Bayesian networks...... are discussed. A simple method for quantification of safety-barrier diagrams is proposed, including situations where safety barriers depend on shared common elements. It is concluded that safety-barrier diagrams provide a useful framework for an electronic data structure that integrates information from risk...... analysis with operational safety management....
On the analysis of local bifurcation and topological horseshoe of a new 4D hyper-chaotic system
Zhou, Leilei; Chen, Zengqiang; Wang, Zhonglin; Wang, Jiezhi
2016-01-01
Highlights: • A new 4D smooth quadratic autonomous system with complex hyper-chaotic dynamics is presented. • The stability of equilibria is observed near the bifurcation points. • The Hopf bifurcation and pitchfork bifurcation are analyzed by using the center manifold theorem and bifurcation theory. • A horseshoe with two-directional expansions in the 4D hyper-chaotic system has been found, which rigorously proves the existence of hyper-chaos in theory. - Abstract: In this paper, a new four-dimensional (4D) smooth quadratic autonomous system with complex hyper-chaotic dynamics is presented and analyzed. The Lyapunov exponent (LE) spectrum, bifurcation diagram and various phase portraits of the system are provided. The stability, Hopf bifurcation and pitchfork bifurcation of equilibrium point are discussed by using the center manifold theorem and bifurcation theory. Numerical simulation results are consistent with the theoretical analysis. Besides, by combining the topological horseshoe theory with a computer-assisted method of Poincaré maps and utilizing the algorithm for finding horseshoes in 3D hyper-chaotic maps, a horseshoe with two-directional expansions in the 4D hyper-chaotic system is successfully found, which rigorously proves the existence of hyper-chaos in theory.
Streamline Patterns and their Bifurcations near a wall with Navier slip Boundary Conditions
Tophøj, Laust; Møller, Søren; Brøns, Morten
2006-01-01
We consider the two-dimensional topology of streamlines near a surface where the Navier slip boundary condition applies. Using transformations to bring the streamfunction in a simple normal form, we obtain bifurcation diagrams of streamline patterns under variation of one or two external parameters....... Topologically, these are identical with the ones previously found for no-slip surfaces. We use the theory to analyze the Stokes flow inside a circle, and show how it can be used to predict new bifurcation phenomena. ©2006 American Institute of Physics...
Bifurcation structures and transient chaos in a four-dimensional Chua model
Hoff, Anderson, E-mail: hoffande@gmail.com; Silva, Denilson T. da; Manchein, Cesar, E-mail: cesar.manchein@udesc.br; Albuquerque, Holokx A., E-mail: holokx.albuquerque@udesc.br
2014-01-10
A four-dimensional four-parameter Chua model with cubic nonlinearity is studied applying numerical continuation and numerical solutions methods. Regarding numerical solution methods, its dynamics is characterized on Lyapunov and isoperiodic diagrams and regarding numerical continuation method, the bifurcation curves are obtained. Combining both methods the bifurcation structures of the model were obtained with the possibility to describe the shrimp-shaped domains and their endoskeletons. We study the effect of a parameter that controls the dimension of the system leading the model to present transient chaos with its corresponding basin of attraction being riddled.
Vortex Breakdown Generated by off-axis Bifurcation in a cylinder with rotating covers
Bisgaard, Anders; Brøns, Morten; Sørensen, Jens Nørkær
2006-01-01
Vortex breakdown of bubble type is studied for the flow in a cylinder with rotating top and bottom covers. For large ratios of the angular velocities of the covers, we observe numerically that the vortex breakdown bubble in the steady regime may occur through the creation of an off-axis vortex ring....... This scenario does not occur in existing bifurcation theory based on a simple degeneracy in the flow field. We extend the theory to cover a non-simple degeneracy, and derive the associated bifurcation diagrams. We show that the vortex breakdown scenario involving a vortex ring can be explained from this theory...
Bifurcations and degenerate periodic points in a three dimensional chaotic fluid flow
Smith, L. D.; Rudman, M.; Lester, D. R.; Metcalfe, G.
2016-01-01
Analysis of the periodic points of a conservative periodic dynamical system uncovers the basic kinematic structure of the transport dynamics and identifies regions of local stability or chaos. While elliptic and hyperbolic points typically govern such behaviour in 3D systems, degenerate (parabolic) points also play an important role. These points represent a bifurcation in local stability and Lagrangian topology. In this study, we consider the ramifications of the two types of degenerate periodic points that occur in a model 3D fluid flow. (1) Period-tripling bifurcations occur when the local rotation angle associated with elliptic points is reversed, creating a reversal in the orientation of associated Lagrangian structures. Even though a single unstable point is created, the bifurcation in local stability has a large influence on local transport and the global arrangement of manifolds as the unstable degenerate point has three stable and three unstable directions, similar to hyperbolic points, and occurs at the intersection of three hyperbolic periodic lines. The presence of period-tripling bifurcation points indicates regions of both chaos and confinement, with the extent of each depending on the nature of the associated manifold intersections. (2) The second type of bifurcation occurs when periodic lines become tangent to local or global invariant surfaces. This bifurcation creates both saddle–centre bifurcations which can create both chaotic and stable regions, and period-doubling bifurcations which are a common route to chaos in 2D systems. We provide conditions for the occurrence of these tangent bifurcations in 3D conservative systems, as well as constraints on the possible types of tangent bifurcation that can occur based on topological considerations.
Bifurcation in a buoyant horizontal laminar jet
Arakeri, Jaywant H.; Das, Debopam; Srinivasan, J.
2000-06-01
The trajectory of a laminar buoyant jet discharged horizontally has been studied. The experimental observations were based on the injection of pure water into a brine solution. Under certain conditions the jet has been found to undergo bifurcation. The bifurcation of the jet occurs in a limited domain of Grashof number and Reynolds number. The regions in which the bifurcation occurs has been mapped in the Reynolds number Grashof number plane. There are three regions where bifurcation does not occur. The various mechanisms that prevent bifurcation have been proposed.
Luo, G.W.; Lv, X.H.; Ma, L.
2008-01-01
A two-degree-of-freedom plastic impact oscillator with a frictional slider is considered. Dynamics of the plastic impact oscillator are analyzed by a three-dimensional map, which describes free flight and sticking solutions of two masses of the system, between impacts, supplemented by transition conditions at the instants of impacts. Piecewise property and singularity are found to exist in the impact Poincare map. The piecewise property of the map is caused by the transitions of free flight and sticking motions of two masses immediately after the impact, and the singularity of the map is generated via the grazing contact of two masses immediately before the impact. These properties of the map have been shown to exhibit particular types of sliding and grazing bifurcations of periodic-impact motions under parameter variation. The influence of piecewise property, grazing singularity and parameter variation on dynamics of the vibro-impact system is analyzed. The global bifurcation diagrams of before-impact velocity as a function of the excitation frequency are plotted to predict much of the qualitative behavior of the system. The global bifurcations of period-N single-impact motions of the plastic impact oscillator are found to exhibit extensive and systematic characteristics. Dynamics of the impact oscillator, in the elastic impact case, is also analyzed. This type of impact is modelled by using the conditions of conservation of momentum and an instantaneous coefficient of restitution rule. The differences in periodic-impact motions and bifurcations are found by making a comparison between dynamic behaviors of the plastic and elastic impact oscillators with a frictional slider. The best progression of the plastic impact oscillator is found to occur in period-1 single-impact sticking motion with large impact velocity. The largest progression of the elastic impact oscillator occurs in period-1 multi-impact motion. The simulative results show that the plastic impact
Hajihosseini, Amirhossein; Maleki, Farzaneh; Rokni Lamooki, Gholam Reza
2011-01-01
Highlights: → We construct a recurrent neural network by generalizing a specific n-neuron network. → Several codimension 1 and 2 bifurcations take place in the newly constructed network. → The newly constructed network has higher capabilities to learn periodic signals. → The normal form theorem is applied to investigate dynamics of the network. → A series of bifurcation diagrams is given to support theoretical results. - Abstract: A class of recurrent neural networks is constructed by generalizing a specific class of n-neuron networks. It is shown that the newly constructed network experiences generic pitchfork and Hopf codimension one bifurcations. It is also proved that the emergence of generic Bogdanov-Takens, pitchfork-Hopf and Hopf-Hopf codimension two, and the degenerate Bogdanov-Takens bifurcation points in the parameter space is possible due to the intersections of codimension one bifurcation curves. The occurrence of bifurcations of higher codimensions significantly increases the capability of the newly constructed recurrent neural network to learn broader families of periodic signals.
Experiments on vibration-driven stick-slip locomotion: A sliding bifurcation perspective
Du, Zhouwei; Fang, Hongbin; Zhan, Xiong; Xu, Jian
2018-05-01
Dry friction appears at the contact interface between two surfaces and is the source of stick-slip vibrations. Instead of being a negative factor, dry friction is essential for vibration-driven locomotion system to take effect. However, the dry-friction-induced stick-slip locomotion has not been fully understood in previous research, especially in terms of experiments. In this paper, we experimentally study the stick-slip dynamics of a vibration-driven locomotion system from a sliding bifurcation perspective. To this end, we first design and build a vibration-driven locomotion prototype based on an internal piezoelectric cantilever. By utilizing the mechanical resonance, the small piezoelectric deformation is significantly amplified to drive the prototype to achieve effective locomotion. Through identifying the stick-slip characteristics in velocity histories, we could categorize the system's locomotion into four types and obtain a stick-slip categorization diagram. In each zone of the diagram the locomotion exhibits qualitatively different stick-slip dynamics. Such categorization diagram is actually a sliding bifurcation diagram; crossing from one stick-slip zone to another corresponds to the triggering of a sliding bifurcation. In addition, a simplified single degree-of-freedom model is established, with the rationality of simplification been explained theoretically and numerically. Based on the equivalent model, a numerical stick-slip categorization is also obtained, which shows good agreement with the experiments both qualitatively and quantitatively. To the best of our knowledge, this is the first work that experimentally generates a sliding bifurcation diagram. The obtained stick-slip categorizations deepen our understanding of stick-slip dynamics in vibration-driven systems and could serve as a base for system design and optimization.
Bifurcation Control of an Electrostatically-Actuated MEMS Actuator with Time-Delay Feedback
Lei Li
2016-10-01
Full Text Available The parametric excitation system consisting of a flexible beam and shuttle mass widely exists in microelectromechanical systems (MEMS, which can exhibit rich nonlinear dynamic behaviors. This article aims to theoretically investigate the nonlinear jumping phenomena and bifurcation conditions of a class of electrostatically-driven MEMS actuators with a time-delay feedback controller. Considering the comb structure consisting of a flexible beam and shuttle mass, the partial differential governing equation is obtained with both the linear and cubic nonlinear parametric excitation. Then, the method of multiple scales is introduced to obtain a slow flow that is analyzed for stability and bifurcation. Results show that time-delay feedback can improve resonance frequency and stability of the system. What is more, through a detailed mathematical analysis, the discriminant of Hopf bifurcation is theoretically derived, and appropriate time-delay feedback force can make the branch from the Hopf bifurcation point stable under any driving voltage value. Meanwhile, through global bifurcation analysis and saddle node bifurcation analysis, theoretical expressions about the system parameter space and maximum amplitude of monostable vibration are deduced. It is found that the disappearance of the global bifurcation point means the emergence of monostable vibration. Finally, detailed numerical results confirm the analytical prediction.
Bifurcation routes and economic stability
Vošvrda, Miloslav
2001-01-01
Roč. 8, č. 14 (2001), s. 43-59 ISSN 1212-074X R&D Projects: GA ČR GA402/00/0439; GA ČR GA402/01/0034; GA ČR GA402/01/0539 Institutional research plan: AV0Z1075907 Keywords : macroeconomic stability * foreign investment phenomenon * the Hopf bifurcation Subject RIV: AH - Economics
Yan-Ke Du
2013-09-01
Full Text Available We study a class of discrete-time bidirectional ring neural network model with delay. We discuss the asymptotic stability of the origin and the existence of Neimark-Sacker bifurcations, by analyzing the corresponding characteristic equation. Employing M-matrix theory and the Lyapunov functional method, global asymptotic stability of the origin is derived. Applying the normal form theory and the center manifold theorem, the direction of the Neimark-Sacker bifurcation and the stability of bifurcating periodic solutions are obtained. Numerical simulations are given to illustrate the main results.
Gap Dependent Bifurcation Behavior of a Nano-Beam Subjected to a Nonlinear Electrostatic Pressure
Mohammad Fathalilou
Full Text Available This paper presents a study on the gap dependent bifurcation behavior of an electro statically-actuated nano-beam. The sizedependent behavior of the beam was taken into account by applying the couple stress theory. Two small and large gap distance regimes have been considered in which the intermolecular vdW and Casimir forces are dominant, respectively. It has been shown that changing the gap size can affect the fundamental frequency of the beam. The bifurcation diagrams for small gap distance revealed that by changing the gap size, the number and type of the fixed points can change. However, for large gap regime, where the Casimir force is the dominant intermolecular force, changing the gap size does not affect the quality of the bifurcation behavior.
Multiple-parameter bifurcation analysis in a Kuramoto model with time delay and distributed shear
Niu, Ben; Zhang, Jiaming; Wei, Junjie
2018-05-01
In this paper, time delay effect and distributed shear are considered in the Kuramoto model. On the Ott-Antonsen's manifold, through analyzing the associated characteristic equation of the reduced functional differential equation, the stability boundary of the incoherent state is derived in multiple-parameter space. Moreover, very rich dynamical behavior such as stability switches inducing synchronization switches can occur in this equation. With the loss of stability, Hopf bifurcating coherent states arise, and the criticality of Hopf bifurcations is determined by applying the normal form theory and the center manifold theorem. On one hand, theoretical analysis indicates that the width of shear distribution and time delay can both eliminate the synchronization then lead the Kuramoto model to incoherence. On the other, time delay can induce several coexisting coherent states. Finally, some numerical simulations are given to support the obtained results where several bifurcation diagrams are drawn, and the effect of time delay and shear is discussed.
Phase-flip bifurcation in a coupled Josephson junction neuron system
Segall, Kenneth, E-mail: ksegall@colgate.edu [Department of Physics and Astronomy, Colgate University, Hamilton, NY 13346 (United States); Guo, Siyang; Crotty, Patrick [Department of Physics and Astronomy, Colgate University, Hamilton, NY 13346 (United States); Schult, Dan [Department of Mathematics, Colgate University, Hamilton, NY 13346 (United States); Miller, Max [Department of Physics and Astronomy, Colgate University, Hamilton, NY 13346 (United States)
2014-12-15
Aiming to understand group behaviors and dynamics of neural networks, we have previously proposed the Josephson junction neuron (JJ neuron) as a fast analog model that mimics a biological neuron using superconducting Josephson junctions. In this study, we further analyze the dynamics of the JJ neuron numerically by coupling one JJ neuron to another. In this coupled system we observe a phase-flip bifurcation, where the neurons synchronize out-of-phase at weak coupling and in-phase at strong coupling. We verify this by simulation of the circuit equations and construct a bifurcation diagram for varying coupling strength using the phase response curve and spike phase difference map. The phase-flip bifurcation could be observed experimentally using standard digital superconducting circuitry.
Li, Chengyuan; Deng, Licai; de Grijs, Richard; Jiang, Dengkai; Xin, Yu
2018-03-01
The bifurcated patterns in the color–magnitude diagrams of blue straggler stars (BSSs) have attracted significant attention. This type of special (but rare) pattern of two distinct blue straggler sequences is commonly interpreted as evidence that cluster core-collapse-driven stellar collisions are an efficient formation mechanism. Here, we report the detection of a bifurcated blue straggler distribution in a young Large Magellanic Cloud cluster, NGC 2173. Because of the cluster’s low central stellar number density and its young age, dynamical analysis shows that stellar collisions alone cannot explain the observed BSSs. Therefore, binary evolution is instead the most viable explanation of the origin of these BSSs. However, the reason why binary evolution would render the color–magnitude distribution of BSSs bifurcated remains unclear. C. Li, L. Deng, and R. de Grijs jointly designed this project.
Phase-flip bifurcation in a coupled Josephson junction neuron system
Segall, Kenneth; Guo, Siyang; Crotty, Patrick; Schult, Dan; Miller, Max
2014-01-01
Aiming to understand group behaviors and dynamics of neural networks, we have previously proposed the Josephson junction neuron (JJ neuron) as a fast analog model that mimics a biological neuron using superconducting Josephson junctions. In this study, we further analyze the dynamics of the JJ neuron numerically by coupling one JJ neuron to another. In this coupled system we observe a phase-flip bifurcation, where the neurons synchronize out-of-phase at weak coupling and in-phase at strong coupling. We verify this by simulation of the circuit equations and construct a bifurcation diagram for varying coupling strength using the phase response curve and spike phase difference map. The phase-flip bifurcation could be observed experimentally using standard digital superconducting circuitry
Bifurcation analysis on a delayed SIS epidemic model with stage structure
Kejun Zhuang
2007-05-01
Full Text Available In this paper, a delayed SIS (Susceptible Infectious Susceptible model with stage structure is investigated. We study the Hopf bifurcations and stability of the model. Applying the normal form theory and the center manifold argument, we derive the explicit formulas determining the properties of the bifurcating periodic solutions. The conditions to guarantee the global existence of periodic solutions are established. Also some numerical simulations for supporting the theoretical are given.
Resonant Homoclinic Flips Bifurcation in Principal Eigendirections
Tiansi Zhang
2013-01-01
Full Text Available A codimension-4 homoclinic bifurcation with one orbit flip and one inclination flip at principal eigenvalue direction resonance is considered. By introducing a local active coordinate system in some small neighborhood of homoclinic orbit, we get the Poincaré return map and the bifurcation equation. A detailed investigation produces the number and the existence of 1-homoclinic orbit, 1-periodic orbit, and double 1-periodic orbits. We also locate their bifurcation surfaces in certain regions.
Agliari, Anna
2006-01-01
In this paper we study some global bifurcations arising in the Puu's oligopoly model when we assume that the producers do not adjust to the best reply but use an adaptive process to obtain at each step the new production. Such bifurcations cause the appearance of a pair of closed invariant curves, one attracting and one repelling, this latter being involved in the subcritical Neimark bifurcation of the Cournot equilibrium point. The aim of the paper is to highlight the relationship between the global bifurcations causing the appearance/disappearance of two invariant closed curves and the homoclinic connections of some saddle cycle, already conjectured in [Agliari A, Gardini L, Puu T. Some global bifurcations related to the appearance of closed invariant curves. Comput Math Simul 2005;68:201-19]. We refine the results obtained in such a paper, showing that the appearance/disappearance of closed invariant curves is not necessarily related to the existence of an attracting cycle. The characterization of the periodicity tongues (i.e. a region of the parameter space in which an attracting cycle exists) associated with a subcritical Neimark bifurcation is also discussed
Sergievskiy Maxim
2018-01-01
Full Text Available Most of object-oriented development technologies rely on the use of the universal modeling language UML; class diagrams play a very important role in the design process play, used to build a software system model. Modern CASE tools, which are the basic tools for object-oriented development, can’t be used to optimize UML diagrams. In this manuscript we will explain how, based on the use of design patterns and anti-patterns, class diagrams could be verified and optimized. Certain transformations can be carried out automatically; in other cases, potential inefficiencies will be indicated and recommendations given. This study also discusses additional CASE tools for validating and optimizing of UML class diagrams. For this purpose, a plugin has been developed that analyzes an XMI file containing a description of class diagrams.
Hockney, Roger
1987-01-01
Algorithmic phase diagrams are a neat and compact representation of the results of comparing the execution time of several algorithms for the solution of the same problem. As an example, the recent results are shown of Gannon and Van Rosendale on the solution of multiple tridiagonal systems of equations in the form of such diagrams. The act of preparing these diagrams has revealed an unexpectedly complex relationship between the best algorithm and the number and size of the tridiagonal systems, which was not evident from the algebraic formulae in the original paper. Even so, for a particular computer, one diagram suffices to predict the best algorithm for all problems that are likely to be encountered the prediction being read directly from the diagram without complex calculation.
Towards classification of the bifurcation structure of a spherical cavitation bubble.
Behnia, Sohrab; Sojahrood, Amin Jafari; Soltanpoor, Wiria; Sarkhosh, Leila
2009-12-01
We focus on a single cavitation bubble driven by ultrasound, a system which is a specimen of forced nonlinear oscillators and is characterized by its extreme sensitivity to the initial conditions. The driven radial oscillations of the bubble are considered to be implicated by the principles of chaos physics and owing to specific ranges of control parameters, can be periodic or chaotic. Despite the growing number of investigations on its dynamics, there is not yet an inclusive yardstick to sort the dynamical behavior of the bubble into classes; also, the response oscillations are so complex that long term prediction on the behavior becomes difficult to accomplish. In this study, the nonlinear dynamics of a bubble oscillator was treated numerically and the simulations were proceeded with bifurcation diagrams. The calculated bifurcation diagrams were compared in an attempt to classify the bubble dynamic characteristics when varying the control parameters. The comparison reveals distinctive bifurcation patterns as a consequence of driving the systems with unequal ratios of R(0)lambda (where R(0) is the bubble initial radius and lambda is the wavelength of the driving ultrasonic wave). Results indicated that systems having the equal ratio of R(0)lambda, share remarkable similarities in their bifurcating behavior and can be classified under a unit category.
[Identification of meridian-acupoint diagrams and meridian diagrams].
Shen, Wei-hong
2008-08-01
In acu-moxibustion literature, there are two kinds of diagrams, meridian-acupoint diagrams and meridian diagrams. Because they are very similar in outline, and people now have seldom seen the typical ancient meridian diagrams, meridian-acupoint diagrams have been being incorrectly considered to be the meridian diagrams for a long time. It results in confusion in acu-moxibustion academia. The present paper stresses its importance in academic research and introduces some methods for identifying them correctly. The key points for identification of meridian-acupoint diagrams and meridian diagrams are: the legend of diagrams and the drawing style of the ancient charts. In addition, the author makes a detailed explanation about some acu-moxibustion charts which are easily confused. In order to distinguish meridian-acupoint diagrams and meridian diagrams correctly, he or she shoulnd understand the diagrams' intrinsic information as much as possible and make a comprehensive analysis about them.
Bifurcation Analysis with Aerodynamic-Structure Uncertainties by the Nonintrusive PCE Method
Linpeng Wang
2017-01-01
Full Text Available An aeroelastic model for airfoil with a third-order stiffness in both pitch and plunge degree of freedom (DOF and the modified Leishman–Beddoes (LB model were built and validated. The nonintrusive polynomial chaos expansion (PCE based on tensor product is applied to quantify the uncertainty of aerodynamic and structure parameters on the aerodynamic force and aeroelastic behavior. The uncertain limit cycle oscillation (LCO and bifurcation are simulated in the time domain with the stochastic PCE method. Bifurcation diagrams with uncertainties were quantified. The Monte Carlo simulation (MCS is also applied for comparison. From the current work, it can be concluded that the nonintrusive polynomial chaos expansion can give an acceptable accuracy and have a much higher calculation efficiency than MCS. For aerodynamic model, uncertainties of aerodynamic parameters affect the aerodynamic force significantly at the stage from separation to stall at upstroke and at the stage from stall to reattach at return. For aeroelastic model, both uncertainties of aerodynamic parameters and structure parameters impact bifurcation position. Structure uncertainty of parameters is more sensitive for bifurcation. When the nonlinear stall flutter and bifurcation are concerned, more attention should be paid to the separation process of aerodynamics and parameters about pitch DOF in structure.
Bifurcations and Chaos of AN Immersed Cantilever Beam in a Fluid and Carrying AN Intermediate Mass
AL-QAISIA, A. A.; HAMDAN, M. N.
2002-06-01
The concern of this work is the local stability and period-doubling bifurcations of the response to a transverse harmonic excitation of a slender cantilever beam partially immersed in a fluid and carrying an intermediate lumped mass. The unimodal form of the non-linear dynamic model describing the beam-mass in-plane large-amplitude flexural vibration, which accounts for axial inertia, non-linear curvature and inextensibility condition, developed in Al-Qaisia et al. (2000Shock and Vibration7 , 179-194), is analyzed and studied for the resonance responses of the first three modes of vibration, using two-term harmonic balance method. Then a consistent second order stability analysis of the associated linearized variational equation is carried out using approximate methods to predict the zones of symmetry breaking leading to period-doubling bifurcation and chaos on the resonance response curves. The results of the present work are verified for selected physical system parameters by numerical simulations using methods of the qualitative theory, and good agreement was obtained between the analytical and numerical results. Also, analytical prediction of the period-doubling bifurcation and chaos boundaries obtained using a period-doubling bifurcation criterion proposed in Al-Qaisia and Hamdan (2001 Journal of Sound and Vibration244, 453-479) are compared with those of computer simulations. In addition, results of the effect of fluid density, fluid depth, mass ratio, mass position and damping on the period-doubling bifurcation diagrams are studies and presented.
Efficient algorithm for bifurcation problems of variational inequalities
Mittelmann, H.D.
1983-01-01
For a class of variational inequalities on a Hilbert space H bifurcating solutions exist and may be characterized as critical points of a functional with respect to the intersection of the level surfaces of another functional and a closed convex subset K of H. In a recent paper [13] we have used a gradient-projection type algorithm to obtain the solutions for discretizations of the variational inequalities. A related but Newton-based method is given here. Global and asymptotically quadratic convergence is proved. Numerical results show that it may be used very efficiently in following the bifurcating branches and that is compares favorably with several other algorithms. The method is also attractive for a class of nonlinear eigenvalue problems (K = H) for which it reduces to a generalized Rayleigh-quotient interaction. So some results are included for the path following in turning-point problems
Voltage stability, bifurcation parameters and continuation methods
Alvarado, F L [Wisconsin Univ., Madison, WI (United States)
1994-12-31
This paper considers the importance of the choice of bifurcation parameter in the determination of the voltage stability limit and the maximum power load ability of a system. When the bifurcation parameter is power demand, the two limits are equivalent. However, when other types of load models and bifurcation parameters are considered, the two concepts differ. The continuation method is considered as a method for determination of voltage stability margins. Three variants of the continuation method are described: the continuation parameter is the bifurcation parameter the continuation parameter is initially the bifurcation parameter, but is free to change, and the continuation parameter is a new `arc length` parameter. Implementations of voltage stability software using continuation methods are described. (author) 23 refs., 9 figs.
Bifurcation from infinity and nodal solutions of quasilinear elliptic differential equations
Bian-Xia Yang
2014-01-01
Full Text Available In this article, we establish a unilateral global bifurcation theorem from infinity for a class of $N$-dimensional p-Laplacian problems. As an application, we study the global behavior of the components of nodal solutions of the problem $$\\displaylines{ \\operatorname{div}(\\varphi_p(\
Recent perspective on coronary artery bifurcation interventions.
Dash, Debabrata
2014-01-01
Coronary bifurcation lesions are frequent in routine practice, accounting for 15-20% of all lesions undergoing percutaneous coronary intervention (PCI). PCI of this subset of lesions is technically challenging and historically has been associated with lower procedural success rates and worse clinical outcomes compared with non-bifurcation lesions. The introduction of drug-eluting stents has dramatically improved the outcomes. The provisional technique of implanting one stent in the main branch remains the default approach in most bifurcation lesions. Selection of the most effective technique for an individual bifurcation is important. The use of two-stent techniques as an intention to treat is an acceptable approach in some bifurcation lesions. However, a large amount of metal is generally left unapposed in the lumen with complex two-stent techniques, which is particularly concerning for the risk of stent thrombosis. New technology and dedicated bifurcation stents may overcome some of the limitations of two-stent techniques and revolutionise the management of bifurcation PCI in the future.
Jianguo Ren
2014-01-01
Full Text Available A new computer virus propagation model with delay and incomplete antivirus ability is formulated and its global dynamics is analyzed. The existence and stability of the equilibria are investigated by resorting to the threshold value R0. By analysis, it is found that the model may undergo a Hopf bifurcation induced by the delay. Correspondingly, the critical value of the Hopf bifurcation is obtained. Using Lyapunov functional approach, it is proved that, under suitable conditions, the unique virus-free equilibrium is globally asymptotically stable if R01. Numerical examples are presented to illustrate possible behavioral scenarios of the mode.
Quantum entanglement and fixed-point bifurcations
Hines, Andrew P.; McKenzie, Ross H.; Milburn, G.J.
2005-01-01
How does the classical phase-space structure for a composite system relate to the entanglement characteristics of the corresponding quantum system? We demonstrate how the entanglement in nonlinear bipartite systems can be associated with a fixed-point bifurcation in the classical dynamics. Using the example of coupled giant spins we show that when a fixed point undergoes a supercritical pitchfork bifurcation, the corresponding quantum state--the ground state--achieves its maximum amount of entanglement near the critical point. We conjecture that this will be a generic feature of systems whose classical limit exhibits such a bifurcation
A case study in bifurcation theory
Khmou, Youssef
This short paper is focused on the bifurcation theory found in map functions called evolution functions that are used in dynamical systems. The most well-known example of discrete iterative function is the logistic map that puts into evidence bifurcation and chaotic behavior of the topology of the logistic function. We propose a new iterative function based on Lorentizan function and its generalized versions, based on numerical study, it is found that the bifurcation of the Lorentzian function is of second-order where it is characterized by the absence of chaotic region.
Bifurcations of non-smooth systems
Angulo, Fabiola; Olivar, Gerard; Osorio, Gustavo A.; Escobar, Carlos M.; Ferreira, Jocirei D.; Redondo, Johan M.
2012-12-01
Non-smooth systems (namely piecewise-smooth systems) have received much attention in the last decade. Many contributions in this area show that theory and applications (to electronic circuits, mechanical systems, …) are relevant to problems in science and engineering. Specially, new bifurcations have been reported in the literature, and this was the topic of this minisymposium. Thus both bifurcation theory and its applications were included. Several contributions from different fields show that non-smooth bifurcations are a hot topic in research. Thus in this paper the reader can find contributions from electronics, energy markets and population dynamics. Also, a carefully-written specific algebraic software tool is presented.
Multistability and gluing bifurcation to butterflies in coupled networks with non-monotonic feedback
Ma Jianfu; Wu Jianhong
2009-01-01
Neural networks with a non-monotonic activation function have been proposed to increase their capacity for memory storage and retrieval, but there is still a lack of rigorous mathematical analysis and detailed discussions of the impact of time lag. Here we consider a two-neuron recurrent network. We first show how supercritical pitchfork bifurcations and a saddle-node bifurcation lead to the coexistence of multiple stable equilibria (multistability) in the instantaneous updating network. We then study the effect of time delay on the local stability of these equilibria and show that four equilibria lose their stability at a certain critical value of time delay, and Hopf bifurcations of these equilibria occur simultaneously, leading to multiple coexisting periodic orbits. We apply centre manifold theory and normal form theory to determine the direction of these Hopf bifurcations and the stability of bifurcated periodic orbits. Numerical simulations show very interesting global patterns of periodic solutions as the time delay is varied. In particular, we observe that these four periodic solutions are glued together along the stable and unstable manifolds of saddle points to develop a butterfly structure through a complicated process of gluing bifurcations of periodic solutions
Diagrams of natural deductions
Popov, S V
1982-01-01
The concept of natural deductions was investigated by the author in his analysis of the complexity of deductions in propositional computations (1975). Here some natural deduction systems are considered, and an analytical procedure proposed which results in a deduction diagram for each system. Each diagram takes the form of an orientated, charge graph, features of which can be used to establish the equivalence of classes of deductions. For each of the natural deduction systems considered, a system of equivalent transformation schemes is derived, which is complete with respect to the given definition of equivalence. 2 references.
Bifurcation Control of Chaotic Dynamical Systems
Wang, Hua O; Abed, Eyad H
1992-01-01
A nonlinear system which exhibits bifurcations, transient chaos, and fully developed chaos is considered, with the goal of illustrating the role of two ideas in the control of chaotic dynamical systems...
Bifurcation structure of successive torus doubling
Sekikawa, Munehisa; Inaba, Naohiko; Yoshinaga, Tetsuya; Tsubouchi, Takashi
2006-01-01
The authors discuss the 'embryology' of successive torus doubling via the bifurcation theory, and assert that the coupled map of a logistic map and a circle map has a structure capable of generating infinite number of torus doublings
Markl, Martin
2002-01-01
Roč. 69, - (2002), s. 161-180 ISSN 0009-725X. [Winter School "Geometry and Physics" /21./. Srní, 13.01.2001-20.01.2001] R&D Projects: GA ČR GA201/99/0675 Keywords : colored operad%cofibrant model%homotopy diagram Subject RIV: BA - General Mathematics
Rosengrant, David
2011-01-01
Multiple representations are a valuable tool to help students learn and understand physics concepts. Furthermore, representations help students learn how to think and act like real scientists. These representations include: pictures, free-body diagrams, energy bar charts, electrical circuits, and, more recently, computer simulations and…
Equational binary decision diagrams
J.F. Groote (Jan Friso); J.C. van de Pol (Jaco)
2000-01-01
textabstractWe incorporate equations in binary decision diagrams (BDD). The resulting objects are called EQ-BDDs. A straightforward notion of ordered EQ-BDDs (EQ-OBDD) is defined, and it is proved that each EQ-BDD is logically equivalent to an EQ-OBDD. Moreover, on EQ-OBDDs satisfiability and
Lindenbergh, R.C.
2002-01-01
The classic Voronoi diagram of a configuration of distinct points in the plane associates to each point that part of the plane that is closer to the point than to any other point in the configuration. In this thesis we no longer require all points to be distinct. After the introduction in
Bifurcation structure and stability in models of opposite-signed vortex pairs
Luzzatto-Fegiz, Paolo, E-mail: Paolo.Luzzatto-Fegiz@damtp.cam.ac.uk [Churchill College, Cambridge CB3 0DS (United Kingdom)
2014-06-01
We employ a recently developed numerical method to examine in detail the properties of opposite-signed, translating vortex pairs. We first consider a uniform-vortex approximation; for this flow, previous studies have found essential differences between rotating and translating configurations, and have encountered numerical difficulties at the boundary between the two types of equilibria. Recently, Luzzatto-Fegiz and Williamson (2012 J. Fluid Mech. 706 323–50) used an imperfect velocity-impulse (IVI) diagram to show that the rotating pairs have a translating counterpart, arising from a bifurcation of the classical translating configurations. In this paper, we expand this IVI diagram to find two new branches of steady vortices, including antisymmetric pairs, as well as vortices without any symmetry. We next consider more realistic models for flows at moderate Reynolds number Re, by computing solution families based on a discretized Chaplygin–Lamb dipole. We find that, as the accuracy of the discretization improves, the bifurcated branches shrink rapidly, while the unstable portion of the basic solution family becomes smaller. These results indicate that the bifurcation structure of moderate-Re flows can be very different from that of solutions that use a single patch per vortex. (papers)
Bifurcation structure and stability in models of opposite-signed vortex pairs
Luzzatto-Fegiz, Paolo
2014-01-01
We employ a recently developed numerical method to examine in detail the properties of opposite-signed, translating vortex pairs. We first consider a uniform-vortex approximation; for this flow, previous studies have found essential differences between rotating and translating configurations, and have encountered numerical difficulties at the boundary between the two types of equilibria. Recently, Luzzatto-Fegiz and Williamson (2012 J. Fluid Mech. 706 323–50) used an imperfect velocity-impulse (IVI) diagram to show that the rotating pairs have a translating counterpart, arising from a bifurcation of the classical translating configurations. In this paper, we expand this IVI diagram to find two new branches of steady vortices, including antisymmetric pairs, as well as vortices without any symmetry. We next consider more realistic models for flows at moderate Reynolds number Re, by computing solution families based on a discretized Chaplygin–Lamb dipole. We find that, as the accuracy of the discretization improves, the bifurcated branches shrink rapidly, while the unstable portion of the basic solution family becomes smaller. These results indicate that the bifurcation structure of moderate-Re flows can be very different from that of solutions that use a single patch per vortex. (papers)
Evaluation of Forming Limit by the 3 Dimensional Local Bifurcation Theory
Nishimura, Ryuichi; Nakazawa, Yoshiaki; Ito, Koichi; Uemura, Gen; Mori, Naomichi
2007-01-01
A theoretical prediction and evaluation method for the sheet metal formability is developed on the basis of the three-dimensional local bifurcation theory previously proposed by authors. The forming limit diagram represented on the plane defined by the ratio of stress component to work-hardening rate is perfectly independent of plastic strain history. The upper and the lower limit of the sheet formability are indicated by the 3D critical line and the Stoeren-Rice's critical line on this plane, respectively. In order to verify the above mentioned behavior of the proposed forming limit diagram, the experimental research is also conducted. From the standpoint of the mechanical instability theory, a new concept called instability factor is introduced. It represents a degree of acceleration by current stress for developing the local bifurcation mode toward a fracture. The instability factor provides a method to evaluate a forming allowance which is useful to appropriate identification for a forming limit and to optimize the forming condition. The proposed criterion provides not only the moment to initiate the necking but also the local bifurcation mode vector and the direction of necking line
Hopf bifurcation in an Internet congestion control model
Li Chunguang; Chen Guanrong; Liao Xiaofeng; Yu Juebang
2004-01-01
We consider an Internet model with a single link accessed by a single source, which responds to congestion signals from the network, and study bifurcation of such a system. By choosing the gain parameter as a bifurcation parameter, we prove that Hopf bifurcation occurs. The stability of bifurcating periodic solutions and the direction of the Hopf bifurcation are determined by applying the normal form theory and the center manifold theorem. Finally, a numerical example is given to verify the theoretical analysis
Discretization analysis of bifurcation based nonlinear amplifiers
Feldkord, Sven; Reit, Marco; Mathis, Wolfgang
2017-09-01
Recently, for modeling biological amplification processes, nonlinear amplifiers based on the supercritical Andronov-Hopf bifurcation have been widely analyzed analytically. For technical realizations, digital systems have become the most relevant systems in signal processing applications. The underlying continuous-time systems are transferred to the discrete-time domain using numerical integration methods. Within this contribution, effects on the qualitative behavior of the Andronov-Hopf bifurcation based systems concerning numerical integration methods are analyzed. It is shown exemplarily that explicit Runge-Kutta methods transform the truncated normalform equation of the Andronov-Hopf bifurcation into the normalform equation of the Neimark-Sacker bifurcation. Dependent on the order of the integration method, higher order terms are added during this transformation.A rescaled normalform equation of the Neimark-Sacker bifurcation is introduced that allows a parametric design of a discrete-time system which corresponds to the rescaled Andronov-Hopf system. This system approximates the characteristics of the rescaled Hopf-type amplifier for a large range of parameters. The natural frequency and the peak amplitude are preserved for every set of parameters. The Neimark-Sacker bifurcation based systems avoid large computational effort that would be caused by applying higher order integration methods to the continuous-time normalform equations.
Bifurcation and chaos in high-frequency peak current mode Buck converter
Chang-Yuan, Chang; Xin, Zhao; Fan, Yang; Cheng-En, Wu
2016-07-01
Bifurcation and chaos in high-frequency peak current mode Buck converter working in continuous conduction mode (CCM) are studied in this paper. First of all, the two-dimensional discrete mapping model is established. Next, reference current at the period-doubling point and the border of inductor current are derived. Then, the bifurcation diagrams are drawn with the aid of MATLAB. Meanwhile, circuit simulations are executed with PSIM, and time domain waveforms as well as phase portraits in i L-v C plane are plotted with MATLAB on the basis of simulation data. After that, we construct the Jacobian matrix and analyze the stability of the system based on the roots of characteristic equations. Finally, the validity of theoretical analysis has been verified by circuit testing. The simulation and experimental results show that, with the increase of reference current I ref, the corresponding switching frequency f is approaching to low-frequency stage continuously when the period-doubling bifurcation happens, leading to the converter tending to be unstable. With the increase of f, the corresponding I ref decreases when the period-doubling bifurcation occurs, indicating the stable working range of the system becomes smaller. Project supported by the National Natural Science Foundation of China (Grant No. 61376029), the Fundamental Research Funds for the Central Universities, China, and the College Graduate Research and Innovation Program of Jiangsu Province, China (Grant No. SJLX15_0092).
Invariants, Attractors and Bifurcation in Two Dimensional Maps with Polynomial Interaction
Hacinliyan, Avadis Simon; Aybar, Orhan Ozgur; Aybar, Ilknur Kusbeyzi
This work will present an extended discrete-time analysis on maps and their generalizations including iteration in order to better understand the resulting enrichment of the bifurcation properties. The standard concepts of stability analysis and bifurcation theory for maps will be used. Both iterated maps and flows are used as models for chaotic behavior. It is well known that when flows are converted to maps by discretization, the equilibrium points remain the same but a richer bifurcation scheme is observed. For example, the logistic map has a very simple behavior as a differential equation but as a map fold and period doubling bifurcations are observed. A way to gain information about the global structure of the state space of a dynamical system is investigating invariant manifolds of saddle equilibrium points. Studying the intersections of the stable and unstable manifolds are essential for understanding the structure of a dynamical system. It has been known that the Lotka-Volterra map and systems that can be reduced to it or its generalizations in special cases involving local and polynomial interactions admit invariant manifolds. Bifurcation analysis of this map and its higher iterates can be done to understand the global structure of the system and the artifacts of the discretization by comparing with the corresponding results from the differential equation on which they are based.
Gritli, Hassène; Belghith, Safya
2017-06-01
An analysis of the passive dynamic walking of a compass-gait biped model under the OGY-based control approach using the impulsive hybrid nonlinear dynamics is presented in this paper. We describe our strategy for the development of a simplified analytical expression of a controlled hybrid Poincaré map and then for the design of a state-feedback control. Our control methodology is based mainly on the linearization of the impulsive hybrid nonlinear dynamics around a desired nominal one-periodic hybrid limit cycle. Our analysis of the controlled walking dynamics is achieved by means of bifurcation diagrams. Some interesting nonlinear phenomena are displayed, such as the period-doubling bifurcation, the cyclic-fold bifurcation, the period remerging, the period bubbling and chaos. A comparison between the raised phenomena in the impulsive hybrid nonlinear dynamics and the hybrid Poincaré map under control was also presented.
Geometrically Induced Interactions and Bifurcations
Binder, Bernd
2010-01-01
In order to evaluate the proper boundary conditions in spin dynamics eventually leading to the emergence of natural and artificial solitons providing for strong interactions and potentials with monopole charges, the paper outlines a new concept referring to a curvature-invariant formalism, where superintegrability is given by a special isometric condition. Instead of referring to the spin operators and Casimir/Euler invariants as the generator of rotations, a curvature-invariant description is introduced utilizing a double Gudermann mapping function (generator of sine Gordon solitons and Mercator projection) cross-relating two angular variables, where geometric phases and rotations arise between surfaces of different curvature. Applying this stereographic projection to a superintegrable Hamiltonian can directly map linear oscillators to Kepler/Coulomb potentials and/or monopoles with Pöschl-Teller potentials and vice versa. In this sense a large scale Kepler/Coulomb (gravitational, electro-magnetic) wave dynamics with a hyperbolic metric could be mapped as a geodesic vertex flow to a local oscillator singularity (Dirac monopole) with spherical metrics and vice versa. Attracting fixed points and dynamic constraints are given by special isometries with magic precession angles. The nonlinear angular encoding directly provides for a Shannon mutual information entropy measure of the geodesic phase space flow. The emerging monopole patterns show relations to spiral Fresnel holography and Berry/Aharonov-Bohm geometric phases subject to bifurcation instabilities and singularities from phase ambiguities due to a local (entropy) overload. Neutral solitons and virtual patterns emerging and mediating in the overlap region between charged or twisted holographic patterns are visualized and directly assigned to the Berry geometric phase revealing the role of photons, neutrons, and neutrinos binding repulsive charges in Coulomb, strong and weak interaction.
Øhrstrøm, Peter
2011-01-01
Some very good arguments can be given in favor of the Augustinean wisdom, according to which it is impossible to provide a satisfactory definition of the concept of time. However, even in the absence of a proper definition, it is possible to deal with conceptual problems regarding time. It can...... be done in terms of analogies and metaphors. In particular, it is attractive to make use of Peirce's diagrams by means of which various kinds of conceptual experimentation can be carried out. This paper investigates how Peircean diagrams can be used within the study of time. In particular, we discuss 1......) the topological properties of time, 2) the implicative structure in tense logic, 3) the notions of open future and branching time models, and finally 4) tenselogical alternatives to branching time models....
McCauley, T.M.; Eskinazi, M.; Henson, L.L.
1989-01-01
This paper discusses the changes in electrical document requirements that occur when construction is complete and a generating station starts commercial operation. The needs of operations and maintenance (O and M) personnel are analyzed and contrasted with those of construction to illustrate areas in which the construction documents (drawings, diagrams, and databases) are difficult to use for work at an operating station. The paper discusses the O and M electrical documents that the Arizona Nuclear Power Project (ANPP) believes are most beneficial for the three operating units at Palo Verde; these are control wiring diagrams and an associated document cross-reference list. The benefits offered by these new, station O and M-oriented documents are weighted against the cost of their creation and their impact on drawing maintenance
Wang, C.-C.; Jang, M.-J.; Yeh, Y.-L.
2007-01-01
This paper studies the bifurcation and nonlinear behaviors of a flexible rotor supported by relative short gas film bearings. A time-dependent mathematical model for gas journal bearings is presented. The finite difference method with successive over relation method is employed to solve the Reynolds' equation. The system state trajectory, Poincare maps, power spectra, and bifurcation diagrams are used to analyze the dynamic behavior of the rotor and journal center in the horizontal and vertical directions under different operating conditions. The analysis reveals a complex dynamic behavior comprising periodic and subharmonic response of the rotor and journal center. This paper shows how the dynamic behavior of this type of system varies with changes in rotor mass and rotational velocity. The results of this study contribute to a further understanding of the nonlinear dynamics of gas film rotor-bearing systems
Bifurcation and chaos of a new discrete fractional-order logistic map
Ji, YuanDong; Lai, Li; Zhong, SuChuan; Zhang, Lu
2018-04-01
The fractional-order discrete maps with chaotic behaviors based on the theory of ;fractional difference; are proposed in recent years. In this paper, instead of using fractional difference, a new fractionalized logistic map is proposed based on the numerical algorithm of fractional differentiation definition. The bifurcation diagrams of this map with various differential orders are given by numerical simulation. The simulation results show that the fractional-order logistic map derived in this manner holds rich dynamical behaviors because of its memory effect. In addition, new types of behaviors of bifurcation and chaos are found, which are different from those of the integer-order and the previous fractional-order logistic maps.
Wilms, R Scott [Los Alamos National Laboratory; Carlson, Bryan [Los Alamos National Laboratory; Coons, James [Los Alamos National Laboratory; Kubic, William [Los Alamos National Laboratory
2008-01-01
This presentation describes the development of the proposed Process Flow Diagram (PFD) for the Tokamak Exhaust Processing System (TEP) of ITER. A brief review of design efforts leading up to the PFD is followed by a description of the hydrogen-like, air-like, and waterlike processes. Two new design values are described; the mostcommon and most-demanding design values. The proposed PFD is shown to meet specifications under the most-common and mostdemanding design values.
Behan, Miles W; Holm, Niels Ramsing; Curzen, Nicholas P
2011-01-01
Background— Controversy persists regarding the correct strategy for bifurcation lesions. Therefore, we combined the patient-level data from 2 large trials with similar methodology: the NORDIC Bifurcation Study (NORDIC I) and the British Bifurcation Coronary Study (BBC ONE). Methods and Results— B...
Eisner, J.; Väth, Martin
2016-01-01
Roč. 135, April (2016), s. 158-193 ISSN 0362-546X Institutional support: RVO:67985840 Keywords : reaction-diffusion system * turing instability * global bifurcation Subject RIV: BA - General Mathematics Impact factor: 1.192, year: 2016 http://www.sciencedirect.com/science/article/pii/S0362546X16000146
Feynman diagram drawing made easy
Baillargeon, M.
1997-01-01
We present a drawing package optimised for Feynman diagrams. These can be constructed interactively with a mouse-driven graphical interface or from a script file, more suitable to work with a diagram generator. It provides most features encountered in Feynman diagrams and allows to modify every part of a diagram after its creation. Special attention has been paid to obtain a high quality printout as easily as possible. This package is written in Tcl/Tk and in C. (orig.)
Ring diagrams and phase transitions
Takahashi, K.
1986-01-01
Ring diagrams at finite temperatures carry most infrared-singular parts among Feynman diagrams. Their effect to effective potentials are in general so significant that one must incorporate them as well as 1-loop diagrams. The author expresses these circumstances in some examples of supercooled phase transitions
Automation of Feynman diagram evaluations
Tentyukov, M.N.
1998-01-01
A C-program DIANA (DIagram ANAlyser) for the automation of Feynman diagram evaluations is presented. It consists of two parts: the analyzer of diagrams and the interpreter of a special text manipulating language. This language can be used to create a source code for analytical or numerical evaluations and to keep the control of the process in general
Bifurcation analysis of a three dimensional system
Yongwen WANG
2018-04-01
Full Text Available In order to enrich the stability and bifurcation theory of the three dimensional chaotic systems, taking a quadratic truncate unfolding system with the triple singularity equilibrium as the research subject, the existence of the equilibrium, the stability and the bifurcation of the system near the equilibrium under different parametric conditions are studied. Using the method of mathematical analysis, the existence of the real roots of the corresponding characteristic equation under the different parametric conditions is analyzed, and the local manifolds of the equilibrium are gotten, then the possible bifurcations are guessed. The parametric conditions under which the equilibrium is saddle-focus are analyzed carefully by the Cardan formula. Moreover, the conditions of codimension-one Hopf bifucation and the prerequisites of the supercritical and subcritical Hopf bifurcation are found by computation. The results show that the system has abundant stability and bifurcation, and can also supply theorical support for the proof of the existence of the homoclinic or heteroclinic loop connecting saddle-focus and the Silnikov's chaos. This method can be extended to study the other higher nonlinear systems.
Bifurcations of Tumor-Immune Competition Systems with Delay
Ping Bi
2014-01-01
Full Text Available A tumor-immune competition model with delay is considered, which consists of two-dimensional nonlinear differential equation. The conditions for the linear stability of the equilibria are obtained by analyzing the distribution of eigenvalues. General formulas for the direction, period, and stability of the bifurcated periodic solutions are given for codimension one and codimension two bifurcations, including Hopf bifurcation, steady-state bifurcation, and B-T bifurcation. Numerical examples and simulations are given to illustrate the bifurcations analysis and obtained results.
Bifurcation and Stability in a Delayed Predator-Prey Model with Mixed Functional Responses
Yafia, R.; Aziz-Alaoui, M. A.; Merdan, H.; Tewa, J. J.
2015-06-01
The model analyzed in this paper is based on the model set forth by Aziz Alaoui et al. [Aziz Alaoui & Daher Okiye, 2003; Nindjin et al., 2006] with time delay, which describes the competition between the predator and prey. This model incorporates a modified version of the Leslie-Gower functional response as well as that of Beddington-DeAngelis. In this paper, we consider the model with one delay consisting of a unique nontrivial equilibrium E* and three others which are trivial. Their dynamics are studied in terms of local and global stabilities and of the description of Hopf bifurcation at E*. At the third trivial equilibrium, the existence of the Hopf bifurcation is proven as the delay (taken as a parameter of bifurcation) that crosses some critical values.
Attractors near grazing–sliding bifurcations
Glendinning, P; Kowalczyk, P; Nordmark, A B
2012-01-01
In this paper we prove, for the first time, that multistability can occur in three-dimensional Fillipov type flows due to grazing–sliding bifurcations. We do this by reducing the study of the dynamics of Filippov type flows around a grazing–sliding bifurcation to the study of appropriately defined one-dimensional maps. In particular, we prove the presence of three qualitatively different types of multiple attractors born in grazing–sliding bifurcations. Namely, a period-two orbit with a sliding segment may coexist with a chaotic attractor, two stable, period-two and period-three orbits with a segment of sliding each may coexist, or a non-sliding and period-three orbit with two sliding segments may coexist
Neimark-Sacker bifurcations and evidence of chaos in a discrete dynamical model of walkers
Rahman, Aminur; Blackmore, Denis
2016-01-01
Bouncing droplets on a vibrating fluid bath can exhibit wave-particle behavior, such as being propelled by interacting with its own wave field. These droplets seem to walk across the bath, and thus are dubbed walkers. Experiments have shown that walkers can exhibit exotic dynamical behavior indicative of chaos. While the integro-differential models developed for these systems agree well with the experiments, they are difficult to analyze mathematically. In recent years, simpler discrete dynamical models have been derived and studied numerically. The numerical simulations of these models show evidence of exotic dynamics such as period doubling bifurcations, Neimark–Sacker (N–S) bifurcations, and even chaos. For example, in [1], based on simulations Gilet conjectured the existence of a supercritical N-S bifurcation as the damping factor in his one- dimensional path model. We prove Gilet’s conjecture and more; in fact, both supercritical and subcritical (N-S) bifurcations are produced by separately varying the damping factor and wave-particle coupling for all eigenmode shapes. Then we compare our theoretical results with some previous and new numerical simulations, and find complete qualitative agreement. Furthermore, evidence of chaos is shown by numerically studying a global bifurcation.
Brandhuber, Andreas; Travaglini, Gabriele
2006-01-01
Over the past two years, the use of on-shell techniques has deepened our understanding of the S-matrix of gauge theories and led to the calculation of many new scattering amplitudes. In these notes we review a particular on-shell method developed recently, the quantum MHV diagrams, and discuss applications to one-loop amplitudes. Furthermore, we briefly discuss the application of D-dimensional generalised unitarity to the calculation of scattering amplitudes in non-supersymmetric Yang-Mills.
Barnett, William H; Cymbalyuk, Gennady S
2014-01-01
The dynamics of individual neurons are crucial for producing functional activity in neuronal networks. An open question is how temporal characteristics can be controlled in bursting activity and in transient neuronal responses to synaptic input. Bifurcation theory provides a framework to discover generic mechanisms addressing this question. We present a family of mechanisms organized around a global codimension-2 bifurcation. The cornerstone bifurcation is located at the intersection of the border between bursting and spiking and the border between bursting and silence. These borders correspond to the blue sky catastrophe bifurcation and the saddle-node bifurcation on an invariant circle (SNIC) curves, respectively. The cornerstone bifurcation satisfies the conditions for both the blue sky catastrophe and SNIC. The burst duration and interburst interval increase as the inverse of the square root of the difference between the corresponding bifurcation parameter and its bifurcation value. For a given set of burst duration and interburst interval, one can find the parameter values supporting these temporal characteristics. The cornerstone bifurcation also determines the responses of silent and spiking neurons. In a silent neuron with parameters close to the SNIC, a pulse of current triggers a single burst. In a spiking neuron with parameters close to the blue sky catastrophe, a pulse of current temporarily silences the neuron. These responses are stereotypical: the durations of the transient intervals-the duration of the burst and the duration of latency to spiking-are governed by the inverse-square-root laws. The mechanisms described here could be used to coordinate neuromuscular control in central pattern generators. As proof of principle, we construct small networks that control metachronal-wave motor pattern exhibited in locomotion. This pattern is determined by the phase relations of bursting neurons in a simple central pattern generator modeled by a chain of
Stability and Bifurcation Analysis in a Maglev System with Multiple Delays
Zhang, Lingling; Huang, Jianhua; Huang, Lihong; Zhang, Zhizhou
This paper considers the time-delayed feedback control for Maglev system with two discrete time delays. We determine constraints on the feedback time delays which ensure the stability of the Maglev system. An algorithm is developed for drawing a two-parametric bifurcation diagram with respect to two delays τ1 and τ2. Direction and stability of periodic solutions are also determined using the normal form method and center manifold theory by Hassard. The complex dynamical behavior of the Maglev system near the domain of stability is confirmed by exhaustive numerical simulation.
Bifurcation of Jovian magnetotail current sheet
P. L. Israelevich
2006-07-01
Full Text Available Multiple crossings of the magnetotail current sheet by a single spacecraft give the possibility to distinguish between two types of electric current density distribution: single-peaked (Harris type current layer and double-peaked (bifurcated current sheet. Magnetic field measurements in the Jovian magnetic tail by Voyager-2 reveal bifurcation of the tail current sheet. The electric current density possesses a minimum at the point of the Bx-component reversal and two maxima at the distance where the magnetic field strength reaches 50% of its value in the tail lobe.
Bifurcation of Jovian magnetotail current sheet
P. L. Israelevich
2006-07-01
Full Text Available Multiple crossings of the magnetotail current sheet by a single spacecraft give the possibility to distinguish between two types of electric current density distribution: single-peaked (Harris type current layer and double-peaked (bifurcated current sheet. Magnetic field measurements in the Jovian magnetic tail by Voyager-2 reveal bifurcation of the tail current sheet. The electric current density possesses a minimum at the point of the B_{x}-component reversal and two maxima at the distance where the magnetic field strength reaches 50% of its value in the tail lobe.
Song Yongli; Tadé, Moses O; Zhang Tonghua
2009-01-01
In this paper, a delayed neural network with unidirectional coupling is considered which consists of two two-dimensional nonlinear differential equation systems with exponential decay where one system receives a delayed input from the other system. Some parameter regions are given for conditional/absolute stability and Hopf bifurcations by using the theory of functional differential equations. Conditions ensuring the stability and direction of the Hopf bifurcation are determined by applying the normal form theory and the centre manifold theorem. We also investigate the spatio-temporal patterns of bifurcating periodic oscillations by using the symmetric bifurcation theory of delay-differential equations combined with representation theory of Lie groups. Then the global continuation of phase-locked periodic solutions is investigated. Numerical simulations are given to illustrate the results obtained
Csaki, Csaba; Grossman, Yuval; Tanedo, Philip; Tsai, Yuhsin
2011-01-01
We present an analysis of the loop-induced magnetic dipole operator in the Randall-Sundrum model of a warped extra dimension with anarchic bulk fermions and an IR brane-localized Higgs. These operators are finite at one-loop order and we explicitly calculate the branching ratio for μ→eγ using the mixed position/momentum space formalism. The particular bound on the anarchic Yukawa and Kaluza-Klein (KK) scales can depend on the flavor structure of the anarchic matrices. It is possible for a generic model to either be ruled out or unaffected by these bounds without any fine-tuning. We quantify how these models realize this surprising behavior. We also review tree-level lepton flavor bounds in these models and show that these are on the verge of tension with the μ→eγ bounds from typical models with a 3 TeV Kaluza-Klein scale. Further, we illuminate the nature of the one-loop finiteness of these diagrams and show how to accurately determine the degree of divergence of a five-dimensional loop diagram using both the five-dimensional and KK formalism. This power counting can be obfuscated in the four-dimensional Kaluza-Klein formalism and we explicitly point out subtleties that ensure that the two formalisms agree. Finally, we remark on the existence of a perturbative regime in which these one-loop results give the dominant contribution.
Discretizing the transcritical and pitchfork bifurcations – conjugacy results
Ló czi, Lajos
2015-01-01
© 2015 Taylor & Francis. We present two case studies in one-dimensional dynamics concerning the discretization of transcritical (TC) and pitchfork (PF) bifurcations. In the vicinity of a TC or PF bifurcation point and under some natural assumptions
Bifurcations of a class of singular biological economic models
Zhang Xue; Zhang Qingling; Zhang Yue
2009-01-01
This paper studies systematically a prey-predator singular biological economic model with time delay. It shows that this model exhibits two bifurcation phenomena when the economic profit is zero. One is transcritical bifurcation which changes the stability of the system, and the other is singular induced bifurcation which indicates that zero economic profit brings impulse, i.e., rapid expansion of the population in biological explanation. On the other hand, if the economic profit is positive, at a critical value of bifurcation parameter, the system undergoes a Hopf bifurcation, i.e., the increase of delay destabilizes the system and bifurcates into small amplitude periodic solution. Finally, by using Matlab software, numerical simulations illustrate the effectiveness of the results obtained here. In addition, we study numerically that the system undergoes a saddle-node bifurcation when the bifurcation parameter goes through critical value of positive economic profit.
Bifurcation structure of a model of bursting pancreatic cells
Mosekilde, Erik; Lading, B.; Yanchuk, S.
2001-01-01
One- and two-dimensional bifurcation studies of a prototypic model of bursting oscillations in pancreatic P-cells reveal a squid-formed area of chaotic dynamics in the parameter plane, with period-doubling bifurcations on one side of the arms and saddle-node bifurcations on the other. The transit......One- and two-dimensional bifurcation studies of a prototypic model of bursting oscillations in pancreatic P-cells reveal a squid-formed area of chaotic dynamics in the parameter plane, with period-doubling bifurcations on one side of the arms and saddle-node bifurcations on the other....... The transition from this structure to the so-called period-adding structure is found to involve a subcritical period-doubling bifurcation and the emergence of type-III intermittency. The period-adding transition itself is not smooth but consists of a saddle-node bifurcation in which (n + 1)-spike bursting...
A Practice-Oriented Bifurcation Analysis for Pulse Energy Converters. Part 2: An Operating Regime
Kolokolov, Yury; Monovskaya, Anna
The paper continues the discussion on bifurcation analysis for applications in practice-oriented solutions for pulse energy conversion systems (PEC-systems). Since a PEC-system represents a nonlinear object with a variable structure, then the description of its dynamics evolution involves bifurcation analysis conceptions. This means the necessity to resolve the conflict-of-units between the notions used to describe natural evolution (i.e. evolution of the operating process towards nonoperating processes and vice versa) and the notions used to describe a desirable artificial regime (i.e. an operating regime). We consider cause-effect relations in the following sequence: nonlinear dynamics-output signal-operating characteristics, where these characteristics include stability and performance. Then regularities of nonlinear dynamics should be translated into regularities of the output signal dynamics, and, after, into an evolutional picture of each operating characteristic. In order to make the translation without losses, we first take into account heterogeneous properties within the structures of the operating process in the parametrical (P-) and phase (X-) spaces, and analyze regularities of the operating stability and performance on the common basis by use of the modified bifurcation diagrams built in joint PX-space. Then, the correspondence between causes (degradation of the operating process stability) and effects (changes of the operating characteristics) is decomposed into three groups of abnormalities: conditionally unavoidable abnormalities (CU-abnormalities); conditionally probable abnormalities (CP-abnormalities); conditionally regular abnormalities (CR-abnormalities). Within each of these groups the evolutional homogeneity is retained. After, the resultant evolution of each operating characteristic is naturally aggregated through the superposition of cause-effect relations in accordance with each of the abnormalities. We demonstrate that the practice
Phase diagram of structure of radial electric field in helical plasmas
Toda, S.; Itoh, K.
2002-01-01
A set of transport equations in toroidal helical plasmas is analyzed, including the bifurcation of the radial electric field. Multiple solutions of E r for the ambipolar condition induces domains of different electric polarities. A structure of the domain interface is analyzed and a phase diagram is obtained in the space of the external control parameters. The region of the reduction of the anomalous transport is identified. (author)
Andrias Meisyal Yuwantoko
2017-03-01
Full Text Available Sebuah diagram urutan dibuat berdasarkan alur yang ada pada deskripsi kasus penggunaan. Alur tersebut dire- presentasikan dalam bentuk interaksi antara aktor dan sistem. Pemeriksaan rancangan diagram urutan perlu dilakukan untuk mengetahui ketidaksesuaian urutan alur kasus penggunaan dengan urutan pesan yang dikirimkan oleh objek-objek pada diagram urutan. Rancangan diagram yang sesuai merupakan kunci ketepatan (correctness implementasi perangkat lunak. Namun, pemeriksaan ketidaksesuaian masih dilakukan secara manual. Hal ini menjadi masalah apabila sebuah proyek perangkat lunak memiliki banyak rancangan diagram dan sumber daya manusia tidak mencukupi. Pemeriksaan membutuhkan waktu yang lama dan memiliki dampak pada waktu pengembangan perangkat lunak. Penelitian ini mengusulkan pembuatan kakas bantu untuk mendeteksi ketidaksesuaian diagram urutan dengan diagram kasus penggunaan. Ketidaksesuaian dilihat dari kemiripan semantik kalimat antara alur pada deskripsi kasus penggunaan dan triplet. Dari hasil pembuatan kakas bantu, kakas bantu yang dibuat dapat mendeteksi ketidaksesuaian diagram urutan dengan diagram kasus penggunaan. Kakas bantu ini diharapkan tidak hanya membantu pemeriksaan rancangan diagram akan tetapi mempercepat waktu pengembangan perangkat lunak.
The bifurcation diagram of drops in a sphere/plane geometry: influence of contact angle hysteresis
de Ruiter, Riëlle; van Gorcum, M.; Semprebon, C.; Duits, Michael H.G.; Brinkmann, M.; Mugele, Friedrich Gunther
2014-01-01
We study liquid drops that are present in a generic geometry, namely the gap in between a sphere and a plane. For the ideal system without contact angle hysteresis, the drop position is solely dependent on the contact angle, drop volume, and sphere/ plane separation distance. Performing a geometric
Comments on the Bifurcation Structure of 1D Maps
Belykh, V.N.; Mosekilde, Erik
1997-01-01
-within-a-box structure of the total bifurcation set. This presents a picture in which the homoclinic orbit bifurcations act as a skeleton for the bifurcational set. At the same time, experimental results on continued subharmonic generation for piezoelectrically amplified sound waves, predating the Feigenbaum theory......, are called into attention....
NUMERICAL HOPF BIFURCATION OF DELAY-DIFFERENTIAL EQUATIONS
无
2006-01-01
In this paper we consider the numerical solution of some delay differential equations undergoing a Hopf bifurcation. We prove that if the delay differential equations have a Hopf bifurcation point atλ=λ*, then the numerical solution of the equation also has a Hopf bifurcation point atλh =λ* + O(h).
Bifurcation of elastic solids with sliding interfaces
Bigoni, D.; Bordignon, N.; Piccolroaz, A.; Stupkiewicz, S.
2018-01-01
Lubricated sliding contact between soft solids is an interesting topic in biomechanics and for the design of small-scale engineering devices. As a model of this mechanical set-up, two elastic nonlinear solids are considered jointed through a frictionless and bilateral surface, so that continuity of the normal component of the Cauchy traction holds across the surface, but the tangential component is null. Moreover, the displacement can develop only in a way that the bodies in contact do neither detach, nor overlap. Surprisingly, this finite strain problem has not been correctly formulated until now, so this formulation is the objective of the present paper. The incremental equations are shown to be non-trivial and different from previously (and erroneously) employed conditions. In particular, an exclusion condition for bifurcation is derived to show that previous formulations based on frictionless contact or `spring-type' interfacial conditions are not able to predict bifurcations in tension, while experiments-one of which, ad hoc designed, is reported-show that these bifurcations are a reality and become possible when the correct sliding interface model is used. The presented results introduce a methodology for the determination of bifurcations and instabilities occurring during lubricated sliding between soft bodies in contact.
Climate bifurcation during the last deglaciation?
Lenton, T.M.; Livina, V.N.; Dakos, V.; Scheffer, M.
2012-01-01
There were two abrupt warming events during the last deglaciation, at the start of the Bolling-Allerod and at the end of the Younger Dryas, but their underlying dynamics are unclear. Some abrupt climate changes may involve gradual forcing past a bifurcation point, in which a prevailing climate state
Bifurcation structure of an optical ring cavity
Kubstrup, C.; Mosekilde, Erik
1996-01-01
One- and two-dimensional continuation techniques are applied to determine the basic bifurcation structure for an optical ring cavity with a nonlinear absorbing element (the Ikeda Map). By virtue of the periodic structure of the map, families of similar solutions develop in parameter space. Within...
Resource competition: a bifurcation theory approach.
Kooi, B.W.; Dutta, P.S.; Feudel, U.
2013-01-01
We develop a framework for analysing the outcome of resource competition based on bifurcation theory. We elaborate our methodology by readdressing the problem of competition of two species for two resources in a chemostat environment. In the case of perfect-essential resources it has been
Digital subtraction angiography of carotid bifurcation
Vries, A.R. de.
1984-01-01
This study demonstrates the reliability of digital subtraction angiography (DSA) by means of intra- and interobserver investigations as well as indicating the possibility of substituting catheterangiography by DSA in the diagnosis of carotid bifurcation. Whenever insufficient information is obtained from the combination of non-invasive investigation and DSA, a catheterangiogram will be necessary. (Auth.)
Percutaneous coronary intervention for coronary bifurcation disease
Lassen, Jens Flensted; Holm, Niels Ramsing; Banning, Adrian
2016-01-01
of combining the opinions of interventional cardiologists with the opinions of a large variety of other scientists on bifurcation management. The present 11th EBC consensus document represents the summary of the up-to-date EBC consensus and recommendations. It points to the fact that there is a multitude...
Bifurcation of self-folded polygonal bilayers
Abdullah, Arif M.; Braun, Paul V.; Hsia, K. Jimmy
2017-09-01
Motivated by the self-assembly of natural systems, researchers have investigated the stimulus-responsive curving of thin-shell structures, which is also known as self-folding. Self-folding strategies not only offer possibilities to realize complicated shapes but also promise actuation at small length scales. Biaxial mismatch strain driven self-folding bilayers demonstrate bifurcation of equilibrium shapes (from quasi-axisymmetric doubly curved to approximately singly curved) during their stimulus-responsive morphing behavior. Being a structurally instable, bifurcation could be used to tune the self-folding behavior, and hence, a detailed understanding of this phenomenon is appealing from both fundamental and practical perspectives. In this work, we investigated the bifurcation behavior of self-folding bilayer polygons. For the mechanistic understanding, we developed finite element models of planar bilayers (consisting of a stimulus-responsive and a passive layer of material) that transform into 3D curved configurations. Our experiments with cross-linked Polydimethylsiloxane samples that change shapes in organic solvents confirmed our model predictions. Finally, we explored a design scheme to generate gripper-like architectures by avoiding the bifurcation of stimulus-responsive bilayers. Our research contributes to the broad field of self-assembly as the findings could motivate functional devices across multiple disciplines such as robotics, artificial muscles, therapeutic cargos, and reconfigurable biomedical devices.
Modified jailed balloon technique for bifurcation lesions.
Saito, Shigeru; Shishido, Koki; Moriyama, Noriaki; Ochiai, Tomoki; Mizuno, Shingo; Yamanaka, Futoshi; Sugitatsu, Kazuya; Tobita, Kazuki; Matsumi, Junya; Tanaka, Yutaka; Murakami, Masato
2017-12-04
We propose a new systematic approach in bifurcation lesions, modified jailed balloon technique (M-JBT), and report the first clinical experience. Side branch occlusion brings with a serious complication and occurs in more than 7.0% of cases during bifurcation stenting. A jailed balloon (JB) is introduced into the side branch (SB), while a stent is placed in the main branch (MB) as crossing SB. The size of the JB is half of the MB stent size. While the proximal end of JB attaching to MB stent, both stent and JB are simultaneously inflated with same pressure. JB is removed and then guidewires are recrossed. Kissing balloon dilatation (KBD) and/or T and protrusion (TAP) stenting are applied as needed. Between February 2015 and February 2016, 233 patients (254 bifurcation lesions including 54 left main trunk disease) underwent percutaneous coronary intervention (PCI) using this technique. Procedure success was achieved in all cases. KBD was performed for 183 lesions and TAP stenting was employed for 31 lesions. Occlusion of SV was not observed in any of the patients. Bench test confirmed less deformity of MB stent in M-JBT compared with conventional-JBT. This is the first report for clinical experiences by using modified jailed balloon technique. This novel M-JBT is safe and effective in the preservation of SB patency during bifurcation stenting. © 2017 Wiley Periodicals, Inc.
Mohan, A.; Soni, N.C.; Moorthy, V.K.
1979-01-01
Ashby's method (see Acta Met., vol. 22, p. 275, 1974) of constructing sintering diagrams has been modified to obtain contribution diagrams directly from the computer. The interplay of sintering variables and mechanisms are studied and the factors that affect the participation of mechanisms in UO 2 are determined. By studying the physical properties, it emerges that the order of inaccuracies is small in most cases and do not affect the diagrams. On the other hand, even a 10% error in activation energies, which is quite plausible, would make a significant difference to the diagram. The main criticism of Ashby's approach is that the numerous properties and equations used, communicate their inaccuracies to the diagrams and make them unreliable. The present study has considerably reduced the number of factors that need to be refined to make the sintering diagrams more meaningful. (Auth.)
Drawing Euler Diagrams with Circles
Stapleton, Gem; Zhang, Leishi; Howse, John; Rodgers, Peter
2010-01-01
Euler diagrams are a popular and intuitive visualization tool which are used in a wide variety of application areas, including biological and medical data analysis. As with other data visualization methods, such as graphs, bar charts, or pie charts, the automated generation of an Euler diagram from a suitable data set would be advantageous, removing the burden of manual data analysis and the subsequent task of drawing an appropriate diagram. Various methods have emerged that automatically dra...
Symmetry, Hopf bifurcation, and the emergence of cluster solutions in time delayed neural networks.
Wang, Zhen; Campbell, Sue Ann
2017-11-01
We consider the networks of N identical oscillators with time delayed, global circulant coupling, modeled by a system of delay differential equations with Z N symmetry. We first study the existence of Hopf bifurcations induced by the coupling time delay and then use symmetric Hopf bifurcation theory to determine how these bifurcations lead to different patterns of symmetric cluster oscillations. We apply our results to a case study: a network of FitzHugh-Nagumo neurons with diffusive coupling. For this model, we derive the asymptotic stability, global asymptotic stability, absolute instability, and stability switches of the equilibrium point in the plane of coupling time delay (τ) and excitability parameter (a). We investigate the patterns of cluster oscillations induced by the time delay and determine the direction and stability of the bifurcating periodic orbits by employing the multiple timescales method and normal form theory. We find that in the region where stability switching occurs, the dynamics of the system can be switched from the equilibrium point to any symmetric cluster oscillation, and back to equilibrium point as the time delay is increased.
Symmetry, Hopf bifurcation, and the emergence of cluster solutions in time delayed neural networks
Wang, Zhen; Campbell, Sue Ann
2017-11-01
We consider the networks of N identical oscillators with time delayed, global circulant coupling, modeled by a system of delay differential equations with ZN symmetry. We first study the existence of Hopf bifurcations induced by the coupling time delay and then use symmetric Hopf bifurcation theory to determine how these bifurcations lead to different patterns of symmetric cluster oscillations. We apply our results to a case study: a network of FitzHugh-Nagumo neurons with diffusive coupling. For this model, we derive the asymptotic stability, global asymptotic stability, absolute instability, and stability switches of the equilibrium point in the plane of coupling time delay (τ) and excitability parameter (a). We investigate the patterns of cluster oscillations induced by the time delay and determine the direction and stability of the bifurcating periodic orbits by employing the multiple timescales method and normal form theory. We find that in the region where stability switching occurs, the dynamics of the system can be switched from the equilibrium point to any symmetric cluster oscillation, and back to equilibrium point as the time delay is increased.
Bifurcations and chaos of a vibration isolation system with magneto-rheological damper
Zhang, Hailong [Magneto-electronics Lab, School of Physics and Technology, Nanjing Normal University, Nanjing 210046 (China); Vibration Control Lab, School of Electrical and Automation Engineering, Nanjing Normal University, Nanjing 210042 (China); Zhang, Ning [Magneto-electronics Lab, School of Physics and Technology, Nanjing Normal University, Nanjing 210046 (China); Min, Fuhong; Yan, Wei; Wang, Enrong, E-mail: erwang@njnu.edu.cn [Vibration Control Lab, School of Electrical and Automation Engineering, Nanjing Normal University, Nanjing 210042 (China)
2016-03-15
Magneto-rheological (MR) damper possesses inherent hysteretic characteristics. We investigate the resulting nonlinear behaviors of a two degree-of-freedom (2-DoF) MR vibration isolation system under harmonic external excitation. A MR damper is identified by employing the modified Bouc-wen hysteresis model. By numerical simulation, we characterize the nonlinear dynamic evolution of period-doubling, saddle node bifurcating and inverse period-doubling using bifurcation diagrams of variations in frequency with a fixed amplitude of the harmonic excitation. The strength of chaos is determined by the Lyapunov exponent (LE) spectrum. Semi-physical experiment on the 2-DoF MR vibration isolation system is proposed. We trace the time history and phase trajectory under certain values of frequency of the harmonic excitation to verify the nonlinear dynamical evolution of period-doubling bifurcations to chaos. The largest LEs computed with the experimental data are also presented, confirming the chaotic motion in the experiment. We validate the chaotic motion caused by the hysteresis of the MR damper, and show the transitions between distinct regimes of stable motion and chaotic motion of the 2-DoF MR vibration isolation system for variations in frequency of external excitation.
Bifurcations and chaos of a vibration isolation system with magneto-rheological damper
Hailong Zhang
2016-03-01
Full Text Available Magneto-rheological (MR damper possesses inherent hysteretic characteristics. We investigate the resulting nonlinear behaviors of a two degree-of-freedom (2-DoF MR vibration isolation system under harmonic external excitation. A MR damper is identified by employing the modified Bouc-wen hysteresis model. By numerical simulation, we characterize the nonlinear dynamic evolution of period-doubling, saddle node bifurcating and inverse period-doubling using bifurcation diagrams of variations in frequency with a fixed amplitude of the harmonic excitation. The strength of chaos is determined by the Lyapunov exponent (LE spectrum. Semi-physical experiment on the 2-DoF MR vibration isolation system is proposed. We trace the time history and phase trajectory under certain values of frequency of the harmonic excitation to verify the nonlinear dynamical evolution of period-doubling bifurcations to chaos. The largest LEs computed with the experimental data are also presented, confirming the chaotic motion in the experiment. We validate the chaotic motion caused by the hysteresis of the MR damper, and show the transitions between distinct regimes of stable motion and chaotic motion of the 2-DoF MR vibration isolation system for variations in frequency of external excitation.
Luo, Kang; Yi, Hong-Liang, E-mail: yihongliang@hit.edu.cn; Tan, He-Ping, E-mail: tanheping@hit.edu.cn [School of Energy Science and Engineering, Harbin Institute of Technology, Harbin 150001 (China)
2014-05-15
Transitions and bifurcations of transient natural convection in a horizontal annulus with radiatively participating medium are numerically investigated using the coupled lattice Boltzmann and direct collocation meshless (LB-DCM) method. As a hybrid approach based on a common multi-scale Boltzmann-type model, the LB-DCM scheme is easy to implement and has an excellent flexibility in dealing with the irregular geometries. Separate particle distribution functions in the LBM are used to calculate the density field, the velocity field and the thermal field. In the radiatively participating medium, the contribution of thermal radiation to natural convection must be taken into account, and it is considered as a radiative term in the energy equation that is solved by the meshless method with moving least-squares (MLS) approximation. The occurrence of various instabilities and bifurcative phenomena is analyzed for different Rayleigh number Ra and Prandtl number Pr with and without radiation. Then, bifurcation diagrams and dual solutions are presented for relevant radiative parameters, such as convection-radiation parameter Rc and optical thickness τ. Numerical results show that the presence of volumetric radiation changes the static temperature gradient of the fluid, and generally results in an increase in the flow critical value. Besides, the existence and development of dual solutions of transient convection in the presence of radiation are greatly affected by radiative parameters. Finally, the advantage of LB-DCM combination is discussed, and the potential benefits of applying the LB-DCM method to multi-field coupling problems are demonstrated.
Toichiro Asada
2007-01-01
Full Text Available We explore numerically a three-dimensional discrete-time Kaldorian macrodynamic model in an open economy with fixed exchange rates, focusing on the effects of variation of the model parameters, the speed of adjustment of the goods market α, and the degree of capital mobility β on the stability of equilibrium and on the existence of business cycles. We determine the stability region in the parameter space and find that increase of α destabilizes the equilibrium more quickly than increase of β. We determine the Hopf-Neimark bifurcation curve along which business cycles are generated, and discuss briefly the occurrence of Arnold tongues. Bifurcation and Lyapunov exponent diagrams are computed providing information on the emergence, persistence, and amplitude of the cycles and illustrating the complex dynamics involved. Examples of cycles and other attractors are presented. Finally, we discuss a two-dimensional variation of the model related to a “wealth effect,” called model 2, and show that in this case, α does not destabilize the equilibrium more quickly than β, and that a Hopf-Neimark bifurcation curve does not exist in the parameter space, therefore model 2 does not produce cycles.
He Lin
2016-01-01
Full Text Available This study considers the bifurcation evolutions for a combining spiral gear transmission through parameter domain structure analysis. The system nonlinear vibration equations are created with piecewise backlash and general errors. Gill’s numerical integration algorithm is implemented in calculating the vibration equation sets. Based on cell-mapping method (CMM, two-dimensional dynamic domain planes have been developed and primarily focused on the parameters of backlash, transmission error, mesh frequency and damping ratio, and so forth. Solution demonstrates that Period-doubling bifurcation happens as the mesh frequency increases; moreover nonlinear discontinuous jump breaks the periodic orbit and also turns the periodic state into chaos suddenly. In transmission error planes, three cell groups which are Period-1, Period-4, and Chaos have been observed, and the boundary cells are the sensitive areas to dynamic response. Considering the parameter planes which consist of damping ratio associated with backlash, transmission error, mesh stiffness, and external load, the solution domain structure reveals that the system step into chaos undergoes Period-doubling cascade with Period-2m (m: integer periodic regions. Direct simulations to obtain the bifurcation diagram and largest Lyapunov exponent (LE match satisfactorily with the parameter domain solutions.
Bifurcation in epigenetics: Implications in development, proliferation, and diseases
Jost, Daniel
2014-01-01
Cells often exhibit different and stable phenotypes from the same DNA sequence. Robustness and plasticity of such cellular states are controlled by diverse transcriptional and epigenetic mechanisms, among them the modification of biochemical marks on chromatin. Here, we develop a stochastic model that describes the dynamics of epigenetic marks along a given DNA region. Through mathematical analysis, we show the emergence of bistable and persistent epigenetic states from the cooperative recruitment of modifying enzymes. We also find that the dynamical system exhibits a critical point and displays, in the presence of asymmetries in recruitment, a bifurcation diagram with hysteresis. These results have deep implications for our understanding of epigenetic regulation. In particular, our study allows one to reconcile within the same formalism the robust maintenance of epigenetic identity observed in differentiated cells, the epigenetic plasticity of pluripotent cells during differentiation, and the effects of epigenetic misregulation in diseases. Moreover, it suggests a possible mechanism for developmental transitions where the system is shifted close to the critical point to benefit from high susceptibility to developmental cues.
Barsuk, Alexandr A.; Paladi, Florentin
2018-04-01
The dynamic behavior of thermodynamic system, described by one order parameter and one control parameter, in a small neighborhood of ordinary and bifurcation equilibrium values of the system parameters is studied. Using the general methods of investigating the branching (bifurcations) of solutions for nonlinear equations, we performed an exhaustive analysis of the order parameter dependences on the control parameter in a small vicinity of the equilibrium values of parameters, including the stability analysis of the equilibrium states, and the asymptotic behavior of the order parameter dependences on the control parameter (bifurcation diagrams). The peculiarities of the transition to an unstable state of the system are discussed, and the estimates of the transition time to the unstable state in the neighborhood of ordinary and bifurcation equilibrium values of parameters are given. The influence of an external field on the dynamic behavior of thermodynamic system is analyzed, and the peculiarities of the system dynamic behavior are discussed near the ordinary and bifurcation equilibrium values of parameters in the presence of external field. The dynamic process of magnetization of a ferromagnet is discussed by using the general methods of bifurcation and stability analysis presented in the paper.
Dynamical analysis of a cubic Liénard system with global parameters
Chen, Hebai; Chen, Xingwu
2015-10-01
In this paper we investigate the dynamical behaviour of a cubic Liénard system with global parameters. After analysing the qualitative properties of all the equilibria and judging the existences of limit cycles and homoclinic loops for the whole parameter plane, we give the bifurcation diagram and phase portraits. Phase portraits are global if there exist limit cycles and local otherwise. We prove that parameters lie in a connected region, not just on a curve, usually in the parameter plane when the system has one homoclinic loop. Moreover, for global parameters we give a positive answer to conjecture 3.2 of (1998 Nonlinearity 11 1505-19) in the case of exactly two equilibria about the existence of some function whose graph is exactly the surface of double limit cycles. Supported by NSFC 11471228, 11172246 and the Fundamental Research Funds for the Central Universities.
Bifurcation Behavior Analysis in a Predator-Prey Model
Nan Wang
2016-01-01
Full Text Available A predator-prey model is studied mathematically and numerically. The aim is to explore how some key factors influence dynamic evolutionary mechanism of steady conversion and bifurcation behavior in predator-prey model. The theoretical works have been pursuing the investigation of the existence and stability of the equilibria, as well as the occurrence of bifurcation behaviors (transcritical bifurcation, saddle-node bifurcation, and Hopf bifurcation, which can deduce a standard parameter controlled relationship and in turn provide a theoretical basis for the numerical simulation. Numerical analysis ensures reliability of the theoretical results and illustrates that three stable equilibria will arise simultaneously in the model. It testifies the existence of Bogdanov-Takens bifurcation, too. It should also be stressed that the dynamic evolutionary mechanism of steady conversion and bifurcation behavior mainly depend on a specific key parameter. In a word, all these results are expected to be of use in the study of the dynamic complexity of ecosystems.
A bifurcation study to guide the design of a landing gear with a combined uplock/downlock mechanism.
Knowles, James A C; Lowenberg, Mark H; Neild, Simon A; Krauskopf, Bernd
2014-12-08
This paper discusses the insights that a bifurcation analysis can provide when designing mechanisms. A model, in the form of a set of coupled steady-state equations, can be derived to describe the mechanism. Solutions to this model can be traced through the mechanism's state versus parameter space via numerical continuation, under the simultaneous variation of one or more parameters. With this approach, crucial features in the response surface, such as bifurcation points, can be identified. By numerically continuing these points in the appropriate parameter space, the resulting bifurcation diagram can be used to guide parameter selection and optimization. In this paper, we demonstrate the potential of this technique by considering an aircraft nose landing gear, with a novel locking strategy that uses a combined uplock/downlock mechanism. The landing gear is locked when in the retracted or deployed states. Transitions between these locked states and the unlocked state (where the landing gear is a mechanism) are shown to depend upon the positions of two fold point bifurcations. By performing a two-parameter continuation, the critical points are traced to identify operational boundaries. Following the variation of the fold points through parameter space, a minimum spring stiffness is identified that enables the landing gear to be locked in the retracted state. The bifurcation analysis also shows that the unlocking of a retracted landing gear should use an unlock force measure, rather than a position indicator, to de-couple the effects of the retraction and locking actuators. Overall, the study demonstrates that bifurcation analysis can enhance the understanding of the influence of design choices over a wide operating range where nonlinearity is significant.
A bifurcation study to guide the design of a landing gear with a combined uplock/downlock mechanism
Knowles, James A. C.; Lowenberg, Mark H.; Neild, Simon A.; Krauskopf, Bernd
2014-01-01
This paper discusses the insights that a bifurcation analysis can provide when designing mechanisms. A model, in the form of a set of coupled steady-state equations, can be derived to describe the mechanism. Solutions to this model can be traced through the mechanism's state versus parameter space via numerical continuation, under the simultaneous variation of one or more parameters. With this approach, crucial features in the response surface, such as bifurcation points, can be identified. By numerically continuing these points in the appropriate parameter space, the resulting bifurcation diagram can be used to guide parameter selection and optimization. In this paper, we demonstrate the potential of this technique by considering an aircraft nose landing gear, with a novel locking strategy that uses a combined uplock/downlock mechanism. The landing gear is locked when in the retracted or deployed states. Transitions between these locked states and the unlocked state (where the landing gear is a mechanism) are shown to depend upon the positions of two fold point bifurcations. By performing a two-parameter continuation, the critical points are traced to identify operational boundaries. Following the variation of the fold points through parameter space, a minimum spring stiffness is identified that enables the landing gear to be locked in the retracted state. The bifurcation analysis also shows that the unlocking of a retracted landing gear should use an unlock force measure, rather than a position indicator, to de-couple the effects of the retraction and locking actuators. Overall, the study demonstrates that bifurcation analysis can enhance the understanding of the influence of design choices over a wide operating range where nonlinearity is significant. PMID:25484601
Feynman diagrams without Feynman parameters
Mendels, E.
1978-01-01
Dimensionally regularized Feynman diagrams are represented by means of products of k-functions. The infinite part of these diagrams is found very easily, also if they are overlapping, and the separation of the several kinds of divergences comes out quite naturally. Ward identities are proven in a transparent way. Series expansions in terms of the external momenta and their inner products are possible
Diagram Techniques in Group Theory
Stedman, Geoffrey E.
2009-09-01
Preface; 1. Elementary examples; 2. Angular momentum coupling diagram techniques; 3. Extension to compact simple phase groups; 4. Symmetric and unitary groups; 5. Lie groups and Lie algebras; 6. Polarisation dependence of multiphoton processes; 7. Quantum field theoretic diagram techniques for atomic systems; 8. Applications; Appendix; References; Indexes.
Contingency diagrams as teaching tools
Mattaini, Mark A.
1995-01-01
Contingency diagrams are particularly effective teaching tools, because they provide a means for students to view the complexities of contingency networks present in natural and laboratory settings while displaying the elementary processes that constitute those networks. This paper sketches recent developments in this visualization technology and illustrates approaches for using contingency diagrams in teaching.
Impact decision support diagrams
Boslough, Mark
2014-10-01
One way to frame the job of planetary defense is to “find the optimal approach for finding the optimal approach” to NEO mitigation. This requires a framework for defining in advance what should be done under various circumstances. The two-dimensional action matrix from the recent NRC report “Defending Planet Earth” can be generalized to a notional “Impact Decision Support Diagram” by extending it into a third dimension. The NRC action matrix incorporated two important axes: size and time-to-impact, but probability of impact is also critical (it is part of the definitions of both the Torino and Palermo scales). Uncertainty has been neglected, but is also crucial. It can be incorporated by subsuming it into the NEO size axis by redefining size to be three standard deviations greater than the best estimate, thereby providing a built-in conservative margin. The independent variable is time-to-impact, which is known with high precision. The other two axes are both quantitative assessments of uncertainty and are both time dependent. Thus, the diagram is entirely an expression of uncertainty. The true impact probability is either one or zero, and the true size does not change. The domain contains information about the current uncertainty, which changes with time (as opposed to reality, which does not change).
Genus Ranges of Chord Diagrams.
Burns, Jonathan; Jonoska, Nataša; Saito, Masahico
2015-04-01
A chord diagram consists of a circle, called the backbone, with line segments, called chords, whose endpoints are attached to distinct points on the circle. The genus of a chord diagram is the genus of the orientable surface obtained by thickening the backbone to an annulus and attaching bands to the inner boundary circle at the ends of each chord. Variations of this construction are considered here, where bands are possibly attached to the outer boundary circle of the annulus. The genus range of a chord diagram is the genus values over all such variations of surfaces thus obtained from a given chord diagram. Genus ranges of chord diagrams for a fixed number of chords are studied. Integer intervals that can be, and those that cannot be, realized as genus ranges are investigated. Computer calculations are presented, and play a key role in discovering and proving the properties of genus ranges.
Symmetry breaking bifurcations of a current sheet
Parker, R.D.; Dewar, R.L.; Johnson, J.L.
1990-01-01
Using a time evolution code with periodic boundary conditions, the viscoresistive hydromagnetic equations describing an initially static, planar current sheet with large Lundquist number have been evolved for times long enough to reach a steady state. A cosh 2 x resistivity model was used. For long periodicity lengths L p , the resistivity gradient drives flows that cause forced reconnection at X point current sheets. Using L p as a bifurcation parameter, two new symmetry breaking bifurcations were found: a transition to an asymmetric island chain with nonzero, positive, or negative phase velocity, and a transition to a static state with alternating large and small islands. These states are reached after a complex transient behavior, which involves a competition between secondary current sheet instability and coalescence
Symmetry breaking bifurcations of a current sheet
Parker, R.D.; Dewar, R.L.; Johnson, J.L.
1988-08-01
Using a time evolution code with periodic boundary conditions, the viscoresistive hydromagnetic equations describing an initially static, planar current sheet with large Lundquist number have been evolved for times long enough to reach a steady state. A cosh 2 x resistivity model was used. For long periodicity lengths, L p , the resistivity gradient drives flows which cause forced reconnection at X point current sheets. Using L p as a bifurcation parameter, two new symmetry breaking bifurcations were found - a transition to an asymmetric island chain with nonzero, positive or negative phase velocity, and a transition to a static state with alternating large and small islands. These states are reached after a complex transient behavior which involves a competition between secondary current sheet instability and coalescence. 31 refs., 6 figs
Experimental Study of Flow in a Bifurcation
Fresconi, Frank; Prasad, Ajay
2003-11-01
An instability known as the Dean vortex occurs in curved pipes with a longitudinal pressure gradient. A similar effect is manifest in the flow in a converging or diverging bifurcation, such as those found in the human respiratory airways. The goal of this study is to characterize secondary flows in a bifurcation. Particle image velocimetry (PIV) and laser-induced fluorescence (LIF) experiments were performed in a clear, plastic model. Results show the strength and migration of secondary vortices. Primary velocity features are also presented along with dispersion patterns from dye visualization. Unsteadiness, associated with a hairpin vortex, was also found at higher Re. This work can be used to assess the dispersion of particles in the lung. Medical delivery systems and pollution effect studies would profit from such an understanding.
Bifurcations and chaos of DNA solitonic dynamics
Gonzalez, J.A.; Martin-Landrove, M.; Carbo, J.R.; Chacon, M.
1994-09-01
We investigated the nonlinear DNA torsional equations proposed by Yakushevich in the presence of damping and external torques. Analytical expressions for some solutions are obtained in the case of the isolated chain. Special attention is paid to the stability of the solutions and the range of soliton interaction in the general case. The bifurcation analysis is performed and prediction of chaos is obtained for some set of parameters. Some biological implications are suggested. (author). 11 refs, 13 figs
Torus bifurcations in multilevel converter systems
Zhusubaliyev, Zhanybai T.; Mosekilde, Erik; Yanochkina, Olga O.
2011-01-01
embedded one into the other and with their basins of attraction delineated by intervening repelling tori. The paper illustrates the coexistence of three stable tori with different resonance behaviors and shows how reconstruction of these tori takes place across the borders of different dynamical regimes....... The paper also demonstrates how pairs of attracting and repelling tori emerge through border-collision torus-birth and border-collision torus-fold bifurcations. © 2011 World Scientific Publishing Company....
Perturbed period-doubling bifurcation. I. Theory
Svensmark, Henrik; Samuelsen, Mogens Rugholm
1990-01-01
-defined way that is a function of the amplitude and the frequency of the signal. New scaling laws between the amplitude of the signal and the detuning δ are found; these scaling laws apply to a variety of quantities, e.g., to the shift of the bifurcation point. It is also found that the stability...... of a microwave-driven Josephson junction confirm the theory. Results should be of interest in parametric-amplification studies....
Sex differences in intracranial arterial bifurcations
Lindekleiv, Haakon M; Valen-Sendstad, Kristian; Morgan, Michael K
2010-01-01
Subarachnoid hemorrhage (SAH) is a serious condition, occurring more frequently in females than in males. SAH is mainly caused by rupture of an intracranial aneurysm, which is formed by localized dilation of the intracranial arterial vessel wall, usually at the apex of the arterial bifurcation. T....... The female preponderance is usually explained by systemic factors (hormonal influences and intrinsic wall weakness); however, the uneven sex distribution of intracranial aneurysms suggests a possible physiologic factor-a local sex difference in the intracranial arteries....
Drift bifurcation detection for dissipative solitons
Liehr, A W; Boedeker, H U; Roettger, M C; Frank, T D; Friedrich, R; Purwins, H-G
2003-01-01
We report on the experimental detection of a drift bifurcation for dissipative solitons, which we observe in the form of current filaments in a planar semiconductor-gas-discharge system. By introducing a new stochastic data analysis technique we find that due to a change of system parameters the dissipative solitons undergo a transition from purely noise-driven objects with Brownian motion to particles with a dynamically stabilized finite velocity
Tulio Rosembuj
2006-12-01
Full Text Available There is no singular globalization, nor is the result of an individual agent. We could start by saying that global action has different angles and subjects who perform it are different, as well as its objectives. The global is an invisible invasion of materials and immediate effects.
Tulio Rosembuj
2006-01-01
There is no singular globalization, nor is the result of an individual agent. We could start by saying that global action has different angles and subjects who perform it are different, as well as its objectives. The global is an invisible invasion of materials and immediate effects.
Energized Oxygen : Speiser Current Sheet Bifurcation
George, D. E.; Jahn, J. M.
2017-12-01
A single population of energized Oxygen (O+) is shown to produce a cross-tail bifurcated current sheet in 2.5D PIC simulations of the magnetotail without the influence of magnetic reconnection. Treatment of oxygen in simulations of space plasmas, specifically a magnetotail current sheet, has been limited to thermal energies despite observations of and mechanisms which explain energized ions. We performed simulations of a homogeneous oxygen background, that has been energized in a physically appropriate manner, to study the behavior of current sheets and magnetic reconnection, specifically their bifurcation. This work uses a 2.5D explicit Particle-In-a-Cell (PIC) code to investigate the dynamics of energized heavy ions as they stream Dawn-to-Dusk in the magnetotail current sheet. We present a simulation study dealing with the response of a current sheet system to energized oxygen ions. We establish a, well known and studied, 2-species GEM Challenge Harris current sheet as a starting point. This system is known to eventually evolve and produce magnetic reconnection upon thinning of the current sheet. We added a uniform distribution of thermal O+ to the background. This 3-species system is also known to eventually evolve and produce magnetic reconnection. We add one additional variable to the system by providing an initial duskward velocity to energize the O+. We also traced individual particle motion within the PIC simulation. Three main results are shown. First, energized dawn- dusk streaming ions are clearly seen to exhibit sustained Speiser motion. Second, a single population of heavy ions clearly produces a stable bifurcated current sheet. Third, magnetic reconnection is not required to produce the bifurcated current sheet. Finally a bifurcated current sheet is compatible with the Harris current sheet model. This work is the first step in a series of investigations aimed at studying the effects of energized heavy ions on magnetic reconnection. This work differs
Para-equilibrium phase diagrams
Pelton, Arthur D.; Koukkari, Pertti; Pajarre, Risto; Eriksson, Gunnar
2014-01-01
Highlights: • A rapidly cooled system may attain a state of para-equilibrium. • In this state rapidly diffusing elements reach equilibrium but others are immobile. • Application of the Phase Rule to para-equilibrium phase diagrams is discussed. • A general algorithm to calculate para-equilibrium phase diagrams is described. - Abstract: If an initially homogeneous system at high temperature is rapidly cooled, a temporary para-equilibrium state may result in which rapidly diffusing elements have reached equilibrium but more slowly diffusing elements have remained essentially immobile. The best known example occurs when homogeneous austenite is quenched. A para-equilibrium phase assemblage may be calculated thermodynamically by Gibbs free energy minimization under the constraint that the ratios of the slowly diffusing elements are the same in all phases. Several examples of calculated para-equilibrium phase diagram sections are presented and the application of the Phase Rule is discussed. Although the rules governing the geometry of these diagrams may appear at first to be somewhat different from those for full equilibrium phase diagrams, it is shown that in fact they obey exactly the same rules with the following provision. Since the molar ratios of non-diffusing elements are the same in all phases at para-equilibrium, these ratios act, as far as the geometry of the diagram is concerned, like “potential” variables (such as T, pressure or chemical potentials) rather than like “normal” composition variables which need not be the same in all phases. A general algorithm to calculate para-equilibrium phase diagrams is presented. In the limit, if a para-equilibrium calculation is performed under the constraint that no elements diffuse, then the resultant phase diagram shows the single phase with the minimum Gibbs free energy at any point on the diagram; such calculations are of interest in physical vapor deposition when deposition is so rapid that phase
A Note on the Bogdanov-Takens Bifurcation in the Romer Model with Learning by Doing
Bella, Giovanni
This paper is aimed at describing the whole set of necessary and sufficient conditions for the emergence of multiple equilibria and global indeterminacy in the standard endogenous growth framework with learning by doing. The novelty of this paper relies on the application of the original Bogdanov-Takens bifurcation theorem, which allows us to characterize the full dynamics of the model, and determine the emergence of an unavoidable poverty trap.
Assigning spectra of chaotic molecules with diabatic correlation diagrams
Rose, J.P.; Kellman, M.E.
1996-01-01
An approach for classifying and organizing spectra of highly excited vibrational states of molecules is investigated. As a specific example, we analyze the spectrum of an effective spectroscopic fitting Hamiltonian for H 2 O. In highly excited spectra, multiple resonance couplings and anharmonicity interact to give branching of the N original normal modes into new anharmonic modes, accompanied by the onset of widespread chaos. The anharmonic modes are identified by means of a bifurcation analysis of the spectroscopic Hamiltonian. A diabatic correlation diagram technique is developed to assign the levels with approximate open-quote open-quote dynamical close-quote close-quote quantum numbers corresponding to the dynamics determined from the bifurcation analysis. The resulting assignment shows significant disturbance from the conventional spectral pattern organization into sequences and progressions. The open-quote open-quote dynamical close-quote close-quote assignment is then converted into an assignment in terms of open-quote open-quote nominal close-quote close-quote quantum numbers that function like the N normal mode quantum numbers at low energy. The nominal assignments are used to reconstruct, as much as possible, an organization of the spectrum resembling the usual separation into sequences and progressions. copyright 1996 American Institute of Physics
Andru?cã Maria Carmen
2013-01-01
The field of globalization has highlighted an interdependence implied by a more harmonious understanding determined by the daily interaction between nations through the inducement of peace and the management of streamlining and the effectiveness of the global economy. For the functioning of the globalization, the developing countries that can be helped by the developed ones must be involved. The international community can contribute to the institution of the development environment of the gl...
Bifurcation theory for finitely smooth planar autonomous differential systems
Han, Maoan; Sheng, Lijuan; Zhang, Xiang
2018-03-01
In this paper we establish bifurcation theory of limit cycles for planar Ck smooth autonomous differential systems, with k ∈ N. The key point is to study the smoothness of bifurcation functions which are basic and important tool on the study of Hopf bifurcation at a fine focus or a center, and of Poincaré bifurcation in a period annulus. We especially study the smoothness of the first order Melnikov function in degenerate Hopf bifurcation at an elementary center. As we know, the smoothness problem was solved for analytic and C∞ differential systems, but it was not tackled for finitely smooth differential systems. Here, we present their optimal regularity of these bifurcation functions and their asymptotic expressions in the finite smooth case.
Bifurcation structure of a model of bursting pancreatic cells
Mosekilde, Erik; Lading, B.; Yanchuk, S.
2001-01-01
. The transition from this structure to the so-called period-adding structure is found to involve a subcritical period-doubling bifurcation and the emergence of type-III intermittency. The period-adding transition itself is not smooth but consists of a saddle-node bifurcation in which (n + 1)-spike bursting...... behavior is born, slightly overlapping with a subcritical period-doubling bifurcation in which n-spike bursting behavior loses its stability.......One- and two-dimensional bifurcation studies of a prototypic model of bursting oscillations in pancreatic P-cells reveal a squid-formed area of chaotic dynamics in the parameter plane, with period-doubling bifurcations on one side of the arms and saddle-node bifurcations on the other...
2006-01-01
Full Text Available We consider a simplified bidirectional associated memory (BAM neural network model with four neurons and multiple time delays. The global existence of periodic solutions bifurcating from Hopf bifurcations is investigated by applying the global Hopf bifurcation theorem due to Wu and Bendixson's criterion for high-dimensional ordinary differential equations due to Li and Muldowney. It is shown that the local Hopf bifurcation implies the global Hopf bifurcation after the second critical value of the sum of two delays. Numerical simulations supporting the theoretical analysis are also included.
Horley, Paul P., E-mail: paul.horley@cimav.edu.mx [Centro de Investigación en Materiales Avanzados, S.C. (CIMAV), Chihuahua/Monterrey, 120 Avenida Miguel de Cervantes, 31109 Chihuahua (Mexico); Kushnir, Mykola Ya. [Yuri Fedkovych Chernivtsi National University, 2 Kotsyubynsky str., 58012 Chernivtsi (Ukraine); Morales-Meza, Mishel [Centro de Investigación en Materiales Avanzados, S.C. (CIMAV), Chihuahua/Monterrey, 120 Avenida Miguel de Cervantes, 31109 Chihuahua (Mexico); Sukhov, Alexander [Institut für Physik, Martin-Luther Universität Halle-Wittenberg, 06120 Halle (Saale) (Germany); Rusyn, Volodymyr [Yuri Fedkovych Chernivtsi National University, 2 Kotsyubynsky str., 58012 Chernivtsi (Ukraine)
2016-04-01
We report on complex magnetization dynamics in a forced spin valve oscillator subjected to a varying magnetic field and a constant spin-polarized current. The transition from periodic to chaotic magnetic motion was illustrated with bifurcation diagrams and Hausdorff dimension – the methods developed for dissipative self-organizing systems. It was shown that bifurcation cascades can be obtained either by tuning the injected spin-polarized current or by changing the magnitude of applied magnetic field. The order–chaos transition in magnetization dynamics can be also directly observed from the hysteresis curves. The resulting complex oscillations are useful for development of spin-valve devices operating in harmonic and chaotic modes.
Causal Diagrams for Empirical Research
Pearl, Judea
1994-01-01
The primary aim of this paper is to show how graphical models can be used as a mathematical language for integrating statistical and subject-matter information. In particular, the paper develops a principled, nonparametric framework for causal inference, in which diagrams are queried to determine if the assumptions available are sufficient for identifiying causal effects from non-experimental data. If so the diagrams can be queried to produce mathematical expressions for causal effects in ter...
Wind Diagrams in Medieval Iceland
Kedwards, Dale
2014-01-01
This article presents a study of the sole wind diagram that survives from medieval Iceland, preserved in the encyclopaedic miscellany in Copenhagen's Arnamagnæan Institute with the shelf mark AM 732b 4to (c. 1300-25). It examines the wind diagram and its accompanying text, an excerpt on the winds...... from Isidore of Seville's Etymologies. It also examines the perimeter of winds on two medieval Icelandic world maps, and the visual traditions from which they draw....
Phase diagrams of the elements
Young, D.A.
1975-01-01
A summary of the pressure-temperature phase diagrams of the elements is presented, with graphs of the experimentally determined solid-solid phase boundaries and melting curves. Comments, including theoretical discussion, are provided for each diagram. The crystal structure of each solid phase is identified and discussed. This work is aimed at encouraging further experimental and theoretical research on phase transitions in the elements
Bayesian Networks and Influence Diagrams
Kjærulff, Uffe Bro; Madsen, Anders Læsø
Probabilistic networks, also known as Bayesian networks and influence diagrams, have become one of the most promising technologies in the area of applied artificial intelligence, offering intuitive, efficient, and reliable methods for diagnosis, prediction, decision making, classification......, troubleshooting, and data mining under uncertainty. Bayesian Networks and Influence Diagrams: A Guide to Construction and Analysis provides a comprehensive guide for practitioners who wish to understand, construct, and analyze intelligent systems for decision support based on probabilistic networks. Intended...
Nonlinear physical systems spectral analysis, stability and bifurcations
Kirillov, Oleg N
2013-01-01
Bringing together 18 chapters written by leading experts in dynamical systems, operator theory, partial differential equations, and solid and fluid mechanics, this book presents state-of-the-art approaches to a wide spectrum of new and challenging stability problems.Nonlinear Physical Systems: Spectral Analysis, Stability and Bifurcations focuses on problems of spectral analysis, stability and bifurcations arising in the nonlinear partial differential equations of modern physics. Bifurcations and stability of solitary waves, geometrical optics stability analysis in hydro- and magnetohydrodynam
Stability and bifurcation analysis in a delayed SIR model
Jiang Zhichao; Wei Junjie
2008-01-01
In this paper, a time-delayed SIR model with a nonlinear incidence rate is considered. The existence of Hopf bifurcations at the endemic equilibrium is established by analyzing the distribution of the characteristic values. A explicit algorithm for determining the direction of the Hopf bifurcation and the stability of the bifurcating periodic solutions are derived by using the normal form and the center manifold theory. Numerical simulations to support the analytical conclusions are carried out
Bifurcation of rupture path by linear and cubic damping force
Dennis L. C., C.; Chew X., Y.; Lee Y., C.
2014-06-01
Bifurcation of rupture path is studied for the effect of linear and cubic damping. Momentum equation with Rayleigh factor was transformed into ordinary differential form. Bernoulli differential equation was obtained and solved by the separation of variables. Analytical or exact solutions yielded the bifurcation was visible at imaginary part when the wave was non dispersive. For the dispersive wave, bifurcation of rupture path was invisible.
Kučera, Milan; Navrátil, J.
2018-01-01
Roč. 166, January (2018), s. 154-180 ISSN 0362-546X Institutional support: RVO:67985840 Keywords : global bifurcation * maximal eigenvalue * positively homogeneous operators Subject RIV: BA - General Mathematics OBOR OECD: Pure mathematics Impact factor: 1.192, year: 2016 http://www. science direct.com/ science /article/pii/S0362546X17302559?via%3Dihub
Kučera, Milan; Navrátil, J.
2018-01-01
Roč. 166, January (2018), s. 154-180 ISSN 0362-546X Institutional support: RVO:67985840 Keywords : global bifurcation * maximal eigenvalue * positively homogeneous operators Subject RIV: BA - General Mathematics OBOR OECD: Pure mathematics Impact factor: 1.192, year: 2016 http://www.sciencedirect.com/science/article/pii/S0362546X17302559?via%3Dihub
A codimension two bifurcation in a railway bogie system
Zhang, Tingting; True, Hans; Dai, Huanyun
2017-01-01
In this paper, a comprehensive analysis is presented to investigate a codimension two bifurcation that exists in a nonlinear railway bogie dynamic system combining theoretical analysis with numerical investigation. By using the running velocity V and the primary longitudinal stiffness (Formula...... coexist in a range of the bifurcation parameters which can lead to jumps in the lateral oscillation amplitude of the railway bogie system. Furthermore, reduce the values of the bifurcation parameters gradually. Firstly, the supercritical Hopf bifurcation turns into a subcritical one with multiple limit...
Predicting bifurcation angle effect on blood flow in the microvasculature.
Yang, Jiho; Pak, Y Eugene; Lee, Tae-Rin
2016-11-01
Since blood viscosity is a basic parameter for understanding hemodynamics in human physiology, great amount of research has been done in order to accurately predict this highly non-Newtonian flow property. However, previous works lacked in consideration of hemodynamic changes induced by heterogeneous vessel networks. In this paper, the effect of bifurcation on hemodynamics in a microvasculature is quantitatively predicted. The flow resistance in a single bifurcation microvessel was calculated by combining a new simple mathematical model with 3-dimensional flow simulation for varying bifurcation angles under physiological flow conditions. Interestingly, the results indicate that flow resistance induced by vessel bifurcation holds a constant value of approximately 0.44 over the whole single bifurcation model below diameter of 60μm regardless of geometric parameters including bifurcation angle. Flow solutions computed from this new model showed substantial decrement in flow velocity relative to other mathematical models, which do not include vessel bifurcation effects, while pressure remained the same. Furthermore, when applying the bifurcation angle effect to the entire microvascular network, the simulation results gave better agreements with recent in vivo experimental measurements. This finding suggests a new paradigm in microvascular blood flow properties, that vessel bifurcation itself, regardless of its angle, holds considerable influence on blood viscosity, and this phenomenon will help to develop new predictive tools in microvascular research. Copyright © 2016 Elsevier Inc. All rights reserved.
Zhioua, M.; El Aroudi, A.; Belghith, S.; Bosque-Moncusí, J. M.; Giral, R.; Al Hosani, K.; Al-Numay, M.
A study of a DC-DC boost converter fed by a photovoltaic (PV) generator and supplying a constant voltage load is presented. The input port of the converter is controlled using fixed frequency pulse width modulation (PWM) based on the loss-free resistor (LFR) concept whose parameter is selected with the aim to force the PV generator to work at its maximum power point. Under this control strategy, it is shown that the system can exhibit complex nonlinear behaviors for certain ranges of parameter values. First, using the nonlinear models of the converter and the PV source, the dynamics of the system are explored in terms of some of its parameters such as the proportional gain of the controller and the output DC bus voltage. To present a comprehensive approach to the overall system behavior under parameter changes, a series of bifurcation diagrams are computed from the circuit-level switched model and from a simplified model both implemented in PSIM© software showing a remarkable agreement. These diagrams show that the first instability that takes place in the system period-1 orbit when a primary parameter is varied is a smooth period-doubling bifurcation and that the nonlinearity of the PV generator is irrelevant for predicting this phenomenon. Different bifurcation scenarios can take place for the resulting period-2 subharmonic regime depending on a secondary bifurcation parameter. The boundary between the desired period-1 orbit and subharmonic oscillation resulting from period-doubling in the parameter space is obtained by calculating the eigenvalues of the monodromy matrix of the simplified model. The results from this model have been validated with time-domain numerical simulation using the circuit-level switched model and also experimentally from a laboratory prototype. This study can help in selecting the parameter values of the circuit in order to delimit the region of period-1 operation of the converter which is of practical interest in PV systems.
Double Hopf bifurcation in delay differential equations
Redouane Qesmi
2014-07-01
Full Text Available The paper addresses the computation of elements of double Hopf bifurcation for retarded functional differential equations (FDEs with parameters. We present an efficient method for computing, simultaneously, the coefficients of center manifolds and normal forms, in terms of the original FDEs, associated with the double Hopf singularity up to an arbitrary order. Finally, we apply our results to a nonlinear model with periodic delay. This shows the applicability of the methodology in the study of delay models arising in either natural or technological problems.
Bifurcation theory for toroidal MHD instabilities
Maschke, E.K.; Morros Tosas, J.; Urquijo, G.
1992-01-01
Using a general representation of magneto-hydrodynamics in terms of stream functions and potentials, proposed earlier, a set of reduced MHD equations for the case of toroidal geometry had been derived by an appropriate ordering with respect to the inverse aspect ratio. When all dissipative terms are neglected in this reduced system, it has the same linear stability limits as the full ideal MHD equations, to the order considered. When including resistivity, thermal conductivity and viscosity, we can apply bifurcation theory to investigate nonlinear stationary solution branches related to various instabilities. In particular, we show that a stationary solution of the internal kink type can be found
Bifurcation into functional niches in adaptation.
White, Justin S; Adami, Christoph
2004-01-01
One of the central questions in evolutionary biology concerns the dynamics of adaptation and diversification. This issue can be addressed experimentally if replicate populations adapting to identical environments can be investigated in detail. We have studied 501 such replicas using digital organisms adapting to at least two fundamentally different functional niches (survival strategies) present in the same environment: one in which fast replication is the way to live, and another where exploitation of the environment's complexity leads to complex organisms with longer life spans and smaller replication rates. While these two modes of survival are closely analogous to those expected to emerge in so-called r and K selection scenarios respectively, the bifurcation of evolutionary histories according to these functional niches occurs in identical environments, under identical selective pressures. We find that the branching occurs early, and leads to drastic phenotypic differences (in fitness, sequence length, and gestation time) that are permanent and irreversible. This study confirms an earlier experimental effort using microorganisms, in that diversification can be understood at least in part in terms of bifurcations on saddle points leading to peak shifts, as in the picture drawn by Sewall Wright.
Ibrahim, K. M.; Jamal, R. K.; Ali, F. H.
2018-05-01
The behaviour of certain dynamical nonlinear systems are described in term as chaos, i.e., systems’ variables change with the time, displaying very sensitivity to initial conditions of chaotic dynamics. In this paper, we study archetype systems of ordinary differential equations in two-dimensional phase spaces of the Rössler model. A system displays continuous time chaos and is explained by three coupled nonlinear differential equations. We study its characteristics and determine the control parameters that lead to different behavior of the system output, periodic, quasi-periodic and chaos. The time series, attractor, Fast Fourier Transformation and bifurcation diagram for different values have been described.
Stability and Bifurcation of a Fishery Model with Crowley-Martin Functional Response
Maiti, Atasi Patra; Dubey, B.
To understand the dynamics of a fishery system, a nonlinear mathematical model is proposed and analyzed. In an aquatic environment, we considered two populations: one is prey and another is predator. Here both the fish populations grow logistically and interaction between them is of Crowley-Martin type functional response. It is assumed that both the populations are harvested and the harvesting effort is assumed to be dynamical variable and tax is considered as a control variable. The existence of equilibrium points and their local stability are examined. The existence of Hopf-bifurcation, stability and direction of Hopf-bifurcation are also analyzed with the help of Center Manifold theorem and normal form theory. The global stability behavior of the positive equilibrium point is also discussed. In order to find the value of optimal tax, the optimal harvesting policy is used. To verify our analytical findings, an extensive numerical simulation is carried out for this model system.
Analysis of Vehicle Steering and Driving Bifurcation Characteristics
Xianbin Wang
2015-01-01
Full Text Available The typical method of vehicle steering bifurcation analysis is based on the nonlinear autonomous vehicle model deriving from the classic two degrees of freedom (2DOF linear vehicle model. This method usually neglects the driving effect on steering bifurcation characteristics. However, in the steering and driving combined conditions, the tyre under different driving conditions can provide different lateral force. The steering bifurcation mechanism without the driving effect is not able to fully reveal the vehicle steering and driving bifurcation characteristics. Aiming at the aforementioned problem, this paper analyzed the vehicle steering and driving bifurcation characteristics with the consideration of driving effect. Based on the 5DOF vehicle system dynamics model with the consideration of driving effect, the 7DOF autonomous system model was established. The vehicle steering and driving bifurcation dynamic characteristics were analyzed with different driving mode and driving torque. Taking the front-wheel-drive system as an example, the dynamic evolution process of steering and driving bifurcation was analyzed by phase space, system state variables, power spectral density, and Lyapunov index. The numerical recognition results of chaos were also provided. The research results show that the driving mode and driving torque have the obvious effect on steering and driving bifurcation characteristics.
Sediment discharge division at two tidally influenced river bifurcations
Sassi, M.G.; Hoitink, A.J.F.; Vermeulen, B.; Hidayat, H.
2013-01-01
[1] We characterize and quantify the sediment discharge division at two tidally influenced river bifurcations in response to mean flow and secondary circulation by employing a boat-mounted acoustic Doppler current profiler (ADCP), to survey transects at bifurcating branches during a semidiurnal
Views on the Hopf bifurcation with respect to voltage instabilities
Roa-Sepulveda, C A [Universidad de Concepcion, Concepcion (Chile). Dept. de Ingenieria Electrica; Knight, U G [Imperial Coll. of Science and Technology, London (United Kingdom). Dept. of Electrical and Electronic Engineering
1994-12-31
This paper presents a sensitivity study of the Hopf bifurcation phenomenon which can in theory appear in power systems, with reference to the dynamics of the process and the impact of demand characteristics. Conclusions are drawn regarding power levels at which these bifurcations could appear and concern the concept of the imaginary axis as a `hard` limit eigenvalue analyses. (author) 20 refs., 31 figs.
Bifurcations of heterodimensional cycles with two saddle points
Geng Fengjie [School of Information Technology, China University of Geosciences (Beijing), Beijing 100083 (China)], E-mail: gengfengjie_hbu@163.com; Zhu Deming [Department of Mathematics, East China Normal University, Shanghai 200062 (China)], E-mail: dmzhu@math.ecnu.edu.cn; Xu Yancong [Department of Mathematics, East China Normal University, Shanghai 200062 (China)], E-mail: yancongx@163.com
2009-03-15
The bifurcations of 2-point heterodimensional cycles are investigated in this paper. Under some generic conditions, we establish the existence of one homoclinic loop, one periodic orbit, two periodic orbits, one 2-fold periodic orbit, and the coexistence of one periodic orbit and heteroclinic loop. Some bifurcation patterns different to the case of non-heterodimensional heteroclinic cycles are revealed.
Bifurcations of heterodimensional cycles with two saddle points
Geng Fengjie; Zhu Deming; Xu Yancong
2009-01-01
The bifurcations of 2-point heterodimensional cycles are investigated in this paper. Under some generic conditions, we establish the existence of one homoclinic loop, one periodic orbit, two periodic orbits, one 2-fold periodic orbit, and the coexistence of one periodic orbit and heteroclinic loop. Some bifurcation patterns different to the case of non-heterodimensional heteroclinic cycles are revealed.
Carpentier, David
1998-01-01
Using the renormalisation group (RG) we study two dimensional electromagnetic coulomb gas and extended Sine-Gordon theories invariant under the modular group SL(2,Z). The flow diagram is established from the scaling equations, and we derive the critical behaviour at the various transition points of the diagram. Following proposal for a SL(2,Z) duality between different quantum Hall fluids, we discuss the analogy between this flow and the global quantum Hall phase diagram.
New detectors for powders diagrams
Convert, P.
1975-01-01
During the last few years, all the classical neutron diffractometers for powders have used one or maybe a few counters. So, it takes a long time to obtain a diagram which causes many disadvantages: 1) very long experiments: one or two days (or flux on the sample about 10 6 n/cm 2 /a); 2) necessity of big samples: many cm 3 ; 3) necessity of having the whole diagram before changing anything in the experiment: magnetic field, temperature, quality of the sample; 4) necessity of having collimators of a few times ten minutes to obtain correct statistics in the diagram. Because of these disadvantages, several attempts have been made to speed up the experimental procedure such as using more counters, the detection of neutrons on a resistive wire, etc. In Grenoble, new position-sensitive detectors have been constructed using a digital technique
Critical bifurcation surfaces of 3D discrete dynamics
Michael Sonis
2000-01-01
Full Text Available This paper deals with the analytical representation of bifurcations of each 3D discrete dynamics depending on the set of bifurcation parameters. The procedure of bifurcation analysis proposed in this paper represents the 3D elaboration and specification of the general algorithm of the n-dimensional linear bifurcation analysis proposed by the author earlier. It is proven that 3D domain of asymptotic stability (attraction of the fixed point for a given 3D discrete dynamics is bounded by three critical bifurcation surfaces: the divergence, flip and flutter surfaces. The analytical construction of these surfaces is achieved with the help of classical Routh–Hurvitz conditions of asymptotic stability. As an application the adjustment process proposed by T. Puu for the Cournot oligopoly model is considered in detail.
Bifurcation of transition paths induced by coupled bistable systems.
Tian, Chengzhe; Mitarai, Namiko
2016-06-07
We discuss the transition paths in a coupled bistable system consisting of interacting multiple identical bistable motifs. We propose a simple model of coupled bistable gene circuits as an example and show that its transition paths are bifurcating. We then derive a criterion to predict the bifurcation of transition paths in a generalized coupled bistable system. We confirm the validity of the theory for the example system by numerical simulation. We also demonstrate in the example system that, if the steady states of individual gene circuits are not changed by the coupling, the bifurcation pattern is not dependent on the number of gene circuits. We further show that the transition rate exponentially decreases with the number of gene circuits when the transition path does not bifurcate, while a bifurcation facilitates the transition by lowering the quasi-potential energy barrier.
Hopf Bifurcation of Compound Stochastic van der Pol System
Shaojuan Ma
2016-01-01
Full Text Available Hopf bifurcation analysis for compound stochastic van der Pol system with a bound random parameter and Gaussian white noise is investigated in this paper. By the Karhunen-Loeve (K-L expansion and the orthogonal polynomial approximation, the equivalent deterministic van der Pol system can be deduced. Based on the bifurcation theory of nonlinear deterministic system, the critical value of bifurcation parameter is obtained and the influence of random strength δ and noise intensity σ on stochastic Hopf bifurcation in compound stochastic system is discussed. At last we found that increased δ can relocate the critical value of bifurcation parameter forward while increased σ makes it backward and the influence of δ is more sensitive than σ. The results are verified by numerical simulations.
Multi-currency Influence Diagrams
Nielsen, Søren Holbech; Nielsen, Thomas Dyhre; Jensen, Finn V.
2007-01-01
When using the influence diagrams framework for solving a decision problem with several different quantitative utilities, the traditional approach has been to convert the utilities into one common currency. This conversion is carried out using a tacit transformation, under the assumption...... that the converted problem is equivalent to the original one. In this paper we present an extension of the influence diagram framework. The extension allows for these decision problems to be modelled in their original form. We present an algorithm that, given a linear conversion function between the currencies...
Diagrams for symmetric product orbifolds
Pakman, Ari; Rastelli, Leonardo; Razamat, Shlomo S.
2009-01-01
We develop a diagrammatic language for symmetric product orbifolds of two-dimensional conformal field theories. Correlation functions of twist operators are written as sums of diagrams: each diagram corresponds to a branched covering map from a surface where the fields are single-valued to the base sphere where twist operators are inserted. This diagrammatic language facilitates the study of the large N limit and makes more transparent the analogy between symmetric product orbifolds and free non-abelian gauge theories. We give a general algorithm to calculate the leading large N contribution to four-point correlators of twist fields.
Plum, Maja
Globalization is often referred to as external to education - a state of affair facing the modern curriculum with numerous challenges. In this paper it is examined as internal to curriculum; analysed as a problematization in a Foucaultian sense. That is, as a complex of attentions, worries, ways...... of reasoning, producing curricular variables. The analysis is made through an example of early childhood curriculum in Danish Pre-school, and the way the curricular variable of the pre-school child comes into being through globalization as a problematization, carried forth by the comparative practices of PISA...
F. Gerard Adams
2008-01-01
The rapid globalization of the world economy is causing fundamental changes in patterns of trade and finance. Some economists have argued that globalization has arrived and that the world is â€œflatâ€ . While the geographic scope of markets has increased, the author argues that new patterns of trade and finance are a result of the discrepancies between â€œoldâ€ countries and â€œnewâ€ . As the differences are gradually wiped out, particularly if knowledge and technology spread worldwide, the t...
Climate bifurcation during the last deglaciation?
T. M. Lenton
2012-07-01
Full Text Available There were two abrupt warming events during the last deglaciation, at the start of the Bølling-Allerød and at the end of the Younger Dryas, but their underlying dynamics are unclear. Some abrupt climate changes may involve gradual forcing past a bifurcation point, in which a prevailing climate state loses its stability and the climate tips into an alternative state, providing an early warning signal in the form of slowing responses to perturbations, which may be accompanied by increasing variability. Alternatively, short-term stochastic variability in the climate system can trigger abrupt climate changes, without early warning. Previous work has found signals consistent with slowing down during the last deglaciation as a whole, and during the Younger Dryas, but with conflicting results in the run-up to the Bølling-Allerød. Based on this, we hypothesise that a bifurcation point was approached at the end of the Younger Dryas, in which the cold climate state, with weak Atlantic overturning circulation, lost its stability, and the climate tipped irreversibly into a warm interglacial state. To test the bifurcation hypothesis, we analysed two different climate proxies in three Greenland ice cores, from the Last Glacial Maximum to the end of the Younger Dryas. Prior to the Bølling warming, there was a robust increase in climate variability but no consistent slowing down signal, suggesting this abrupt change was probably triggered by a stochastic fluctuation. The transition to the warm Bølling-Allerød state was accompanied by a slowing down in climate dynamics and an increase in climate variability. We suggest that the Bølling warming excited an internal mode of variability in Atlantic meridional overturning circulation strength, causing multi-centennial climate fluctuations. However, the return to the Younger Dryas cold state increased climate stability. We find no consistent evidence for slowing down during the Younger Dryas, or in a longer
Zhang Jiangang; Li Xianfeng; Chu Yandong; Yu Jianning; Chang Yingxiang
2009-01-01
In this paper, complex dynamical behavior of a class of centrifugal flywheel governor system is studied. These systems have a rich variety of nonlinear behavior, which are investigated here by numerically integrating the Lagrangian equations of motion. A tiny change in parameters can lead to an enormous difference in the long-term behavior of the system. Bubbles of periodic orbits may also occur within the bifurcation sequence. Hyperchaotic behavior is also observed in cases where two of the Lyapunov exponents are positive, one is zero, and one is negative. The routes to chaos are analyzed using Poincare maps, which are found to be more complicated than those of nonlinear rotational machines. Periodic and chaotic motions can be clearly distinguished by all of the analytical tools applied here, namely Poincare sections, bifurcation diagrams, Lyapunov exponents, and Lyapunov dimensions. This paper proposes a parametric open-plus-closed-loop approach to controlling chaos, which is capable of switching from chaotic motion to any desired periodic orbit. The theoretical work and numerical simulations of this paper can be extended to other systems. Finally, the results of this paper are of practical utility to designers of rotational machines.
Smondyrev, M.A.
1985-01-01
The perturbation theory for the polaron energy is systematically treated on the diagrammatic basis. Feynman diagrams being constructed allow to calculate the polaron energy up to the third order in powers of the coupling constant. Similar calculations are performed for the average number of virtual phonons
Algorithmic approach to diagram techniques
Ponticopoulos, L.
1980-10-01
An algorithmic approach to diagram techniques of elementary particles is proposed. The definition and axiomatics of the theory of algorithms are presented, followed by the list of instructions of an algorithm formalizing the construction of graphs and the assignment of mathematical objects to them. (T.A.)
Bayesian Networks and Influence Diagrams
Kjærulff, Uffe Bro; Madsen, Anders Læsø
Bayesian Networks and Influence Diagrams: A Guide to Construction and Analysis, Second Edition, provides a comprehensive guide for practitioners who wish to understand, construct, and analyze intelligent systems for decision support based on probabilistic networks. This new edition contains six new...
Bifurcations and Patterns in Nonlinear Dissipative Systems
Guenter Ahlers
2005-05-27
This project consists of experimental investigations of heat transport, pattern formation, and bifurcation phenomena in non-linear non-equilibrium fluid-mechanical systems. These issues are studies in Rayleigh-B\\'enard convection, using both pure and multicomponent fluids. They are of fundamental scientific interest, but also play an important role in engineering, materials science, ecology, meteorology, geophysics, and astrophysics. For instance, various forms of convection are important in such diverse phenomena as crystal growth from a melt with or without impurities, energy production in solar ponds, flow in the earth's mantle and outer core, geo-thermal stratifications, and various oceanographic and atmospheric phenomena. Our work utilizes computer-enhanced shadowgraph imaging of flow patterns, sophisticated digital image analysis, and high-resolution heat transport measurements.
The bifurcations of nearly flat origami
Santangelo, Christian
Self-folding origami structures provide one means of fabricating complex, three-dimensional structures from a flat, two-dimensional sheet. Self-folding origami structures have been fabricated on scales ranging from macroscopic to microscopic and can have quite complicated structures with hundreds of folds arranged in complex patterns. I will describe our efforts to understand the mechanics and energetics of self-folding origami structures. Though the dimension of the configuration space of an origami structure scales with the size of the boundary and not with the number of vertices in the interior of the structure, a typical origami structure is also floppy in the sense that there are many possible ways to assign fold angles consistently. I will discuss our theoretical progress in understanding the geometry of the configuration space of origami. For random origami, the number of possible bifurcations grows surprisingly quickly even when the dimension of the configuration space is small. EFRI ODISSEI-1240441, DMR-0846582.
Transport Bifurcation in a Rotating Tokamak Plasma
Highcock, E. G.; Barnes, M.; Schekochihin, A. A.; Parra, F. I.; Roach, C. M.; Cowley, S. C.
2010-01-01
The effect of flow shear on turbulent transport in tokamaks is studied numerically in the experimentally relevant limit of zero magnetic shear. It is found that the plasma is linearly stable for all nonzero flow shear values, but that subcritical turbulence can be sustained nonlinearly at a wide range of temperature gradients. Flow shear increases the nonlinear temperature gradient threshold for turbulence but also increases the sensitivity of the heat flux to changes in the temperature gradient, except over a small range near the threshold where the sensitivity is decreased. A bifurcation in the equilibrium gradients is found: for a given input of heat, it is possible, by varying the applied torque, to trigger a transition to significantly higher temperature and flow gradients.
Bifurcated SEN with Fluid Flow Conditioners
F. Rivera-Perez
2014-01-01
Full Text Available This work evaluates the performance of a novel design for a bifurcated submerged entry nozzle (SEN used for the continuous casting of steel slabs. The proposed design incorporates fluid flow conditioners attached on SEN external wall. The fluid flow conditioners impose a pseudosymmetric pattern in the upper zone of the mold by inhibiting the fluid exchange between the zones created by conditioners. The performance of the SEN with fluid flow conditioners is analyzed through numerical simulations using the CFD technique. Numerical results were validated by means of physical simulations conducted on a scaled cold water model. Numerical and physical simulations confirmed that the performance of the proposed SEN is superior to a traditional one. Fluid flow conditioners reduce the liquid free surface fluctuations and minimize the occurrence of vortexes at the free surface.
Oscillatory bifurcation for semilinear ordinary differential equations
Tetsutaro Shibata
2016-06-01
\\] where $f(u = u + (1/2\\sin^k u$ ($k \\ge 2$ and $\\lambda > 0$ is a bifurcation parameter. It is known that $\\lambda$ is parameterized by the maximum norm $\\alpha = \\Vert u_\\lambda\\Vert_\\infty$ of the solution $u_\\lambda$ associated with $\\lambda$ and is written as $\\lambda = \\lambda(k,\\alpha$. When we focus on the asymptotic behavior of $\\lambda(k,\\alpha$ as $\\alpha \\to \\infty$, it is natural to expect that $\\lambda(k, \\alpha \\to \\pi^2/4$, and its convergence rate is common to $k$. Contrary to this expectation, we show that $\\lambda(2n_1+1,\\alpha$ tends to $\\pi^2/4$ faster than $\\lambda(2n_2,\\alpha$ as $\\alpha \\to \\infty$, where $n_1\\ge 1,\\ n_2 \\ge 1$ are arbitrary given integers.
Equilibrium-torus bifurcation in nonsmooth systems
Zhusubahyev, Z.T.; Mosekilde, Erik
2008-01-01
Considering a set of two coupled nonautonomous differential equations with discontinuous right-hand sides describing the behavior of a DC/DC power converter, we discuss a border-collision bifurcation that can lead to the birth of a two-dimensional invariant torus from a stable node equilibrium...... point. We obtain the chart of dynamic modes and show that there is a region of parameter space in which the system has a single stable node equilibrium point. Under variation of the parameters, this equilibrium may disappear as it collides with a discontinuity boundary between two smooth regions...... in the phase space. The disappearance of the equilibrium point is accompanied by the soft appearance of an unstable focus period-1 orbit surrounded by a resonant or ergodic torus. Detailed numerical calculations are supported by a theoretical investigation of the normal form map that represents the piecewise...
Clausius entropy for arbitrary bifurcate null surfaces
Baccetti, Valentina; Visser, Matt
2014-01-01
Jacobson’s thermodynamic derivation of the Einstein equations was originally applied only to local Rindler horizons. But at least some parts of that construction can usefully be extended to give meaningful results for arbitrary bifurcate null surfaces. As presaged in Jacobson’s original article, this more general construction sharply brings into focus the questions: is entropy objectively ‘real’? Or is entropy in some sense subjective and observer-dependent? These innocent questions open a Pandora’s box of often inconclusive debate. A consensus opinion, though certainly not universally held, seems to be that Clausius entropy (thermodynamic entropy, defined via a Clausius relation dS=đQ/T) should be objectively real, but that the ontological status of statistical entropy (Shannon or von Neumann entropy) is much more ambiguous, and much more likely to be observer-dependent. This question is particularly pressing when it comes to understanding Bekenstein entropy (black hole entropy). To perhaps further add to the confusion, we shall argue that even the Clausius entropy can often be observer-dependent. In the current article we shall conclusively demonstrate that one can meaningfully assign a notion of Clausius entropy to arbitrary bifurcate null surfaces—effectively defining a ‘virtual Clausius entropy’ for arbitrary ‘virtual (local) causal horizons’. As an application, we see that we can implement a version of the generalized second law (GSL) for this virtual Clausius entropy. This version of GSL can be related to certain (nonstandard) integral variants of the null energy condition. Because the concepts involved are rather subtle, we take some effort in being careful and explicit in developing our framework. In future work we will apply this construction to generalize Jacobson’s derivation of the Einstein equations. (paper)
Bondarenko, Vladimir E.; Cymbalyuk, Gennady S.; Patel, Girish; DeWeerth, Stephen P.; Calabrese, Ronald L.
2004-01-01
Oscillatory activity in the central nervous system is associated with various functions, like motor control, memory formation, binding, and attention. Quasiperiodic oscillations are rarely discussed in the neurophysiological literature yet they may play a role in the nervous system both during normal function and disease. Here we use a physical system and a model to explore scenarios for how quasiperiodic oscillations might arise in neuronal networks. An oscillatory system of two mutually inhibitory neuronal units is a ubiquitous network module found in nervous systems and is called a half-center oscillator. Previously we created a half-center oscillator of two identical oscillatory silicon (analog Very Large Scale Integration) neurons and developed a mathematical model describing its dynamics. In the mathematical model, we have shown that an in-phase limit cycle becomes unstable through a subcritical torus bifurcation. However, the existence of this torus bifurcation in experimental silicon two-neuron system was not rigorously demonstrated or investigated. Here we demonstrate the torus predicted by the model for the silicon implementation of a half-center oscillator using complex time series analysis, including bifurcation diagrams, mapping techniques, correlation functions, amplitude spectra, and correlation dimensions, and we investigate how the properties of the quasiperiodic oscillations depend on the strengths of coupling between the silicon neurons. The potential advantages and disadvantages of quasiperiodic oscillations (torus) for biological neural systems and artificial neural networks are discussed
Fractional noise destroys or induces a stochastic bifurcation
Yang, Qigui, E-mail: qgyang@scut.edu.cn [School of Sciences, South China University of Technology, Guangzhou 510640 (China); Zeng, Caibin, E-mail: zeng.cb@mail.scut.edu.cn [School of Sciences, South China University of Technology, Guangzhou 510640 (China); School of Automation Science and Engineering, South China University of Technology, Guangzhou 510640 (China); Wang, Cong, E-mail: wangcong@scut.edu.cn [School of Automation Science and Engineering, South China University of Technology, Guangzhou 510640 (China)
2013-12-15
Little seems to be known about the stochastic bifurcation phenomena of non-Markovian systems. Our intention in this paper is to understand such complex dynamics by a simple system, namely, the Black-Scholes model driven by a mixed fractional Brownian motion. The most interesting finding is that the multiplicative fractional noise not only destroys but also induces a stochastic bifurcation under some suitable conditions. So it opens a possible way to explore the theory of stochastic bifurcation in the non-Markovian framework.
Optimization Design and Application of Underground Reinforced Concrete Bifurcation Pipe
Chao Su
2015-01-01
Full Text Available Underground reinforced concrete bifurcation pipe is an important part of conveyance structure. During construction, the workload of excavation and concrete pouring can be significantly decreased according to optimized pipe structure, and the engineering quality can be improved. This paper presents an optimization mathematical model of underground reinforced concrete bifurcation pipe structure according to real working status of several common pipe structures from real cases. Then, an optimization design system was developed based on Particle Swarm Optimization algorithm. Furthermore, take the bifurcation pipe of one hydropower station as an example: optimization analysis was conducted, and accuracy and stability of the optimization design system were verified successfully.
Arctic melt ponds and bifurcations in the climate system
Sudakov, I.; Vakulenko, S. A.; Golden, K. M.
2015-05-01
Understanding how sea ice melts is critical to climate projections. In the Arctic, melt ponds that develop on the surface of sea ice floes during the late spring and summer largely determine their albedo - a key parameter in climate modeling. Here we explore the possibility of a conceptual sea ice climate model passing through a bifurcation point - an irreversible critical threshold as the system warms, by incorporating geometric information about melt pond evolution. This study is based on a bifurcation analysis of the energy balance climate model with ice-albedo feedback as the key mechanism driving the system to bifurcation points.
Bifurcation of learning and structure formation in neuronal maps
Marschler, Christian; Faust-Ellsässer, Carmen; Starke, Jens
2014-01-01
to map formation in the laminar nucleus of the barn owl's auditory system. Using equation-free methods, we perform a bifurcation analysis of spatio-temporal structure formation in the associated synaptic-weight matrix. This enables us to analyze learning as a bifurcation process and follow the unstable...... states as well. A simple time translation of the learning window function shifts the bifurcation point of structure formation and goes along with traveling waves in the map, without changing the animal's sound localization performance....
The Butterfly Diagram Internal Structure
Ternullo, Maurizio
2013-01-01
A time-latitude diagram, where the spotgroup area is taken into account, is presented for cycles 12 through 23. The results show that the spotted area is concentrated in few, small portions ( k nots ) of the Butterfly Diagram (BD). The BD may be described as a cluster of knots. Knots are distributed in the butterfly wings in a seemingly randomly way. A knot may appear at either lower or higher latitudes than previous ones, in spite of the prevalent tendency to appear at lower and lower latitudes. Accordingly, the spotted area centroid, far from continuously drifting equatorward, drifts poleward or remains stationary in any hemisphere for significant fractions (≈ 1/3) of the cycle total duration. In a relevant number of semicycles, knots seem to form two roughly parallel, oblique c hains , separated by an underspotted band. This picture suggests that two (or more) ''activity streams'' approach the equator at a rate higher than the spot zone as a whole.
Susanna Bisogni
2018-01-01
Full Text Available The cosmological model is at present not tested between the redshift of the farthest observed supernovae (z ~ 1.4 and that of the Cosmic Microwave Background (z ~ 1,100. Here we introduce a new method to measure the cosmological parameters: we show that quasars can be used as “standard candles” by employing the non-linear relation between their intrinsic UV and X-ray emission as an absolute distance indicator. We built a sample of ~1,900 quasars with available UV and X-ray observations, and produced a Hubble Diagram up to z ~ 5. The analysis of the quasar Hubble Diagram, when used in combination with supernovae, provides robust constraints on the matter and energy content in the cosmos. The application of this method to forthcoming, larger quasar samples, will also provide tight constraints on the dark energy equation of state and its possible evolution with time.
Causal diagrams in systems epidemiology
Joffe Michael
2012-03-01
Full Text Available Abstract Methods of diagrammatic modelling have been greatly developed in the past two decades. Outside the context of infectious diseases, systematic use of diagrams in epidemiology has been mainly confined to the analysis of a single link: that between a disease outcome and its proximal determinant(s. Transmitted causes ("causes of causes" tend not to be systematically analysed. The infectious disease epidemiology modelling tradition models the human population in its environment, typically with the exposure-health relationship and the determinants of exposure being considered at individual and group/ecological levels, respectively. Some properties of the resulting systems are quite general, and are seen in unrelated contexts such as biochemical pathways. Confining analysis to a single link misses the opportunity to discover such properties. The structure of a causal diagram is derived from knowledge about how the world works, as well as from statistical evidence. A single diagram can be used to characterise a whole research area, not just a single analysis - although this depends on the degree of consistency of the causal relationships between different populations - and can therefore be used to integrate multiple datasets. Additional advantages of system-wide models include: the use of instrumental variables - now emerging as an important technique in epidemiology in the context of mendelian randomisation, but under-used in the exploitation of "natural experiments"; the explicit use of change models, which have advantages with respect to inferring causation; and in the detection and elucidation of feedback.
Causal diagrams in systems epidemiology.
Joffe, Michael; Gambhir, Manoj; Chadeau-Hyam, Marc; Vineis, Paolo
2012-03-19
Methods of diagrammatic modelling have been greatly developed in the past two decades. Outside the context of infectious diseases, systematic use of diagrams in epidemiology has been mainly confined to the analysis of a single link: that between a disease outcome and its proximal determinant(s). Transmitted causes ("causes of causes") tend not to be systematically analysed.The infectious disease epidemiology modelling tradition models the human population in its environment, typically with the exposure-health relationship and the determinants of exposure being considered at individual and group/ecological levels, respectively. Some properties of the resulting systems are quite general, and are seen in unrelated contexts such as biochemical pathways. Confining analysis to a single link misses the opportunity to discover such properties.The structure of a causal diagram is derived from knowledge about how the world works, as well as from statistical evidence. A single diagram can be used to characterise a whole research area, not just a single analysis - although this depends on the degree of consistency of the causal relationships between different populations - and can therefore be used to integrate multiple datasets.Additional advantages of system-wide models include: the use of instrumental variables - now emerging as an important technique in epidemiology in the context of mendelian randomisation, but under-used in the exploitation of "natural experiments"; the explicit use of change models, which have advantages with respect to inferring causation; and in the detection and elucidation of feedback.
Scheil-Gulliver Constituent Diagrams
Pelton, Arthur D.; Eriksson, Gunnar; Bale, Christopher W.
2017-06-01
During solidification of alloys, conditions often approach those of Scheil-Gulliver cooling in which it is assumed that solid phases, once precipitated, remain unchanged. That is, they no longer react with the liquid or with each other. In the case of equilibrium solidification, equilibrium phase diagrams provide a valuable means of visualizing the effects of composition changes upon the final microstructure. In the present study, we propose for the first time the concept of Scheil-Gulliver constituent diagrams which play the same role as that in the case of Scheil-Gulliver cooling. It is shown how these diagrams can be calculated and plotted by the currently available thermodynamic database computing systems that combine Gibbs energy minimization software with large databases of optimized thermodynamic properties of solutions and compounds. Examples calculated using the FactSage system are presented for the Al-Li and Al-Mg-Zn systems, and for the Au-Bi-Sb-Pb system and its binary and ternary subsystems.
CISM Session on Bifurcation and Stability of Dissipative Systems
1993-01-01
The first theme concerns the plastic buckling of structures in the spirit of Hill’s classical approach. Non-bifurcation and stability criteria are introduced and post-bifurcation analysis performed by asymptotic development method in relation with Hutchinson’s work. Some recent results on the generalized standard model are given and their connection to Hill’s general formulation is presented. Instability phenomena of inelastic flow processes such as strain localization and necking are discussed. The second theme concerns stability and bifurcation problems in internally damaged or cracked colids. In brittle fracture or brittle damage, the evolution law of crack lengths or damage parameters is time-independent like in plasticity and leads to a similar mathematical description of the quasi-static evolution. Stability and non-bifurcation criteria in the sense of Hill can be again obtained from the discussion of the rate response.
Bifurcation dynamics of the tempered fractional Langevin equation
Zeng, Caibin, E-mail: macbzeng@scut.edu.cn; Yang, Qigui, E-mail: qgyang@scut.edu.cn [School of Mathematics, South China University of Technology, Guangzhou 510640 (China); Chen, YangQuan, E-mail: ychen53@ucmerced.edu [MESA LAB, School of Engineering, University of California, Merced, 5200 N. Lake Road, Merced, California 95343 (United States)
2016-08-15
Tempered fractional processes offer a useful extension for turbulence to include low frequencies. In this paper, we investigate the stochastic phenomenological bifurcation, or stochastic P-bifurcation, of the Langevin equation perturbed by tempered fractional Brownian motion. However, most standard tools from the well-studied framework of random dynamical systems cannot be applied to systems driven by non-Markovian noise, so it is desirable to construct possible approaches in a non-Markovian framework. We first derive the spectral density function of the considered system based on the generalized Parseval's formula and the Wiener-Khinchin theorem. Then we show that it enjoys interesting and diverse bifurcation phenomena exchanging between or among explosive-like, unimodal, and bimodal kurtosis. Therefore, our procedures in this paper are not merely comparable in scope to the existing theory of Markovian systems but also provide a possible approach to discern P-bifurcation dynamics in the non-Markovian settings.
Deformable 4DCT lung registration with vessel bifurcations
Hilsmann, A.; Vik, T.; Kaus, M.; Franks, K.; Bissonette, J.P.; Purdie, T.; Beziak, A.; Aach, T.
2007-01-01
In radiotherapy planning of lung cancer, breathing motion causes uncertainty in the determination of the target volume. Image registration makes it possible to get information about the deformation of the lung and the tumor movement in the respiratory cycle from a few images. A dedicated, automatic, landmark-based technique was developed that finds corresponding vessel bifurcations. Hereby, we developed criteria to characterize pronounced bifurcations for which correspondence finding was more stable and accurate. The bifurcations were extracted from automatically segmented vessel trees in maximum inhale and maximum exhale CT thorax data sets. To find corresponding bifurcations in both data sets we used the shape context approach of Belongie et al. Finally, a volumetric lung deformation was obtained using thin-plate spline interpolation and affine registration. The method is evaluated on 10 4D-CT data sets of patients with lung cancer. (orig.)
Multiple bifurcations and periodic 'bubbling' in a delay population model
Peng Mingshu
2005-01-01
In this paper, the flip bifurcation and periodic doubling bifurcations of a discrete population model without delay influence is firstly studied and the phenomenon of Feigenbaum's cascade of periodic doublings is also observed. Secondly, we explored the Neimark-Sacker bifurcation in the delay population model (two-dimension discrete dynamical systems) and the unique stable closed invariant curve which bifurcates from the nontrivial fixed point. Finally, a computer-assisted study for the delay population model is also delved into. Our computer simulation shows that the introduction of delay effect in a nonlinear difference equation derived from the logistic map leads to much richer dynamic behavior, such as stable node → stable focus → an lower-dimensional closed invariant curve (quasi-periodic solution, limit cycle) or/and stable periodic solutions → chaotic attractor by cascading bubbles (the combination of potential period doubling and reverse period-doubling) and the sudden change between two different attractors, etc
Bifurcation theory for hexagonal agglomeration in economic geography
Ikeda, Kiyohiro
2014-01-01
This book contributes to an understanding of how bifurcation theory adapts to the analysis of economic geography. It is easily accessible not only to mathematicians and economists, but also to upper-level undergraduate and graduate students who are interested in nonlinear mathematics. The self-organization of hexagonal agglomeration patterns of industrial regions was first predicted by the central place theory in economic geography based on investigations of southern Germany. The emergence of hexagonal agglomeration in economic geography models was envisaged by Krugman. In this book, after a brief introduction of central place theory and new economic geography, the missing link between them is discovered by elucidating the mechanism of the evolution of bifurcating hexagonal patterns. Pattern formation by such bifurcation is a well-studied topic in nonlinear mathematics, and group-theoretic bifurcation analysis is a well-developed theoretical tool. A finite hexagonal lattice is used to express uniformly distri...
Periodic solutions and bifurcations of delay-differential equations
He Jihuan
2005-01-01
In this Letter a simple but effective iteration method is proposed to search for limit cycles or bifurcation curves of delay-differential equations. An example is given to illustrate its convenience and effectiveness
Defining Electron Bifurcation in the Electron-Transferring Flavoprotein Family.
Garcia Costas, Amaya M; Poudel, Saroj; Miller, Anne-Frances; Schut, Gerrit J; Ledbetter, Rhesa N; Fixen, Kathryn R; Seefeldt, Lance C; Adams, Michael W W; Harwood, Caroline S; Boyd, Eric S; Peters, John W
2017-11-01
Electron bifurcation is the coupling of exergonic and endergonic redox reactions to simultaneously generate (or utilize) low- and high-potential electrons. It is the third recognized form of energy conservation in biology and was recently described for select electron-transferring flavoproteins (Etfs). Etfs are flavin-containing heterodimers best known for donating electrons derived from fatty acid and amino acid oxidation to an electron transfer respiratory chain via Etf-quinone oxidoreductase. Canonical examples contain a flavin adenine dinucleotide (FAD) that is involved in electron transfer, as well as a non-redox-active AMP. However, Etfs demonstrated to bifurcate electrons contain a second FAD in place of the AMP. To expand our understanding of the functional variety and metabolic significance of Etfs and to identify amino acid sequence motifs that potentially enable electron bifurcation, we compiled 1,314 Etf protein sequences from genome sequence databases and subjected them to informatic and structural analyses. Etfs were identified in diverse archaea and bacteria, and they clustered into five distinct well-supported groups, based on their amino acid sequences. Gene neighborhood analyses indicated that these Etf group designations largely correspond to putative differences in functionality. Etfs with the demonstrated ability to bifurcate were found to form one group, suggesting that distinct conserved amino acid sequence motifs enable this capability. Indeed, structural modeling and sequence alignments revealed that identifying residues occur in the NADH- and FAD-binding regions of bifurcating Etfs. Collectively, a new classification scheme for Etf proteins that delineates putative bifurcating versus nonbifurcating members is presented and suggests that Etf-mediated bifurcation is associated with surprisingly diverse enzymes. IMPORTANCE Electron bifurcation has recently been recognized as an electron transfer mechanism used by microorganisms to maximize
Ergodicity-breaking bifurcations and tunneling in hyperbolic transport models
Giona, M.; Brasiello, A.; Crescitelli, S.
2015-11-01
One of the main differences between parabolic transport, associated with Langevin equations driven by Wiener processes, and hyperbolic models related to generalized Kac equations driven by Poisson processes, is the occurrence in the latter of multiple stable invariant densities (Frobenius multiplicity) in certain regions of the parameter space. This phenomenon is associated with the occurrence in linear hyperbolic balance equations of a typical bifurcation, referred to as the ergodicity-breaking bifurcation, the properties of which are thoroughly analyzed.
Bunch lengthening with bifurcation in electron storage rings
Kim, Eun-San; Hirata, Kohji [National Lab. for High Energy Physics, Tsukuba, Ibaraki (Japan)
1996-08-01
The mapping which shows equilibrium particle distribution in synchrotron phase space for electron storage rings is discussed with respect to some localized constant wake function based on the Gaussian approximation. This mapping shows multi-periodic states as well as double bifurcation in dynamical states of the equilibrium bunch length. When moving around parameter space, the system shows a transition/bifurcation which is not always reversible. These results derived by mapping are confirmed by multiparticle tracking. (author)
Iterative Controller Tuning for Process with Fold Bifurcations
Huusom, Jakob Kjøbsted; Poulsen, Niels Kjølstad; Jørgensen, Sten Bay
2007-01-01
Processes involving fold bifurcation are notoriously difficult to control in the vicinity of the fold where most often optimal productivity is achieved . In cases with limited process insight a model based control synthesis is not possible. This paper uses a data driven approach with an improved...... version of iterative feedback tuning to optimizing a closed loop performance criterion, as a systematic tool for tuning process with fold bifurcations....
Bifurcated states of the error-field-induced magnetic islands
Zheng, L.-J.; Li, B.; Hazeltine, R.D.
2008-01-01
We find that the formation of the magnetic islands due to error fields shows bifurcation when neoclassical effects are included. The bifurcation, which follows from including bootstrap current terms in a description of island growth in the presence of error fields, provides a path to avoid the island-width pole in the classical description. The theory offers possible theoretical explanations for the recent DIII-D and JT-60 experimental observations concerning confinement deterioration with increasing error field
Using Affinity Diagrams to Evaluate Interactive Prototypes
Lucero, Andrés
2015-01-01
our particular use of affinity diagramming in prototype evaluations. We reflect on a decade’s experience using affinity diagramming across a number of projects, both in industry and academia. Our affinity diagramming process in interaction design has been tailored and consists of four stages: creating...
Zhang Hailong; Zhang Ning; Wang Enrong; Min Fuhong
2016-01-01
The magneto-rheological damper (MRD) is a promising device used in vehicle semi-active suspension systems, for its continuous adjustable damping output. However, the innate nonlinear hysteresis characteristic of MRD may cause the nonlinear behaviors. In this work, a two-degree-of-freedom (2-DOF) MR suspension system was established first, by employing the modified Bouc–Wen force–velocity (F–v) hysteretic model. The nonlinear dynamic response of the system was investigated under the external excitation of single-frequency harmonic and bandwidth-limited stochastic road surface. The largest Lyapunov exponent (LLE) was used to detect the chaotic area of the frequency and amplitude of harmonic excitation, and the bifurcation diagrams, time histories, phase portraits, and power spectrum density (PSD) diagrams were used to reveal the dynamic evolution process in detail. Moreover, the LLE and Kolmogorov entropy (K entropy) were used to identify whether the system response was random or chaotic under stochastic road surface. The results demonstrated that the complex dynamical behaviors occur under different external excitation conditions. The oscillating mechanism of alternating periodic oscillations, quasi-periodic oscillations, and chaotic oscillations was observed in detail. The chaotic regions revealed that chaotic motions may appear in conditions of mid-low frequency and large amplitude, as well as small amplitude and all frequency. The obtained parameter regions where the chaotic motions may appear are useful for design of structural parameters of the vibration isolation, and the optimization of control strategy for MR suspension system. (paper)
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...
Bifurcated equilibria in centrifugally confined plasma
Shamim, I.; Teodorescu, C.; Guzdar, P. N.; Hassam, A. B.; Clary, R.; Ellis, R.; Lunsford, R.
2008-01-01
A bifurcation theory and associated computational model are developed to account for abrupt transitions observed recently on the Maryland Centrifugal eXperiment (MCX) [R. F. Ellis et al. Phys. Plasmas 8, 2057 (2001)], a supersonically rotating magnetized plasma that relies on centrifugal forces to prevent thermal expansion of plasma along the magnetic field. The observed transitions are from a well-confined, high-rotation state (HR-mode) to a lower-rotation, lesser-confined state (O-mode). A two-dimensional time-dependent magnetohydrodynamics code is used to simulate the dynamical equilibrium states of the MCX configuration. In addition to the expected viscous drag on the core plasma rotation, a momentum loss term is added that models the friction of plasma on the enhanced level of neutrals expected in the vicinity of the insulators at the throats of the magnetic mirror geometry. At small values of the external rotation drive, the plasma is not well-centrifugally confined and hence experiences the drag from near the insulators. Beyond a critical value of the external drive, the system makes an abrupt transition to a well-centrifugally confined state in which the plasma has pulled away from the end insulator plates; more effective centrifugal confinement lowers the plasma mass near the insulators allowing runaway increases in the rotation speed. The well-confined steady state is reached when the external drive is balanced by only the viscosity of the core plasma. A clear hysteresis phenomenon is shown.
Bursting oscillations, bifurcation and synchronization in neuronal systems
Wang Haixia [School of Science, Nanjing University of Science and Technology, Nanjing 210094 (China); Wang Qingyun, E-mail: drwangqy@gmail.com [Department of Dynamics and Control, Beihang University, Beijing 100191 (China); Lu Qishao [Department of Dynamics and Control, Beihang University, Beijing 100191 (China)
2011-08-15
Highlights: > We investigate bursting oscillations and related bifurcation in the modified Morris-Lecar neuron. > Two types of fast-slow bursters are analyzed in detail. > We show the properties of some crucial bifurcation points. > Synchronization transition and the neural excitability are explored in the coupled bursters. - Abstract: This paper investigates bursting oscillations and related bifurcation in the modified Morris-Lecar neuron. It is shown that for some appropriate parameters, the modified Morris-Lecar neuron can exhibit two types of fast-slow bursters, that is 'circle/fold cycle' bursting and 'subHopf/homoclinic' bursting with class 1 and class 2 neural excitability, which have different neuro-computational properties. By means of the analysis of fast-slow dynamics and phase plane, we explore bifurcation mechanisms associated with the two types of bursters. Furthermore, the properties of some crucial bifurcation points, which can determine the type of the burster, are studied by the stability and bifurcation theory. In addition, we investigate the influence of the coupling strength on synchronization transition and the neural excitability in two electrically coupled bursters with the same bursting type. More interestingly, the multi-time-scale synchronization transition phenomenon is found as the coupling strength varies.
Bifurcation magnetic resonance in films magnetized along hard magnetization axis
Vasilevskaya, Tatiana M., E-mail: t_vasilevs@mail.ru [Ulyanovsk State University, Leo Tolstoy 42, 432017 Ulyanovsk (Russian Federation); Sementsov, Dmitriy I.; Shutyi, Anatoliy M. [Ulyanovsk State University, Leo Tolstoy 42, 432017 Ulyanovsk (Russian Federation)
2012-09-15
We study low-frequency ferromagnetic resonance in a thin film magnetized along the hard magnetization axis performing an analysis of magnetization precession dynamics equations and numerical simulation. Two types of films are considered: polycrystalline uniaxial films and single-crystal films with cubic magnetic anisotropy. An additional (bifurcation) resonance initiated by the bistability, i.e. appearance of two closely spaced equilibrium magnetization states is registered. The modification of dynamic modes provoked by variation of the frequency, amplitude, and magnetic bias value of the ac field is studied. Both steady and chaotic magnetization precession modes are registered in the bifurcation resonance range. - Highlights: Black-Right-Pointing-Pointer An additional bifurcation resonance arises in a case of a thin film magnetized along HMA. Black-Right-Pointing-Pointer Bifurcation resonance occurs due to the presence of two closely spaced equilibrium magnetization states. Black-Right-Pointing-Pointer Both regular and chaotic precession modes are realized within bifurcation resonance range. Black-Right-Pointing-Pointer Appearance of dynamic bistability is typical for bifurcation resonance.
Bifurcation magnetic resonance in films magnetized along hard magnetization axis
Vasilevskaya, Tatiana M.; Sementsov, Dmitriy I.; Shutyi, Anatoliy M.
2012-01-01
We study low-frequency ferromagnetic resonance in a thin film magnetized along the hard magnetization axis performing an analysis of magnetization precession dynamics equations and numerical simulation. Two types of films are considered: polycrystalline uniaxial films and single-crystal films with cubic magnetic anisotropy. An additional (bifurcation) resonance initiated by the bistability, i.e. appearance of two closely spaced equilibrium magnetization states is registered. The modification of dynamic modes provoked by variation of the frequency, amplitude, and magnetic bias value of the ac field is studied. Both steady and chaotic magnetization precession modes are registered in the bifurcation resonance range. - Highlights: ► An additional bifurcation resonance arises in a case of a thin film magnetized along HMA. ► Bifurcation resonance occurs due to the presence of two closely spaced equilibrium magnetization states. ► Both regular and chaotic precession modes are realized within bifurcation resonance range. ► Appearance of dynamic bistability is typical for bifurcation resonance.
Diagram, a Learning Environment for Initiation to Object-Oriented Modeling with UML Class Diagrams
Py, Dominique; Auxepaules, Ludovic; Alonso, Mathilde
2013-01-01
This paper presents Diagram, a learning environment for object-oriented modelling (OOM) with UML class diagrams. Diagram an open environment, in which the teacher can add new exercises without constraints on the vocabulary or the size of the diagram. The interface includes methodological help, encourages self-correcting and self-monitoring, and…
Diagram Size vs. Layout Flaws: Understanding Quality Factors of UML Diagrams
Störrle, Harald
2016-01-01
, though, is our third goal of extending our analysis aspects of diagram quality. Method: We improve our definition of diagram size and add a (provisional) definition of diagram quality as the number of topographic layout flaws. We apply these metrics on 60 diagrams of the five most commonly used types...... of UML diagram. We carefully analyze the structure of our diagram samples to ensure representativeness. We correlate diagram size and layout quality with modeler performance data obtained in previous experiments. The data set is the largest of its kind (n-156). Results: We replicate earlier findings......, and extend them to two new diagram types. We provide an improved definition of diagram size, and provide a definition of topographic layout quality, which is one more step towards a comprehensive definition of diagram quality as such. Both metrics are shown to be objectively applicable. We quantify...
Voronoi Diagrams Without Bounding Boxes
Sang, E. T. K.
2015-10-01
We present a technique for presenting geographic data in Voronoi diagrams without having to specify a bounding box. The method restricts Voronoi cells to points within a user-defined distance of the data points. The mathematical foundation of the approach is presented as well. The cell clipping method is particularly useful for presenting geographic data that is spread in an irregular way over a map, as for example the Dutch dialect data displayed in Figure 2. The automatic generation of reasonable cell boundaries also makes redundant a frequently used solution to this problem that requires data owners to specify region boundaries, as in Goebl (2010) and Nerbonne et al (2011).
Multi-currency Influence Diagrams
Nielsen, Søren Holbech; Nielsen, Thomas Dyhre; Jensen, Finn Verner
2004-01-01
Solution of decision problems, which involve utilities of several currencies, have traditionally required the problems to be converted into decision problems involving utilities of only one currency. This conversion are carried out using a tacit transformation, under the assumption...... that the converted problem is equivalent to the original one. In this paper we present an extension of the Influence Diagram framework, which allows for these decision problems to be modelled in their original form. We present an algorithm that, given a conversion function between the currencies, discovers...
Phase diagrams for surface alloys
Christensen, Asbjørn; Ruban, Andrei; Stoltze, Per
1997-01-01
We discuss surface alloy phases and their stability based on surface phase diagrams constructed from the surface energy as a function of the surface composition. We show that in the simplest cases of pseudomorphic overlayers there are four generic classes of systems, characterized by the sign...... is based on density-functional calculations using the coherent-potential approximation and on effective-medium theory. We give self-consistent density-functional results for the segregation energy and surface mixing energy for all combinations of the transition and noble metals. Finally we discuss...
Bifurcation analysis and stability design for aircraft longitudinal motion with high angle of attack
Xin Qi
2015-02-01
Full Text Available Bifurcation analysis and stability design for aircraft longitudinal motion are investigated when the nonlinearity in flight dynamics takes place severely at high angle of attack regime. To predict the special nonlinear flight phenomena, bifurcation theory and continuation method are employed to systematically analyze the nonlinear motions. With the refinement of the flight dynamics for F-8 Crusader longitudinal motion, a framework is derived to identify the stationary bifurcation and dynamic bifurcation for high-dimensional system. Case study shows that the F-8 longitudinal motion undergoes saddle node bifurcation, Hopf bifurcation, Zero-Hopf bifurcation and branch point bifurcation under certain conditions. Moreover, the Hopf bifurcation renders series of multiple frequency pitch oscillation phenomena, which deteriorate the flight control stability severely. To relieve the adverse effects of these phenomena, a stabilization control based on gain scheduling and polynomial fitting for F-8 longitudinal motion is presented to enlarge the flight envelope. Simulation results validate the effectiveness of the proposed scheme.
Diagrams benefit symbolic problem-solving.
Chu, Junyi; Rittle-Johnson, Bethany; Fyfe, Emily R
2017-06-01
The format of a mathematics problem often influences students' problem-solving performance. For example, providing diagrams in conjunction with story problems can benefit students' understanding, choice of strategy, and accuracy on story problems. However, it remains unclear whether providing diagrams in conjunction with symbolic equations can benefit problem-solving performance as well. We tested the impact of diagram presence on students' performance on algebra equation problems to determine whether diagrams increase problem-solving success. We also examined the influence of item- and student-level factors to test the robustness of the diagram effect. We worked with 61 seventh-grade students who had received 2 months of pre-algebra instruction. Students participated in an experimenter-led classroom session. Using a within-subjects design, students solved algebra problems in two matched formats (equation and equation-with-diagram). The presence of diagrams increased equation-solving accuracy and the use of informal strategies. This diagram benefit was independent of student ability and item complexity. The benefits of diagrams found previously for story problems generalized to symbolic problems. The findings are consistent with cognitive models of problem-solving and suggest that diagrams may be a useful additional representation of symbolic problems. © 2017 The British Psychological Society.
Philip Tröster
2018-02-01
Full Text Available A cGMP signaling cascade composed of C-type natriuretic peptide, the guanylyl cyclase receptor Npr2 and cGMP-dependent protein kinase I (cGKI controls the bifurcation of sensory axons upon entering the spinal cord during embryonic development. However, the impact of axon bifurcation on sensory processing in adulthood remains poorly understood. To investigate the functional consequences of impaired axon bifurcation during adult stages we generated conditional mouse mutants of Npr2 and cGKI (Npr2fl/fl;Wnt1Cre and cGKIKO/fl;Wnt1Cre that lack sensory axon bifurcation in the absence of additional phenotypes observed in the global knockout mice. Cholera toxin labeling in digits of the hind paw demonstrated an altered shape of sensory neuron termination fields in the spinal cord of conditional Npr2 mouse mutants. Behavioral testing of both sexes indicated that noxious heat sensation and nociception induced by chemical irritants are impaired in the mutants, whereas responses to cold sensation, mechanical stimulation, and motor coordination are not affected. Recordings from C-fiber nociceptors in the hind limb skin showed that Npr2 function was not required to maintain normal heat sensitivity of peripheral nociceptors. Thus, the altered behavioral responses to noxious heat found in Npr2fl/fl;Wnt1Cre mice is not due to an impaired C-fiber function. Overall, these data point to a critical role of axonal bifurcation for the processing of pain induced by heat or chemical stimuli.
Bifurcation and Fractal of the Coupled Logistic Map
Wang, Xingyuan; Luo, Chao
The nature of the fixed points of the coupled Logistic map is researched, and the boundary equation of the first bifurcation of the coupled Logistic map in the parameter space is given out. Using the quantitative criterion and rule of system chaos, i.e., phase graph, bifurcation graph, power spectra, the computation of the fractal dimension, and the Lyapunov exponent, the paper reveals the general characteristics of the coupled Logistic map transforming from regularity to chaos, the following conclusions are shown: (1) chaotic patterns of the coupled Logistic map may emerge out of double-periodic bifurcation and Hopf bifurcation, respectively; (2) during the process of double-period bifurcation, the system exhibits self-similarity and scale transform invariability in both the parameter space and the phase space. From the research of the attraction basin and Mandelbrot-Julia set of the coupled Logistic map, the following conclusions are indicated: (1) the boundary between periodic and quasiperiodic regions is fractal, and that indicates the impossibility to predict the moving result of the points in the phase plane; (2) the structures of the Mandelbrot-Julia sets are determined by the control parameters, and their boundaries have the fractal characteristic.
Secondary Channel Bifurcation Geometry: A Multi-dimensional Problem
Gaeuman, D.; Stewart, R. L.
2017-12-01
The construction of secondary channels (or side channels) is a popular strategy for increasing aquatic habitat complexity in managed rivers. Such channels, however, frequently experience aggradation that prevents surface water from entering the side channels near their bifurcation points during periods of relatively low discharge. This failure to maintain an uninterrupted surface water connection with the main channel can reduce the habitat value of side channels for fish species that prefer lotic conditions. Various factors have been proposed as potential controls on the fate of side channels, including water surface slope differences between the main and secondary channels, the presence of main channel secondary circulation, transverse bed slopes, and bifurcation angle. A quantitative assessment of more than 50 natural and constructed secondary channels in the Trinity River of northern California indicates that bifurcations can assume a variety of configurations that are formed by different processes and whose longevity is governed by different sets of factors. Moreover, factors such as bifurcation angle and water surface slope vary with discharge level and are continuously distributed in space, such that they must be viewed as a multi-dimensional field rather than a single-valued attribute that can be assigned to a particular bifurcation.
Shells, orbit bifurcations, and symmetry restorations in Fermi systems
Magner, A. G., E-mail: magner@kinr.kiev.ua; Koliesnik, M. V. [NASU, Institute for Nuclear Research (Ukraine); Arita, K. [Nagoya Institute of Technology, Department of Physics (Japan)
2016-11-15
The periodic-orbit theory based on the improved stationary-phase method within the phase-space path integral approach is presented for the semiclassical description of the nuclear shell structure, concerning themain topics of the fruitful activity ofV.G. Soloviev. We apply this theory to study bifurcations and symmetry breaking phenomena in a radial power-law potential which is close to the realistic Woods–Saxon one up to about the Fermi energy. Using the realistic parametrization of nuclear shapes we explain the origin of the double-humped fission barrier and the asymmetry in the fission isomer shapes by the bifurcations of periodic orbits. The semiclassical origin of the oblate–prolate shape asymmetry and tetrahedral shapes is also suggested within the improved periodic-orbit approach. The enhancement of shell structures at some surface diffuseness and deformation parameters of such shapes are explained by existence of the simple local bifurcations and new non-local bridge-orbit bifurcations in integrable and partially integrable Fermi-systems. We obtained good agreement between the semiclassical and quantum shell-structure components of the level density and energy for several surface diffuseness and deformation parameters of the potentials, including their symmetry breaking and bifurcation values.
Stochastic Bifurcation Analysis of an Elastically Mounted Flapping Airfoil
Bose Chandan
2018-01-01
Full Text Available The present paper investigates the effects of noisy flow fluctuations on the fluid-structure interaction (FSI behaviour of a span-wise flexible wing modelled as a two degree-of-freedom elastically mounted flapping airfoil. In the sterile flow conditions, the system undergoes a Hopf bifurcation as the free-stream velocity exceeds a critical limit resulting in a stable limit-cycle oscillation (LCO from a fixed point response. On the other hand, the qualitative dynamics changes from a stochastic fixed point to a random LCO through an intermittent state in the presence of irregular flow fluctuations. The probability density function depicts the most probable system state in the phase space. A phenomenological bifurcation (P-bifurcation analysis based on the transition in the topology associated with the structure of the joint probability density function (pdf of the response variables has been carried out. The joint pdf corresponding to the stochastic fixed point possesses a Dirac delta function like structure with a sharp single peak around zero. As the mean flow speed crosses the critical value, the joint pdf bifurcates to a crater-like structure indicating the occurrence of a P-bifurcation. The intermittent state is characterized by the co-existence of the unimodal as well as the crater like structure.
Disconnected Diagrams in Lattice QCD
Gambhir, Arjun Singh
In this work, we present state-of-the-art numerical methods and their applications for computing a particular class of observables using lattice quantum chromodynamics (Lattice QCD), a discretized version of the fundamental theory of quarks and gluons. These observables require calculating so called "disconnected diagrams" and are important for understanding many aspects of hadron structure, such as the strange content of the proton. We begin by introducing the reader to the key concepts of Lattice QCD and rigorously define the meaning of disconnected diagrams through an example of the Wick contractions of the nucleon. Subsequently, the calculation of observables requiring disconnected diagrams is posed as the computationally challenging problem of finding the trace of the inverse of an incredibly large, sparse matrix. This is followed by a brief primer of numerical sparse matrix techniques that overviews broadly used methods in Lattice QCD and builds the background for the novel algorithm presented in this work. We then introduce singular value deflation as a method to improve convergence of trace estimation and analyze its effects on matrices from a variety of fields, including chemical transport modeling, magnetohydrodynamics, and QCD. Finally, we apply this method to compute observables such as the strange axial charge of the proton and strange sigma terms in light nuclei. The work in this thesis is innovative for four reasons. First, we analyze the effects of deflation with a model that makes qualitative predictions about its effectiveness, taking only the singular value spectrum as input, and compare deflated variance with different types of trace estimator noise. Second, the synergy between probing methods and deflation is investigated both experimentally and theoretically. Third, we use the synergistic combination of deflation and a graph coloring algorithm known as hierarchical probing to conduct a lattice calculation of light disconnected matrix elements
Disconnected Diagrams in Lattice QCD
Gambhir, Arjun [College of William and Mary, Williamsburg, VA (United States)
2017-08-01
In this work, we present state-of-the-art numerical methods and their applications for computing a particular class of observables using lattice quantum chromodynamics (Lattice QCD), a discretized version of the fundamental theory of quarks and gluons. These observables require calculating so called \\disconnected diagrams" and are important for understanding many aspects of hadron structure, such as the strange content of the proton. We begin by introducing the reader to the key concepts of Lattice QCD and rigorously define the meaning of disconnected diagrams through an example of the Wick contractions of the nucleon. Subsequently, the calculation of observables requiring disconnected diagrams is posed as the computationally challenging problem of finding the trace of the inverse of an incredibly large, sparse matrix. This is followed by a brief primer of numerical sparse matrix techniques that overviews broadly used methods in Lattice QCD and builds the background for the novel algorithm presented in this work. We then introduce singular value deflation as a method to improve convergence of trace estimation and analyze its effects on matrices from a variety of fields, including chemical transport modeling, magnetohydrodynamics, and QCD. Finally, we apply this method to compute observables such as the strange axial charge of the proton and strange sigma terms in light nuclei. The work in this thesis is innovative for four reasons. First, we analyze the effects of deflation with a model that makes qualitative predictions about its effectiveness, taking only the singular value spectrum as input, and compare deflated variance with different types of trace estimator noise. Second, the synergy between probing methods and deflation is investigated both experimentally and theoretically. Third, we use the synergistic combination of deflation and a graph coloring algorithm known as hierarchical probing to conduct a lattice calculation of light disconnected matrix elements
Sediment sorting at a side channel bifurcation
van Denderen, Pepijn; Schielen, Ralph; Hulscher, Suzanne
2017-04-01
Side channels have been constructed to reduce the flood risk and to increase the ecological value of the river. In various Dutch side channels large aggradation in these channels occurred after construction. Measurements show that the grain size of the deposited sediment in the side channel is smaller than the grain size found on the bed of the main channel. This suggest that sorting occurs at the bifurcation of the side channel. The objective is to reproduce with a 2D morphological model the fining of the bed in the side channel and to study the effect of the sediment sorting on morphodynamic development of the side channel. We use a 2D Delft3D model with two sediment fractions. The first fraction corresponds with the grain size that can be found on the bed of the main channel and the second fraction corresponds with the grain size found in the side channel. With the numerical model we compute several side channel configurations in which we vary the length and the width of the side channel, and the curvature of the upstream channel. From these computations we can derive the equilibrium state and the time scale of the morphodynamic development of the side channel. Preliminary results show that even when a simple sediment transport relation is used, like Engelund & Hansen, more fine sediment enters the side channel than coarse sediment. This is as expected, and is probably related to the bed slope effects which are a function of the Shields parameter. It is expected that by adding a sill at the entrance of the side channel the slope effect increases. This might reduce the amount of coarse sediment which enters the side channel even more. It is unclear whether the model used is able to reproduce the effect of such a sill correctly as modelling a sill and reproducing the correct hydrodynamic and morphodynamic behaviour is not straightforward in a 2D model. Acknowledgements: This research is funded by STW, part of the Dutch Organization for Scientific Research under
Herrmann, Enrico [Walter Burke Institute for Theoretical Physics, California Institute of Technology,Pasadena, CA 91125 (United States); Trnka, Jaroslav [Center for Quantum Mathematics and Physics (QMAP),Department of Physics, University of California,Davis, CA 95616 (United States)
2016-11-22
We study on-shell diagrams for gravity theories with any number of supersymmetries and find a compact Grassmannian formula in terms of edge variables of the graphs. Unlike in gauge theory where the analogous form involves only dlog-factors, in gravity there is a non-trivial numerator as well as higher degree poles in the edge variables. Based on the structure of the Grassmannian formula for N=8 supergravity we conjecture that gravity loop amplitudes also possess similar properties. In particular, we find that there are only logarithmic singularities on cuts with finite loop momentum and that poles at infinity are present, in complete agreement with the conjecture presented in http://dx.doi.org/10.1007/JHEP06(2015)202.
Phase diagram of ammonium nitrate
Dunuwille, Mihindra; Yoo, Choong-Shik
2013-01-01
Ammonium Nitrate (AN) is a fertilizer, yet becomes an explosive upon a small addition of chemical impurities. The origin of enhanced chemical sensitivity in impure AN (or AN mixtures) is not well understood, posing significant safety issues in using AN even today. To remedy the situation, we have carried out an extensive study to investigate the phase stability of AN and its mixtures with hexane (ANFO–AN mixed with fuel oil) and Aluminum (Ammonal) at high pressures and temperatures, using diamond anvil cells (DAC) and micro-Raman spectroscopy. The results indicate that pure AN decomposes to N 2 , N 2 O, and H 2 O at the onset of the melt, whereas the mixtures, ANFO and Ammonal, decompose at substantially lower temperatures. The present results also confirm the recently proposed phase IV-IV ′ transition above 17 GPa and provide new constraints for the melting and phase diagram of AN to 40 GPa and 400°C
VORONOI DIAGRAMS WITHOUT BOUNDING BOXES
E. T. K. Sang
2015-10-01
Full Text Available We present a technique for presenting geographic data in Voronoi diagrams without having to specify a bounding box. The method restricts Voronoi cells to points within a user-defined distance of the data points. The mathematical foundation of the approach is presented as well. The cell clipping method is particularly useful for presenting geographic data that is spread in an irregular way over a map, as for example the Dutch dialect data displayed in Figure 2. The automatic generation of reasonable cell boundaries also makes redundant a frequently used solution to this problem that requires data owners to specify region boundaries, as in Goebl (2010 and Nerbonne et al (2011.
Anatomy of geodesic Witten diagrams
Chen, Heng-Yu; Kuo, En-Jui [Department of Physics and Center for Theoretical Sciences, National Taiwan University,Taipei 10617, Taiwan (China); Kyono, Hideki [Department of Physics, Kyoto University,Kitashirakawa Oiwake-cho, Kyoto 606-8502 (Japan)
2017-05-12
We revisit the so-called “Geodesic Witten Diagrams” (GWDs) https://www.doi.org/10.1007/JHEP01(2016)146, proposed to be the holographic dual configuration of scalar conformal partial waves, from the perspectives of CFT operator product expansions. To this end, we explicitly consider three point GWDs which are natural building blocks of all possible four point GWDs, discuss their gluing procedure through integration over spectral parameter, and this leads us to a direct identification with the integral representation of CFT conformal partial waves. As a main application of this general construction, we consider the holographic dual of the conformal partial waves for external primary operators with spins. Moreover, we consider the closely related “split representation” for the bulk to bulk spinning propagator, to demonstrate how ordinary scalar Witten diagram with arbitrary spin exchange, can be systematically decomposed into scalar GWDs. We also discuss how to generalize to spinning cases.
Stereo 3D spatial phase diagrams
Kang, Jinwu, E-mail: kangjw@tsinghua.edu.cn; Liu, Baicheng, E-mail: liubc@tsinghua.edu.cn
2016-07-15
Phase diagrams serve as the fundamental guidance in materials science and engineering. Binary P-T-X (pressure–temperature–composition) and multi-component phase diagrams are of complex spatial geometry, which brings difficulty for understanding. The authors constructed 3D stereo binary P-T-X, typical ternary and some quaternary phase diagrams. A phase diagram construction algorithm based on the calculated phase reaction data in PandaT was developed. And the 3D stereo phase diagram of Al-Cu-Mg ternary system is presented. These phase diagrams can be illustrated by wireframe, surface, solid or their mixture, isotherms and isopleths can be generated. All of these can be displayed by the three typical display ways: electronic shutter, polarization and anaglyph (for example red-cyan glasses). Especially, they can be printed out with 3D stereo effect on paper, and watched by the aid of anaglyph glasses, which makes 3D stereo book of phase diagrams come to reality. Compared with the traditional illustration way, the front of phase diagrams protrude from the screen and the back stretches far behind of the screen under 3D stereo display, the spatial structure can be clearly and immediately perceived. These 3D stereo phase diagrams are useful in teaching and research. - Highlights: • Stereo 3D phase diagram database was constructed, including binary P-T-X, ternary, some quaternary and real ternary systems. • The phase diagrams can be watched by active shutter or polarized or anaglyph glasses. • The print phase diagrams retains 3D stereo effect which can be achieved by the aid of anaglyph glasses.
Selected topics on the nonrelativistic diagram technique
Blokhintsev, L.D.; Narodetskij, I.M.
1983-01-01
The construction of the diagrams describing various processes in the four-particle systems is considered. It is shown that these diagrams, in particular the diagrams corresponding to the simple mechanisms often used in nuclear and atomic reaction theory, are readily obtained from the Faddeev-Yakubovsky equations. The covariant four-dimensional formalism of nonrelativistic Feynman graphs and its connection to the three-dimensional graph technique are briefly discussed
EXPERIMENTAL STUDY ON SEDIMENT DISTRIBUTION AT CHANNEL BIFURCATION
G.M. Tarekul ISLAM; M.R. KABIR; Ainun NISHAT
2002-01-01
This paper presents the experimental results on the distribution of sediments at channel bifurcation.The experiments have been conducted in a physical model of channel bifurcation. It consists of a straight main channel which bifurcates into two branch channels of different widths. The test rig is a mobile bed with fixed bank. Four different noses have been used to study the phenomenon. For each nose, three upstream discharges viz. 20 l/s, 30 l/s and 40 l/s have been employed. From the measured data, discharges and sediment transport ratios per unit width are calculated in the downstream branches.These data have been set to the general nodal point relation and a set of equations has been developed to describe the distribution of sediments to the downstream branches for different nose angles.
Adaptive Control of Electromagnetic Suspension System by HOPF Bifurcation
Aming Hao
2013-01-01
Full Text Available EMS-type maglev system is essentially nonlinear and unstable. It is complicated to design a stable controller for maglev system which is under large-scale disturbance and parameter variance. Theory analysis expresses that this phenomenon corresponds to a HOPF bifurcation in mathematical model. An adaptive control law which adjusts the PID control parameters is given in this paper according to HOPF bifurcation theory. Through identification of the levitated mass, the controller adjusts the feedback coefficient to make the system far from the HOPF bifurcation point and maintain the stability of the maglev system. Simulation result indicates that adjusting proportion gain parameter using this method can extend the state stability range of maglev system and avoid the self-excited vibration efficiently.
Hopf bifurcation and chaos in macroeconomic models with policy lag
Liao Xiaofeng; Li Chuandong; Zhou Shangbo
2005-01-01
In this paper, we consider the macroeconomic models with policy lag, and study how lags in policy response affect the macroeconomic stability. The local stability of the nonzero equilibrium of this equation is investigated by analyzing the corresponding transcendental characteristic equation of its linearized equation. Some general stability criteria involving the policy lag and the system parameter are derived. By choosing the policy lag as a bifurcation parameter, the model is found to undergo a sequence of Hopf bifurcation. The direction and stability of the bifurcating periodic solutions are determined by using the normal form theory and the center manifold theorem. Moreover, we show that the government can stabilize the intrinsically unstable economy if the policy lag is sufficiently short, but the system become locally unstable when the policy lag is too long. We also find the chaotic behavior in some range of the policy lag
Bifurcated equilibria in two-dimensional MHD with diamagnetic effects
Ottaviani, M.; Tebaldi, C.
1998-12-01
In this work we analyzed the sequence of bifurcated equilibria in two-dimensional reduced magnetohydrodynamics. Diamagnetic effects are studied under the assumption of a constant equilibrium pressure gradient, not altered by the formation of the magnetic island. The formation of an island when the symmetric equilibrium becomes unstable is studied as a function of the tearing mode stability parameter Δ' and of the diamagnetic frequency, by employing fixed-points numerical techniques and an initial value code. At larger values of Δ' a tangent bifurcation takes place, above which no small island solutions exist. This bifurcation persists up to fairly large values of the diamagnetic frequency (of the order of one tenth of the Alfven frequency). The implications of this phenomenology for the intermittent MHD dynamics observed in tokamaks is discussed. (authors)
Bifurcations of propellant burning rate at oscillatory pressure
Novozhilov, Boris V. [N. N. Semenov Institute of Chemical Physics, Russian Academy of Science, 4 Kosygina St., Moscow 119991 (Russian Federation)
2006-06-15
A new phenomenon, the disparity between pressure and propellant burning rate frequencies, has revealed in numerical studies of propellant burning rate response to oscillatory pressure. As is clear from the linear approximation, under small pressure amplitudes, h, pressure and propellant burning rate oscillations occur with equal period T (T-solution). In the paper, however, it is shown that at a certain critical value of the parameter h the system in hand undergoes a bifurcation so that the T-solution converts to oscillations with period 2T (2T-solution). When the bifurcation parameter h increases, the subsequent behavior of the system becomes complicated. It is obtained a sequence of period doubling to 4T-solution and 8T-solution. Beyond a certain value of the bifurcation parameter h an apparently fully chaotic solution is found. These effects undoubtedly should be taken into account in studies of oscillatory processes in combustion chambers. (Abstract Copyright [2006], Wiley Periodicals, Inc.)
Dynamical systems V bifurcation theory and catastrophe theory
1994-01-01
Bifurcation theory and catastrophe theory are two of the best known areas within the field of dynamical systems. Both are studies of smooth systems, focusing on properties that seem to be manifestly non-smooth. Bifurcation theory is concerned with the sudden changes that occur in a system when one or more parameters are varied. Examples of such are familiar to students of differential equations, from phase portraits. Moreover, understanding the bifurcations of the differential equations that describe real physical systems provides important information about the behavior of the systems. Catastrophe theory became quite famous during the 1970's, mostly because of the sensation caused by the usually less than rigorous applications of its principal ideas to "hot topics", such as the characterization of personalities and the difference between a "genius" and a "maniac". Catastrophe theory is accurately described as singularity theory and its (genuine) applications. The authors of this book, the first printing of w...
Bifurcation analysis of a delayed mathematical model for tumor growth
Khajanchi, Subhas
2015-01-01
In this study, we present a modified mathematical model of tumor growth by introducing discrete time delay in interaction terms. The model describes the interaction between tumor cells, healthy tissue cells (host cells) and immune effector cells. The goal of this study is to obtain a better compatibility with reality for which we introduced the discrete time delay in the interaction between tumor cells and host cells. We investigate the local stability of the non-negative equilibria and the existence of Hopf-bifurcation by considering the discrete time delay as a bifurcation parameter. We estimate the length of delay to preserve the stability of bifurcating periodic solutions, which gives an idea about the mode of action for controlling oscillations in the tumor growth. Numerical simulations of the model confirm the analytical findings
Bifurcations in the optimal elastic foundation for a buckling column
Rayneau-Kirkhope, Daniel; Farr, Robert; Ding, K.; Mao, Yong
2010-01-01
We investigate the buckling under compression of a slender beam with a distributed lateral elastic support, for which there is an associated cost. For a given cost, we study the optimal choice of support to protect against Euler buckling. We show that with only weak lateral support, the optimum distribution is a delta-function at the centre of the beam. When more support is allowed, we find numerically that the optimal distribution undergoes a series of bifurcations. We obtain analytical expressions for the buckling load around the first bifurcation point and corresponding expansions for the optimal position of support. Our theoretical predictions, including the critical exponent of the bifurcation, are confirmed by computer simulations.
Bifurcations in the optimal elastic foundation for a buckling column
Rayneau-Kirkhope, Daniel, E-mail: ppxdr@nottingham.ac.u [School of Physics and Astronomy, University of Nottingham, Nottingham, NG7 2RD (United Kingdom); Farr, Robert [Unilever R and D, Olivier van Noortlaan 120, AT3133, Vlaardingen (Netherlands); London Institute for Mathematical Sciences, 22 South Audley Street, Mayfair, London (United Kingdom); Ding, K. [Department of Physics, Fudan University, Shanghai, 200433 (China); Mao, Yong [School of Physics and Astronomy, University of Nottingham, Nottingham, NG7 2RD (United Kingdom)
2010-12-01
We investigate the buckling under compression of a slender beam with a distributed lateral elastic support, for which there is an associated cost. For a given cost, we study the optimal choice of support to protect against Euler buckling. We show that with only weak lateral support, the optimum distribution is a delta-function at the centre of the beam. When more support is allowed, we find numerically that the optimal distribution undergoes a series of bifurcations. We obtain analytical expressions for the buckling load around the first bifurcation point and corresponding expansions for the optimal position of support. Our theoretical predictions, including the critical exponent of the bifurcation, are confirmed by computer simulations.
Bifurcation-free design method of pulse energy converter controllers
Kolokolov, Yury; Ustinov, Pavel; Essounbouli, Najib; Hamzaoui, Abdelaziz
2009-01-01
In this paper, a design method of pulse energy converter (PEC) controllers is proposed. This method develops a classical frequency domain design, based on the small signal modeling, by means of an addition of a nonlinear dynamics analysis stage. The main idea of the proposed method consists in fact that the PEC controller, designed with an application of the small signal modeling, is tuned after with taking into the consideration an essentially nonlinear nature of the PEC that makes it possible to avoid bifurcation phenomena in the PEC dynamics at the design stage (bifurcation-free design). Also application of the proposed method allows an improvement of the designed controller performance. The application of this bifurcation-free design method is demonstrated on an example of the controller design of direct current-direct current (DC-DC) buck converter with an input electromagnetic interference filter.
An Approach to Robust Control of the Hopf Bifurcation
Giacomo Innocenti
2011-01-01
Full Text Available The paper illustrates a novel approach to modify the Hopf bifurcation nature via a nonlinear state feedback control, which leaves the equilibrium properties unchanged. This result is achieved by recurring to linear and nonlinear transformations, which lead the system to locally assume the ordinary differential equation representation. Third-order models are considered, since they can be seen as proper representatives of a larger class of systems. The explicit relationship between the control input and the Hopf bifurcation nature is obtained via a frequency approach, that does not need the computation of the center manifold.
Communication: Mode bifurcation of droplet motion under stationary laser irradiation
Takabatake, Fumi [Department of Physics, Graduate School of Science, Kyoto University, Kyoto 606-8502 (Japan); Department of Bioengineering and Robotics, Graduate School of Engineering, Tohoku University, Sendai, Miyagi 980-8579 (Japan); Yoshikawa, Kenichi [Faculty of Life and Medical Sciences, Doshisha University, Kyotanabe, Kyoto 610-0394 (Japan); Ichikawa, Masatoshi, E-mail: ichi@scphys.kyoto-u.ac.jp [Department of Physics, Graduate School of Science, Kyoto University, Kyoto 606-8502 (Japan)
2014-08-07
The self-propelled motion of a mm-sized oil droplet floating on water, induced by a local temperature gradient generated by CW laser irradiation is reported. The circular droplet exhibits two types of regular periodic motion, reciprocal and circular, around the laser spot under suitable laser power. With an increase in laser power, a mode bifurcation from rectilinear reciprocal motion to circular motion is caused. The essential aspects of this mode bifurcation are discussed in terms of spontaneous symmetry-breaking under temperature-induced interfacial instability, and are theoretically reproduced with simple coupled differential equations.
Transportation and concentration inequalities for bifurcating Markov chains
Penda, S. Valère Bitseki; Escobar-Bach, Mikael; Guillin, Arnaud
2017-01-01
We investigate the transportation inequality for bifurcating Markov chains which are a class of processes indexed by a regular binary tree. Fitting well models like cell growth when each individual gives birth to exactly two offsprings, we use transportation inequalities to provide useful...... concentration inequalities.We also study deviation inequalities for the empirical means under relaxed assumptions on the Wasserstein contraction for the Markov kernels. Applications to bifurcating nonlinear autoregressive processes are considered for point-wise estimates of the non-linear autoregressive...
Bifurcated transition of radial transport in the HIEI tandem mirror
Sakai, O.; Yasaka, Y.
1995-01-01
Transition to a high radial confinement mode in a mirror plasma is triggered by limiter biasing. Sheared plasma rotation is induced in the high confinement phase which is characterized by reduction of edge turbulence and a confinement enhancement factor of 2-4. Edge plasma parameters related to radial confinement show a hysteresis phenomenon as a function of bias voltage or bias current, leading to the fact that transition from low to high confinement mode occurs between the bifurcated states. A transition model based on azimuthal momentum balance is employed to clarify physics of the observed bifurcation. copyright 1995 American Institute of Physics
Bifurcation analysis of nephron pressure and flow regulation
Barfred, Mikael; Mosekilde, Erik; Holstein-Rathlou, N.-H.
1996-01-01
One- and two-dimensional continuation techniques are applied to study the bifurcation structure of a model of renal flow and pressure control. Integrating the main physiological mechanisms by which the individual nephron regulates the incoming blood flow, the model describes the interaction between...... the tubuloglomerular feedback and the response of the afferent arteriole. It is shown how a Hopf bifurcation leads the system to perform self-sustained oscillations if the feedback gain becomes sufficiently strong, and how a further increase of this parameter produces a folded structure of overlapping period...
Discretizing the transcritical and pitchfork bifurcations – conjugacy results
Lóczi, Lajos
2015-01-07
© 2015 Taylor & Francis. We present two case studies in one-dimensional dynamics concerning the discretization of transcritical (TC) and pitchfork (PF) bifurcations. In the vicinity of a TC or PF bifurcation point and under some natural assumptions on the one-step discretization method of order (Formula presented.) , we show that the time- (Formula presented.) exact and the step-size- (Formula presented.) discretized dynamics are topologically equivalent by constructing a two-parameter family of conjugacies in each case. As a main result, we prove that the constructed conjugacy maps are (Formula presented.) -close to the identity and these estimates are optimal.
Backward Bifurcation in a Cholera Model: A Case Study of Outbreak in Zimbabwe and Haiti
Sharma, Sandeep; Kumari, Nitu
In this paper, a nonlinear deterministic model is proposed with a saturated treatment function. The expression of the basic reproduction number for the proposed model was obtained. The global dynamics of the proposed model was studied using the basic reproduction number and theory of dynamical systems. It is observed that proposed model exhibits backward bifurcation as multiple endemic equilibrium points exist when R0 cholera in the community. We also obtain a unique endemic equilibria when R0 > 1. The global stability of unique endemic equilibria is performed using the geometric approach. An extensive numerical study is performed to support our analytical results. Finally, we investigate two major cholera outbreaks, Zimbabwe (2008-09) and Haiti (2010), with the help of the present study.
Stage line diagram: An age-conditional reference diagram for tracking development
Buuren, S. van; Ooms, J.C.L.
2009-01-01
This paper presents a method for calculating stage line diagrams, a novel type of reference diagram useful for tracking developmental processes over time. Potential fields of applications include: dentistry (tooth eruption), oncology (tumor grading, cancer staging), virology (HIV infection and
Stage line diagram: an age-conditional reference diagram for tracking development.
Van Buuren, S.; Ooms, J.C.L.
2009-01-01
This paper presents a method for calculating stage line diagrams, a novel type of reference diagram useful for tracking developmental processes over time. Potential fields of applications include: dentistry (tooth eruption), oncology (tumor grading, cancer staging), virology (HIV infection and
Kan-On, Yukio
2007-04-01
This paper is concerned with the bifurcation structure of positive stationary solutions for a generalized Lotka-Volterra competition model with diffusion. To establish the structure, the bifurcation theory and the interval arithmetic are employed.
CERPHASE: Computer-generated phase diagrams
Ruys, A.J.; Sorrell, C.C.; Scott, F.H.
1990-01-01
CERPHASE is a collection of computer programs written in the programming language basic and developed for the purpose of teaching the principles of phase diagram generation from the ideal solution model of thermodynamics. Two approaches are used in the generation of the phase diagrams: freezing point depression and minimization of the free energy of mixing. Binary and ternary phase diagrams can be generated as can diagrams containing the ideal solution parameters used to generate the actual phase diagrams. Since the diagrams generated utilize the ideal solution model, data input required from the operator is minimal: only the heat of fusion and melting point of each component. CERPHASE is menu-driven and user-friendly, containing simple instructions in the form of screen prompts as well as a HELP file to guide the operator. A second purpose of CERPHASE is in the prediction of phase diagrams in systems for which no experimentally determined phase diagrams are available, enabling the estimation of suitable firing or sintering temperatures for otherwise unknown systems. Since CERPHASE utilizes ideal solution theory, there are certain limitations imposed on the types of systems that can be predicted reliably. 6 refs., 13 refs
How design guides learning from matrix diagrams
van der Meij, Jan; Amelsvoort, Marije; Anjewierden, Anjo
2017-01-01
Compared to text, diagrams are superior in their ability to structure and summarize information and to show relations between concepts and ideas. Perceptual cues, like arrows, are expected to improve the retention of diagrams by guiding the learner towards important elements or showing a preferred
Diagram of state of stiff amphiphilic macromolecules
Markov, Vladimir A.; Vasilevskaya, Valentina V.; Khalatur, Pavel G.; ten Brinke, Gerrit; Khokhlov, Alexei R.
2007-01-01
We studied coil-globule transitions in stiff-chain amphiphilic macromolecules via computer modeling and constructed phase diagrams for such molecules in terms of solvent quality and persistence length. We showed that the shape of the phase diagram essentially depends on the macromolecule degree of
Compact flow diagrams for state sequences
Buchin, Kevin; Buchin, Maike; Gudmundsson, Joachim; Horton, Michael; Sijben, Stef
2017-01-01
We introduce the concept of using a flow diagram to compactly represent the segmentation of a large number of state sequences according to a set of criteria. We argue that this flow diagram representation gives an intuitive summary that allows the user to detect patterns within the segmentations. In
Compact flow diagrams for state sequences
Buchin, K.A.; Buchin, M.E.; Gudmundsson, J.; Horton, M.J.; Sijben, S.
2016-01-01
We introduce the concept of compactly representing a large number of state sequences, e.g., sequences of activities, as a flow diagram. We argue that the flow diagram representation gives an intuitive summary that allows the user to detect patterns among large sets of state sequences. Simplified,
How Design Guides Learning from Matrix Diagrams
van der Meij, Jan; van Amelsvoort, Marije; Anjewierden, Anjo
2017-01-01
Compared to text, diagrams are superior in their ability to structure and summarize information and to show relations between concepts and ideas. Perceptual cues, like arrows, are expected to improve the retention of diagrams by guiding the learner towards important elements or showing a preferred reading sequence. In our experiment, we analyzed…
Phase diagram of ammonium nitrate
Dunuwille, Mihindra; Yoo, Choong-Shik, E-mail: csyoo@wsu.edu [Department of Chemistry and Institute for Shock Physics, Washington State University, Pullman, Washington 99164 (United States)
2013-12-07
Ammonium Nitrate (AN) is a fertilizer, yet becomes an explosive upon a small addition of chemical impurities. The origin of enhanced chemical sensitivity in impure AN (or AN mixtures) is not well understood, posing significant safety issues in using AN even today. To remedy the situation, we have carried out an extensive study to investigate the phase stability of AN and its mixtures with hexane (ANFO–AN mixed with fuel oil) and Aluminum (Ammonal) at high pressures and temperatures, using diamond anvil cells (DAC) and micro-Raman spectroscopy. The results indicate that pure AN decomposes to N{sub 2}, N{sub 2}O, and H{sub 2}O at the onset of the melt, whereas the mixtures, ANFO and Ammonal, decompose at substantially lower temperatures. The present results also confirm the recently proposed phase IV-IV{sup ′} transition above 17 GPa and provide new constraints for the melting and phase diagram of AN to 40 GPa and 400°C.
De Forcrand, Philippe; Forcrand, Philippe de; Philipsen, Owe
2006-01-01
We summarize our recent results on the phase diagram of QCD with N_f=2+1 quark flavors, as a function of temperature T and quark chemical potential \\mu. Using staggered fermions, lattices with temporal extent N_t=4, and the exact RHMC algorithm, we first determine the critical line in the quark mass plane (m_{u,d},m_s) where the finite temperature transition at \\mu=0 is second order. We confirm that the physical point lies on the crossover side of this line. Our data are consistent with a tricritical point at (m_{u,d},m_s) = (0,\\sim 500) MeV. Then, using an imaginary chemical potential, we determine in which direction this second-order line moves as the chemical potential is turned on. Contrary to standard expectations, we find that the region of first-order transitions shrinks in the presence of a chemical potential, which is inconsistent with the presence of a QCD critical point at small chemical potential. The emphasis is put on clarifying the translation of our results from lattice to physical units, and ...
Operations space diagram for ECRH and ECCD
Bindslev, Henrik
2004-01-01
A Clemmov-Mullaly-Allis (CMA) type diagram, the ECW-CMA diagram, for representing the operational possibilities of electron cyclotron heating and current drive (ECRH/ECCD) systems for fusion plasmas is presented. In this diagram, with normalized density and normalized magnetic field coordinates, the parameter range in which it is possible to achieve a given task (e.g. O-mode current drive for stabilizing a neoclassical tearing mode) appears as a region. With also the Greenwald density limit shown, this diagram condenses the information on operational possibilities, facilitating the overview required at the design phase. At the operations phase it may also prove useful in setting up experimental scenarios by showing operational possibilities, avoiding the need for survey type ray-tracing at the initial planning stages. The diagram may also serve the purpose of communicating operational possibilities to non-experts. JET and ITER like plasmas are used, but the method is generic. (author)
Operations space diagram for ECRH and ECCD
Bindslev, H.
2004-01-01
at the design phase. At the operations phase it may also prove useful in setting up experimental scenarios by showing operational possibilities, avoiding the need for survey type ray-tracing at the initial planning stages. The diagram may also serve the purpose of communicating operational possibilities to non......A Clemmov-Mullaly-Allis (CMA) type diagram, the ECW-CMA diagram, for representing the operational possibilities of electron cyclotron heating and current drive (ECRH/ECCD) systems for fusion plasmas is presented. In this diagram, with normalized density and normalized magnetic field coordinates......, the parameter range in which it is possible to achieve a given task (e.g. O-mode current drive for stabilizing a neoclassical tearing mode) appears as a region. With also the Greenwald density limit shown, this diagram condenses the information on operational possibilities, facilitating the overview required...
Necessary and sufficient conditions for Hopf bifurcation in tri-neuron equation with a delay
Liu Xiaoming; Liao Xiaofeng
2009-01-01
In this paper, we consider the delayed differential equations modeling three-neuron equations with only a time delay. Using the time delay as a bifurcation parameter, necessary and sufficient conditions for Hopf bifurcation to occur are derived. Numerical results indicate that for this model, Hopf bifurcation is likely to occur at suitable delay parameter values.
Local bifurcation analysis in nuclear reactor dynamics by Sotomayor’s theorem
Pirayesh, Behnam; Pazirandeh, Ali; Akbari, Monireh
2016-01-01
Highlights: • When the feedback reactivity is considered as a nonlinear function some complex behaviors may emerge in the system such as local bifurcation phenomenon. • The qualitative behaviors of a typical nuclear reactor near its equilibrium points have been studied analytically. • Comprehensive analytical bifurcation analyses presented in this paper are transcritical bifurcation, saddle- node bifurcation and pitchfork bifurcation. - Abstract: In this paper, a qualitative approach has been used to explore nuclear reactor behaviors with nonlinear feedback. First, a system of four dimensional ordinary differential equations governing the dynamics of a typical nuclear reactor is introduced. These four state variables are the relative power of the reactor, the relative concentration of delayed neutron precursors, the fuel temperature and the coolant temperature. Then, the qualitative behaviors of the dynamical system near its equilibria have been studied analytically by using local bifurcation theory and Sotomayor’s theorem. The results indicated that despite the uncertainty of the reactivity, we can analyze the qualitative behavior changes of the reactor from the bifurcation point of view. Notably, local bifurcations that were considered in this paper include transcritical bifurcation, saddle-node bifurcation and pitchfork bifurcation. The theoretical analysis showed that these three types of local bifurcations may occur in the four dimensional dynamical system. In addition, to confirm the analytical results the numerical simulations are given.
Ma, Junhai; Yang, Wenhui; Lou, Wandong
This paper establishes an oligopolistic game model under the carbon emission reduction constraint and investigates its complex characteristics like bifurcation and chaos. Two oligopolistic manufacturers comprise three mixed game models, aiming to explore the variation in the status of operating system as per the upgrading of benchmark reward-penalty mechanism. Firstly, we set up these basic models that are respectively distinguished with carbon emission quantity and study these models using different game methods. Then, we concentrate on one typical game model to further study the dynamic complexity of variations in the system status, through 2D bifurcation diagrams and 4D parameter adjustment features based on the bounded rationality scheme for price, and the adaptive scheme for carbon emission. The results show that the carbon emission constraint has significant influence on the status variation of two-oligopolistic game operating systems no matter whether it is stable or chaotic. Besides, the new carbon emission regulation meets government supervision target and achieves the goal of being environment friendly by motivating the system to operate with lower carbon emission.
Bifurcation of limit cycles for cubic reversible systems
Yi Shao
2014-04-01
Full Text Available This article is concerned with the bifurcation of limit cycles of a class of cubic reversible system having a center at the origin. We prove that this system has at least four limit cycles produced by the period annulus around the center under cubic perturbations
Chaos and bifurcations in periodic windows observed in plasmas
Qin, J.; Wang, L.; Yuan, D.P.; Gao, P.; Zhang, B.Z.
1989-01-01
We report the experimental observations of deterministic chaos in a steady-state plasma which is not driven by any extra periodic forces. Two routes to chaos have been found, period-doubling and intermittent chaos. The fine structures in chaos such as periodic windows and bifurcations in windows have also been observed
Coronary bifurcation lesions treated with simple or complex stenting
Behan, Miles W; Holm, Niels R; de Belder, Adam J
2016-01-01
AIMS: Randomized trials of coronary bifurcation stenting have shown better outcomes from a simple (provisional) strategy rather than a complex (planned two-stent) strategy in terms of short-term efficacy and safety. Here, we report the 5-year all-cause mortality based on pooled patient-level data...
The Boundary-Hopf-Fold Bifurcation in Filippov Systems
Efstathiou, Konstantinos; Liu, Xia; Broer, Henk W.
2015-01-01
This paper studies the codimension-3 boundary-Hopf-fold (BHF) bifurcation of planar Filippov systems. Filippov systems consist of at least one discontinuity boundary locally separating the phase space to disjoint components with different dynamics. Such systems find applications in several fields,
Stability and Hopf bifurcation analysis of a new system
Huang Kuifei; Yang Qigui
2009-01-01
In this paper, a new chaotic system is introduced. The system contains special cases as the modified Lorenz system and conjugate Chen system. Some subtle characteristics of stability and Hopf bifurcation of the new chaotic system are thoroughly investigated by rigorous mathematical analysis and symbolic computations. Meanwhile, some numerical simulations for justifying the theoretical analysis are also presented.
Pitchfork bifurcation and vibrational resonance in a fractional-order ...
The fractional-order damping mainly determines the pattern of the vibrational resonance. There is a bifurcation point of the fractional order which, in the case of double-well potential, transforms vibrational resonance pattern from a single resonance to a double resonance, while in the case of single-well potential, transforms ...
Nonintegrability of the unfolding of the fold-Hopf bifurcation
Yagasaki, Kazuyuki
2018-02-01
We consider the unfolding of the codimension-two fold-Hopf bifurcation and prove its meromorphic nonintegrability in the meaning of Bogoyavlenskij for almost all parameter values. Our proof is based on a generalized version of the Morales-Ramis-Simó theory for non-Hamiltonian systems and related variational equations up to second order are used.
Bifurcations and complete chaos for the diamagnetic Kepler problem
Hansen, Kai T.
1995-03-01
We describe the structure of bifurcations in the unbounded classical diamagnetic Kepler problem. We conjecture that this system does not have any stable orbits and that the nonwandering set is described by a complete trinary symbolic dynamics for scaled energies larger than ɛc=0.328 782. . ..
Bifurcations and Complete Chaos for the Diamagnetic Kepler Problem
Hansen, Kai T.
1995-01-01
We describe the structure of bifurcations in the unbounded classical Diamagnetic Kepler problem. We conjecture that this system does not have any stable orbits and that the non-wandering set is described by a complete trinary symbolic dynamics for scaled energies larger then $\\epsilon_c=0.328782\\ldots$.
Stability of Bifurcating Stationary Solutions of the Artificial Compressible System
Teramoto, Yuka
2018-02-01
The artificial compressible system gives a compressible approximation of the incompressible Navier-Stokes system. The latter system is obtained from the former one in the zero limit of the artificial Mach number ɛ which is a singular limit. The sets of stationary solutions of both systems coincide with each other. It is known that if a stationary solution of the incompressible system is asymptotically stable and the velocity field of the stationary solution satisfies an energy-type stability criterion, then it is also stable as a solution of the artificial compressible one for sufficiently small ɛ . In general, the range of ɛ shrinks when the spectrum of the linearized operator for the incompressible system approaches to the imaginary axis. This can happen when a stationary bifurcation occurs. It is proved that when a stationary bifurcation from a simple eigenvalue occurs, the range of ɛ can be taken uniformly near the bifurcation point to conclude the stability of the bifurcating solution as a solution of the artificial compressible system.
Long term results of kissing stents in the aortic bifurcation
Hinnen, J.W.; Konickx, M.A.; Meerwaldt, Robbert; Kolkert, J.L.P.; van der Palen, Jacobus Adrianus Maria; Huisman, A.B.
2015-01-01
BACKGROUND: To evaluate the long-term outcome after aortoiliac kissing stent placement and to analyze variables, which potentially influence the outcome of endovascular reconstruction of the aortic bifurcation. METHODS: All patients treated with aortoiliac kissing stents at our institution between
Femoral bifurcation with ipsilateral tibia hemimelia: Early outcome of ...
Hereby, we present a case report of a 2-year-old boy who first presented in our orthopedic clinic as a 12-day-old neonate, with a grossly deformed right lower limb from a combination of complete tibia hemimelia and ipsilateral femoral bifurcation. Excision of femoral exostosis, knee disarticulation and prosthetic fitting gives ...
Hopf bifurcation formula for first order differential-delay equations
Rand, Richard; Verdugo, Anael
2007-09-01
This work presents an explicit formula for determining the radius of a limit cycle which is born in a Hopf bifurcation in a class of first order constant coefficient differential-delay equations. The derivation is accomplished using Lindstedt's perturbation method.
Direction and stability of bifurcating solutions for a Signorini problem
Eisner, J.; Kučera, Milan; Recke, L.
2015-01-01
Roč. 113, January (2015), s. 357-371 ISSN 0362-546X Institutional support: RVO:67985840 Keywords : Signorini problem * variational inequality * bifurcation direction Subject RIV: BA - General Mathematics Impact factor: 1.125, year: 2015 http://www.sciencedirect.com/science/article/pii/S0362546X14003228
Smooth bifurcation for a Signorini problem on a rectangle
Eisner, J.; Kučera, Milan; Recke, L.
2012-01-01
Roč. 137, č. 2 (2012), s. 131-138 ISSN 0862-7959 R&D Projects: GA AV ČR IAA100190805 Institutional research plan: CEZ:AV0Z10190503 Keywords : Signorini problem * smooth bifurcation * variational inequality Subject RIV: BA - General Mathematics http://dml.cz/dmlcz/142859
Bifurcation analysis and the travelling wave solutions of the Klein
In this paper, we investigate the bifurcations and dynamic behaviour of travelling wave solutions of the Klein–Gordon–Zakharov equations given in Shang et al, Comput. Math. Appl. 56, 1441 (2008). Under different parameter conditions, we obtain some exact explicit parametric representations of travelling wave solutions by ...
Heteroclinic Bifurcation Behaviors of a Duffing Oscillator with Delayed Feedback
Shao-Fang Wen
2018-01-01
Full Text Available The heteroclinic bifurcation and chaos of a Duffing oscillator with forcing excitation under both delayed displacement feedback and delayed velocity feedback are studied by Melnikov method. The Melnikov function is analytically established to detect the necessary conditions for generating chaos. Through the analysis of the analytical necessary conditions, we find that the influences of the delayed displacement feedback and delayed velocity feedback are separable. Then the influences of the displacement and velocity feedback parameters on heteroclinic bifurcation and threshold value of chaotic motion are investigated individually. In order to verify the correctness of the analytical conditions, the Duffing oscillator is also investigated by numerical iterative method. The bifurcation curves and the largest Lyapunov exponents are provided and compared. From the analysis of the numerical simulation results, it could be found that two types of period-doubling bifurcations occur in the Duffing oscillator, so that there are two paths leading to the chaos in this oscillator. The typical dynamical responses, including time histories, phase portraits, and Poincare maps, are all carried out to verify the conclusions. The results reveal some new phenomena, which is useful to design or control this kind of system.
Bifurcation Analysis and Chaos Control in a Discrete Epidemic System
Wei Tan
2015-01-01
Full Text Available The dynamics of discrete SI epidemic model, which has been obtained by the forward Euler scheme, is investigated in detail. By using the center manifold theorem and bifurcation theorem in the interior R+2, the specific conditions for the existence of flip bifurcation and Neimark-Sacker bifurcation have been derived. Numerical simulation not only presents our theoretical analysis but also exhibits rich and complex dynamical behavior existing in the case of the windows of period-1, period-3, period-5, period-6, period-7, period-9, period-11, period-15, period-19, period-23, period-34, period-42, and period-53 orbits. Meanwhile, there appears the cascade of period-doubling 2, 4, 8 bifurcation and chaos sets from the fixed point. These results show the discrete model has more richer dynamics compared with the continuous model. The computations of the largest Lyapunov exponents more than 0 confirm the chaotic behaviors of the system x→x+δ[rN(1-N/K-βxy/N-(μ+mx], y→y+δ[βxy/N-(μ+dy]. Specifically, the chaotic orbits at an unstable fixed point are stabilized by using the feedback control method.
Epidemic model with vaccinated age that exhibits backward bifurcation
Yang Junyuan; Zhang Fengqin; Li Xuezhi
2009-01-01
Vaccination of susceptibilities is included in a transmission model for a disease that confers immunity. In this paper, interplay of vaccination strategy together with vaccine efficacy and the vaccinated age is studied. In particular, vaccine efficacy can lead to a backward bifurcation. At the same time, we also discuss an abstract formulation of the problem, and establish the well-posedness of the model.
Bifurcation methods of dynamical systems for handling nonlinear ...
physics pp. 863–868. Bifurcation methods of dynamical systems for handling nonlinear wave equations. DAHE FENG and JIBIN LI. Center for Nonlinear Science Studies, School of Science, Kunming University of Science and Technology .... (b) It can be shown from (15) and (18) that the balance between the weak nonlinear.
Bifurcation analysis of wind-driven flows with MOM4
Bernsen, E.; Dijkstra, H.A.; Wubs, F.W.
2009-01-01
In this paper, the methodology of bifurcation analysis is applied to the explicit time-stepping ocean model MOM4 using a Jacobian–Free Newton–Krylov (JFNK) approach. We in detail present the implementation of the JFNK method in MOM4 but restrict the preconditioning technique to the case for which
Chemical reaction systems with a homoclinic bifurcation: an inverse problem
Plesa, T.; Vejchodský, Tomáš; Erban, R.
2016-01-01
Roč. 54, č. 10 (2016), s. 1884-1915 ISSN 0259-9791 EU Projects: European Commission(XE) 328008 - STOCHDETBIOMODEL Institutional support: RVO:67985840 Keywords : nonnegative dynamical systems * bifurcations * oscillations Subject RIV: BA - General Mathematics Impact factor: 1.308, year: 2016 http://link.springer.com/article/10.1007%2Fs10910-016-0656-1
Bifurcation Analysis of Spiral Growth Processes in Plants
Andersen, C.A.; Ernstsen, C.N.; Mosekilde, Erik
1999-01-01
In order to examine the significance of different assumptions about the range of the inhibitory forces, we have performed a series of bifurcation analyses of a simple model that can explain the formation of helical structures in phyllotaxis. Computer simulations are used to illustrate the role...
Smooth bifurcation for variational inequalities based on Lagrange multipliers
Eisner, Jan; Kučera, Milan; Recke, L.
2006-01-01
Roč. 19, č. 9 (2006), s. 981-1000 ISSN 0893-4983 R&D Projects: GA AV ČR(CZ) IAA100190506 Institutional research plan: CEZ:AV0Z10190503 Keywords : abstract variational inequality * bifurcation * Lagrange multipliers Subject RIV: BA - General Mathematics
Experimental bifurcation analysis of an impact oscillator – Determining stability
Bureau, Emil; Schilder, Frank; Elmegård, Michael
2014-01-01
We propose and investigate three different methods for assessing stability of dynamical equilibrium states during experimental bifurcation analysis, using a control-based continuation method. The idea is to modify or turn off the control at an equilibrium state and study the resulting behavior...
Regularization of the Boundary-Saddle-Node Bifurcation
Xia Liu
2018-01-01
Full Text Available In this paper we treat a particular class of planar Filippov systems which consist of two smooth systems that are separated by a discontinuity boundary. In such systems one vector field undergoes a saddle-node bifurcation while the other vector field is transversal to the boundary. The boundary-saddle-node (BSN bifurcation occurs at a critical value when the saddle-node point is located on the discontinuity boundary. We derive a local topological normal form for the BSN bifurcation and study its local dynamics by applying the classical Filippov’s convex method and a novel regularization approach. In fact, by the regularization approach a given Filippov system is approximated by a piecewise-smooth continuous system. Moreover, the regularization process produces a singular perturbation problem where the original discontinuous set becomes a center manifold. Thus, the regularization enables us to make use of the established theories for continuous systems and slow-fast systems to study the local behavior around the BSN bifurcation.
Topography of Aortic Bifurcation in a Black Kenyan Population ...
After removal of abdominal viscera, peritoneum, fibrofatty connective tissue, inferior vena cava was removed to expose the termination of abdominal aorta. Vertebral level, angle and asymmetry of bifurcation were recorded. Data were analysed by SPSS version 17.0 for windows and are presented in tables and bar charts.
Adaptive global synchrony of inferior olive neurons
Lee, Keum W; Singh, Sahjendra N
2009-01-01
This paper treats the question of global adaptive synchronization of inferior olive neurons (IONs) based on the immersion and invariance approach. The ION exhibits a variety of orbits as the parameter (termed the bifurcation parameter), which appears in its nonlinear functions, is varied. It is seen that once the bifurcation parameter exceeds a critical value, the stability of the equilibrium point of the ION is lost, and periodic orbits are born. The size and shape of the orbits depend on the value of the bifurcation parameter. It is assumed that bifurcation parameters of the IONs are not known. The orbits of IONs beginning from arbitrary initial conditions are not synchronized. For the synchronization of the IONs, a non-certainty equivalent adaptation law is derived. The control system has a modular structure consisting of an identifier and a control module. Using the Lyapunov approach, it is shown that in the closed-loop system, global synchronization of the neurons with a prescribed relative phase is accomplished, and the estimated bifurcation parameters converge to the true parameters. Unlike the certainty-equivalent adaptive control systems, an interesting feature of the designed control system is that whenever the estimated parameters coincide with the true values, the parameter estimates remain frozen thereafter, and the closed-loop system recovers the performance of the deterministic closed-loop system. Simulation results are presented which show that in the closed-loop system, the synchrony of neurons with prescribed phases is accomplished despite the uncertainties in the bifurcation parameters.
Hailong, Zhang; Enrong, Wang; Fuhong, Min; Ning, Zhang
2016-03-01
The magneto-rheological damper (MRD) is a promising device used in vehicle semi-active suspension systems, for its continuous adjustable damping output. However, the innate nonlinear hysteresis characteristic of MRD may cause the nonlinear behaviors. In this work, a two-degree-of-freedom (2-DOF) MR suspension system was established first, by employing the modified Bouc-Wen force-velocity (F-v) hysteretic model. The nonlinear dynamic response of the system was investigated under the external excitation of single-frequency harmonic and bandwidth-limited stochastic road surface. The largest Lyapunov exponent (LLE) was used to detect the chaotic area of the frequency and amplitude of harmonic excitation, and the bifurcation diagrams, time histories, phase portraits, and power spectrum density (PSD) diagrams were used to reveal the dynamic evolution process in detail. Moreover, the LLE and Kolmogorov entropy (K entropy) were used to identify whether the system response was random or chaotic under stochastic road surface. The results demonstrated that the complex dynamical behaviors occur under different external excitation conditions. The oscillating mechanism of alternating periodic oscillations, quasi-periodic oscillations, and chaotic oscillations was observed in detail. The chaotic regions revealed that chaotic motions may appear in conditions of mid-low frequency and large amplitude, as well as small amplitude and all frequency. The obtained parameter regions where the chaotic motions may appear are useful for design of structural parameters of the vibration isolation, and the optimization of control strategy for MR suspension system. Projects supported by the National Natural Science Foundation of China (Grant Nos. 51475246, 51277098, and 51075215), the Research Innovation Program for College Graduates of Jiangsu Province China (Grant No. KYLX15 0725), and the Natural Science Foundation of Jiangsu Province of China (Grant No. BK20131402).
Bifurcation analysis of delay-induced resonances of the El-Niño Southern Oscillation.
Krauskopf, Bernd; Sieber, Jan
2014-09-08
Models of global climate phenomena of low to intermediate complexity are very useful for providing an understanding at a conceptual level. An important aspect of such models is the presence of a number of feedback loops that feature considerable delay times, usually due to the time it takes to transport energy (for example, in the form of hot/cold air or water) around the globe. In this paper, we demonstrate how one can perform a bifurcation analysis of the behaviour of a periodically forced system with delay in dependence on key parameters. As an example, we consider the El-Niño Southern Oscillation (ENSO), which is a sea-surface temperature (SST) oscillation on a multi-year scale in the basin of the Pacific Ocean. One can think of ENSO as being generated by an interplay between two feedback effects, one positive and one negative, which act only after some delay that is determined by the speed of transport of SST anomalies across the Pacific. We perform here a case study of a simple delayed-feedback oscillator model for ENSO, which is parametrically forced by annual variation. More specifically, we use numerical bifurcation analysis tools to explore directly regions of delay-induced resonances and other stability boundaries in this delay-differential equation model for ENSO.
The selection pressures induced non-smooth infectious disease model and bifurcation analysis
Qin, Wenjie; Tang, Sanyi
2014-01-01
Highlights: • A non-smooth infectious disease model to describe selection pressure is developed. • The effect of selection pressure on infectious disease transmission is addressed. • The key factors which are related to the threshold value are determined. • The stabilities and bifurcations of model have been revealed in more detail. • Strategies for the prevention of emerging infectious disease are proposed. - Abstract: Mathematical models can assist in the design strategies to control emerging infectious disease. This paper deduces a non-smooth infectious disease model induced by selection pressures. Analysis of this model reveals rich dynamics including local, global stability of equilibria and local sliding bifurcations. Model solutions ultimately stabilize at either one real equilibrium or the pseudo-equilibrium on the switching surface of the present model, depending on the threshold value determined by some related parameters. Our main results show that reducing the threshold value to a appropriate level could contribute to the efficacy on prevention and treatment of emerging infectious disease, which indicates that the selection pressures can be beneficial to prevent the emerging infectious disease under medical resource limitation
Numerical bifurcation analysis of conformal formulations of the Einstein constraints
Holst, M.; Kungurtsev, V.
2011-01-01
The Einstein constraint equations have been the subject of study for more than 50 years. The introduction of the conformal method in the 1970s as a parametrization of initial data for the Einstein equations led to increased interest in the development of a complete solution theory for the constraints, with the theory for constant mean curvature (CMC) spatial slices and closed manifolds completely developed by 1995. The first general non-CMC existence result was establish by Holst et al. in 2008, with extensions to rough data by Holst et al. in 2009, and to vacuum spacetimes by Maxwell in 2009. The non-CMC theory remains mostly open; moreover, recent work of Maxwell on specific symmetry models sheds light on fundamental nonuniqueness problems with the conformal method as a parametrization in non-CMC settings. In parallel with these mathematical developments, computational physicists have uncovered surprising behavior in numerical solutions to the extended conformal thin sandwich formulation of the Einstein constraints. In particular, numerical evidence suggests the existence of multiple solutions with a quadratic fold, and a recent analysis of a simplified model supports this conclusion. In this article, we examine this apparent bifurcation phenomena in a methodical way, using modern techniques in bifurcation theory and in numerical homotopy methods. We first review the evidence for the presence of bifurcation in the Hamiltonian constraint in the time-symmetric case. We give a brief introduction to the mathematical framework for analyzing bifurcation phenomena, and then develop the main ideas behind the construction of numerical homotopy, or path-following, methods in the analysis of bifurcation phenomena. We then apply the continuation software package AUTO to this problem, and verify the presence of the fold with homotopy-based numerical methods. We discuss these results and their physical significance, which lead to some interesting remaining questions to
Near threshold expansion of Feynman diagrams
Mendels, E.
2005-01-01
The near threshold expansion of Feynman diagrams is derived from their configuration space representation, by performing all x integrations. The general scalar Feynman diagram is considered, with an arbitrary number of external momenta, an arbitrary number of internal lines and an arbitrary number of loops, in n dimensions and all masses may be different. The expansions are considered both below and above threshold. Rules, giving real and imaginary part, are derived. Unitarity of a sunset diagram with I internal lines is checked in a direct way by showing that its imaginary part is equal to the phase space integral of I particles
Between Analogue and Digital Diagrams
Zoltan Bun
2012-10-01
Full Text Available This essay is about the interstitial. About how the diagram, as a method of design, has lead fromthe analogue deconstruction of the eighties to the digital processes of the turn of the millennium.Specifically, the main topic of the text is the interpretation and the critique of folding (as a diagramin the beginning of the nineties. It is necessary then to unfold its relationship with immediatelypreceding and following architectural trends, that is to say we have to look both backwards andforwards by about a decade. The question is the context of folding, the exchange of the analogueworld for the digital. To understand the process it is easier to investigate from the fields of artand culture, rather than from the intentionally perplicated1 thoughts of Gilles Deleuze. Both fieldsare relevant here because they can similarly be used as the yardstick against which the era itselfit measured. The cultural scene of the eighties and nineties, including performing arts, movies,literature and philosophy, is a wide milieu of architecture. Architecture responds parallel to itsera; it reacts to it, and changes with it and within it. Architecture is a medium, it has always beena medium, yet the relations are transformed. That’s not to say that technical progress, for exampleusing CAD-software and CNC-s, has led to the digital thinking of certain movements ofarchitecture, (it is at most an indirect tool. But the ‘up-to-dateness’ of the discipline, however,a kind of non-servile reading of an ‘applied culture’ or ‘used philosophy’2 could be the key.(We might recall here, parenthetically, the fortunes of the artistic in contemporary mass society.The proliferation of museums, the magnification of the figure of the artist, the existence of amassive consumption of printed and televised artistic images, the widespread appetite for informationabout the arts, all reflect, of course, an increasingly leisured society, but also relateprecisely to the fact
Low-resolution remeshing using the localized restricted voronoi diagram
Yan, Dongming; Bao, Guanbo; Zhang, Xiaopeng; Wonka, Peter
2014-01-01
A big problem in triangular remeshing is to generate meshes when the triangle size approaches the feature size in the mesh. The main obstacle for Centroidal Voronoi Tessellation (CVT)-based remeshing is to compute a suitable Voronoi diagram. In this paper, we introduce the localized restricted Voronoi diagram (LRVD) on mesh surfaces. The LRVD is an extension of the restricted Voronoi diagram (RVD), but it addresses the problem that the RVD can contain Voronoi regions that consist of multiple disjoint surface patches. Our definition ensures that each Voronoi cell in the LRVD is a single connected region. We show that the LRVD is a useful extension to improve several existing mesh-processing techniques, most importantly surface remeshing with a low number of vertices. While the LRVD and RVD are identical in most simple configurations, the LRVD is essential when sampling a mesh with a small number of points and for sampling surface areas that are in close proximity to other surface areas, e.g., nearby sheets. To compute the LRVD, we combine local discrete clustering with a global exact computation. © 1995-2012 IEEE.
Low-resolution remeshing using the localized restricted voronoi diagram
Yan, Dongming
2014-10-01
A big problem in triangular remeshing is to generate meshes when the triangle size approaches the feature size in the mesh. The main obstacle for Centroidal Voronoi Tessellation (CVT)-based remeshing is to compute a suitable Voronoi diagram. In this paper, we introduce the localized restricted Voronoi diagram (LRVD) on mesh surfaces. The LRVD is an extension of the restricted Voronoi diagram (RVD), but it addresses the problem that the RVD can contain Voronoi regions that consist of multiple disjoint surface patches. Our definition ensures that each Voronoi cell in the LRVD is a single connected region. We show that the LRVD is a useful extension to improve several existing mesh-processing techniques, most importantly surface remeshing with a low number of vertices. While the LRVD and RVD are identical in most simple configurations, the LRVD is essential when sampling a mesh with a small number of points and for sampling surface areas that are in close proximity to other surface areas, e.g., nearby sheets. To compute the LRVD, we combine local discrete clustering with a global exact computation. © 1995-2012 IEEE.
Zhu, Zhi-Wen; Zhang, Qing-Xin; Xu, Jia
2014-01-01
A kind of shape memory alloy (SMA) hysteretic nonlinear model was developed, and the nonlinear dynamics and bifurcation characteristics of the SMA thin film subjected to in-plane stochastic excitation were investigated. Van der Pol difference item was introduced to describe the hysteretic phenomena of the SMA strain–stress curves, and the nonlinear dynamic model of the SMA thin film subjected to in-plane stochastic excitation was developed. The conditions of global stochastic stability of the system were determined in singular boundary theory, and the probability density function of the system response was obtained. Finally, the conditions of stochastic Hopf bifurcation were analyzed. The results of theoretical analysis and numerical simulation indicate that self-excited vibration is induced by the hysteretic nonlinear characteristics of SMA, and stochastic Hopf bifurcation appears when the bifurcation parameter was changed; there are two limit cycles in the stationary probability density of the dynamic response of the system in some cases, which means that there are two vibration amplitudes whose probabilities are both very high, and jumping phenomena between the two vibration amplitudes appear with the change in conditions. The results obtained in this current paper are helpful for the application of the SMA thin film in stochastic vibration fields. - Highlights: • Hysteretic nonlinear model of shape memory alloy was developed. • Van der Pol item was introduced to interpret hysteretic strain–stress curves. • Nonlinear dynamic characteristics of the shape memory alloy film were analyzed. • Jumping phenomena were observed in the change of the parameters
Voronoi diagram and microstructure of weldment
Cho, Jung Ho [Chungbuk National University, Cheongju (Korea, Republic of)
2015-01-15
Voronoi diagram, one of the well-known space decomposition algorithms has been applied to express the microstructure of a weldment for the first time due to the superficial analogy between a Voronoi cell and a metal's grain. The area of the Voronoi cells can be controlled by location and the number of the seed points. This can be correlated to the grain size in the microstructure and the number of nuclei formed. The feasibility of representing coarse and fine grain structures were tested through Voronoi diagrams and it is applied to expression of cross-sectional bead shape of a typical laser welding. As result, it successfully described coarsened grain size of heat affected zone and columnar crystals in fusion zone. Although Voronoi diagram showed potential as a microstructure prediction tool through this feasible trial but direct correlation control variable of Voronoi diagram to solidification process parameter is still remained as further works.
Covariant diagrams for one-loop matching
Zhang, Zhengkang
2016-10-01
We present a diagrammatic formulation of recently-revived covariant functional approaches to one-loop matching from an ultraviolet (UV) theory to a low-energy effective field theory. Various terms following from a covariant derivative expansion (CDE) are represented by diagrams which, unlike conventional Feynman diagrams, involve gaugecovariant quantities and are thus dubbed ''covariant diagrams.'' The use of covariant diagrams helps organize and simplify one-loop matching calculations, which we illustrate with examples. Of particular interest is the derivation of UV model-independent universal results, which reduce matching calculations of specific UV models to applications of master formulas. We show how such derivation can be done in a more concise manner than the previous literature, and discuss how additional structures that are not directly captured by existing universal results, including mixed heavy-light loops, open covariant derivatives, and mixed statistics, can be easily accounted for.
A novel decision diagrams extension method
Li, Shumin; Si, Shubin; Dui, Hongyan; Cai, Zhiqiang; Sun, Shudong
2014-01-01
Binary decision diagram (BDD) is a graph-based representation of Boolean functions. It is a directed acyclic graph (DAG) based on Shannon's decomposition. Multi-state multi-valued decision diagram (MMDD) is a natural extension of BDD for the symbolic representation and manipulation of the multi-valued logic functions. This paper proposes a decision diagram extension method based on original BDD/MMDD while the scale of a reliability system is extended. Following a discussion of decomposition and physical meaning of BDD and MMDD, the modeling method of BDD/MMDD based on original BDD/MMDD is introduced. Three case studies are implemented to demonstrate the presented methods. Compared with traditional BDD and MMDD generation methods, the decision diagrams extension method is more computationally efficient as shown through the running time
Covariant diagrams for one-loop matching
Zhang, Zhengkang [Michigan Center for Theoretical Physics (MCTP), University of Michigan,450 Church Street, Ann Arbor, MI 48109 (United States); Deutsches Elektronen-Synchrotron (DESY),Notkestraße 85, 22607 Hamburg (Germany)
2017-05-30
We present a diagrammatic formulation of recently-revived covariant functional approaches to one-loop matching from an ultraviolet (UV) theory to a low-energy effective field theory. Various terms following from a covariant derivative expansion (CDE) are represented by diagrams which, unlike conventional Feynman diagrams, involve gauge-covariant quantities and are thus dubbed “covariant diagrams.” The use of covariant diagrams helps organize and simplify one-loop matching calculations, which we illustrate with examples. Of particular interest is the derivation of UV model-independent universal results, which reduce matching calculations of specific UV models to applications of master formulas. We show how such derivation can be done in a more concise manner than the previous literature, and discuss how additional structures that are not directly captured by existing universal results, including mixed heavy-light loops, open covariant derivatives, and mixed statistics, can be easily accounted for.
Covariant diagrams for one-loop matching
Zhang, Zhengkang [Michigan Univ., Ann Arbor, MI (United States). Michigan Center for Theoretical Physics; Deutsches Elektronen-Synchrotron (DESY), Hamburg (Germany)
2016-10-15
We present a diagrammatic formulation of recently-revived covariant functional approaches to one-loop matching from an ultraviolet (UV) theory to a low-energy effective field theory. Various terms following from a covariant derivative expansion (CDE) are represented by diagrams which, unlike conventional Feynman diagrams, involve gaugecovariant quantities and are thus dubbed ''covariant diagrams.'' The use of covariant diagrams helps organize and simplify one-loop matching calculations, which we illustrate with examples. Of particular interest is the derivation of UV model-independent universal results, which reduce matching calculations of specific UV models to applications of master formulas. We show how such derivation can be done in a more concise manner than the previous literature, and discuss how additional structures that are not directly captured by existing universal results, including mixed heavy-light loops, open covariant derivatives, and mixed statistics, can be easily accounted for.
Covariant diagrams for one-loop matching
Zhang, Zhengkang
2017-01-01
We present a diagrammatic formulation of recently-revived covariant functional approaches to one-loop matching from an ultraviolet (UV) theory to a low-energy effective field theory. Various terms following from a covariant derivative expansion (CDE) are represented by diagrams which, unlike conventional Feynman diagrams, involve gauge-covariant quantities and are thus dubbed “covariant diagrams.” The use of covariant diagrams helps organize and simplify one-loop matching calculations, which we illustrate with examples. Of particular interest is the derivation of UV model-independent universal results, which reduce matching calculations of specific UV models to applications of master formulas. We show how such derivation can be done in a more concise manner than the previous literature, and discuss how additional structures that are not directly captured by existing universal results, including mixed heavy-light loops, open covariant derivatives, and mixed statistics, can be easily accounted for.
Compatible growth models and stand density diagrams
Smith, N.J.; Brand, D.G.
1988-01-01
This paper discusses a stand average growth model based on the self-thinning rule developed and used to generate stand density diagrams. Procedures involved in testing are described and results are included
Lattice and Phase Diagram in QCD
Lombardo, Maria Paola
2008-01-01
Model calculations have produced a number of very interesting expectations for the QCD Phase Diagram, and the task of a lattice calculations is to put these studies on a quantitative grounds. I will give an overview of the current status of the lattice analysis of the QCD phase diagram, from the quantitative results of mature calculations at zero and small baryochemical potential, to the exploratory studies of the colder, denser phase.
Finding and Accessing Diagrams in Biomedical Publications
Kuhn, Tobias; Luong, ThaiBinh; Krauthammer, Michael
2012-01-01
Complex relationships in biomedical publications are often communicated by diagrams such as bar and line charts, which are a very effective way of summarizing and communicating multi-faceted data sets. Given the ever-increasing amount of published data, we argue that the precise retrieval of such diagrams is of great value for answering specific and otherwise hard-to-meet information needs. To this end, we demonstrate the use of advanced image processing and classification for identifying bar...
Ferroelectric Phase Diagram of PVDF:PMMA
Li, Mengyuan; Stingelin, Natalie; Michels, Jasper J.; Spijkman, Mark-Jan; Asadi, Kamal; Feldman, Kirill; Blom, Paul W. M.; de Leeuw, Dago M.
2012-01-01
We have investigated the ferroelectric phase diagram of poly(vinylidene fluoride) (PVDF) and poly(methyl methacrylate) (PMMA). The binary nonequilibrium temperature composition diagram was determined and melting of alpha- and beta-phase PVDF was identified. Ferroelectric beta-PVDF:PMMA blend films were made by melting, ice quenching, and subsequent annealing above the glass transition temperature of PMMA, close to the melting temperature of PVDF. Addition of PMMA suppresses the crystallizatio...
CERN. Geneva
2013-01-01
For decades the central theoretical tool for computing scattering amplitudes has been the Feynman diagram. However, Feynman diagrams are just too slow, even on fast computers, to be able to go beyond the leading order in QCD, for complicated events with many jets of hadrons in the final state. Such events are produced copiously at the LHC, and constitute formidable backgrounds to many searches for new physics. Over the past few years, alternative methods that go beyond ...
The application of diagrams in architectural design
Dulić Olivera
2014-01-01
Full Text Available Diagrams in architecture represent the visualization of the thinking process, or selective abstraction of concepts or ideas translated into the form of drawings. In addition, they provide insight into the way of thinking about and in architecture, thus creating a balance between the visual and the conceptual. The subject of research presented in this paper are diagrams as a specific kind of architectural representation, and possibilities and importance of their application in the design process. Diagrams are almost old as architecture itself, and they are an element of some of the most important studies of architecture during all periods of history - which results in a large number of different definitions of diagrams, but also very different conceptualizations of their features, functions and applications. The diagrams become part of contemporary architectural discourse during the eighties and nineties of the twentieth century, especially through the work of architects like Bernard Tschumi, Peter Eisenman, Rem Koolhaas, SANAA and others. The use of diagrams in the design process allows unification of some of the essential aspects of the profession: architectural representation and design process, as well as the question of the concept of architectural and urban design at a time of rapid changes at all levels of contemporary society. The aim of the research is the analysis of the diagram as a specific medium for processing large amounts of information that the architect should consider and incorporate into the architectural work. On that basis, it is assumed that an architectural diagram allows the creator the identification and analysis of specific elements or ideas of physical form, thereby constantly maintaining concept of the integrity of the architectural work.
Atomic energy levels and Grotrian diagrams
Bashkin, Stanley
1975-01-01
Atomic Energy Levels and Grotrian Diagrams, Volume I: Hydrogen I - Phosphorus XV presents diagrams of various elements that show their energy level and electronic transitions. The book covers the first 15 elements according to their atomic number. The text will be of great use to researchers and practitioners of fields such as astrophysics that requires pictorial representation of the energy levels and electronic transitions of elements.
An Introduction to Binary Decision Diagrams
Andersen, Henrik Reif
1996-01-01
This note is a short introduction to Binary Decision Diagrams (BDDs). It provides some background knowledge and describes the core algorithms. It is used in the course "C4340 Advanced Algorithms" at the Technical University of Denmark, autumn 1996.......This note is a short introduction to Binary Decision Diagrams (BDDs). It provides some background knowledge and describes the core algorithms. It is used in the course "C4340 Advanced Algorithms" at the Technical University of Denmark, autumn 1996....
Gluing Ladder Feynman Diagrams into Fishnets
Basso, Benjamin; Dixon, Lance J.; Stanford University, CA; University of California, Santa Barbara, CA
2017-01-01
We use integrability at weak coupling to compute fishnet diagrams for four-point correlation functions in planar Φ "4 theory. Our results are always multilinear combinations of ladder integrals, which are in turn built out of classical polylogarithms. The Steinmann relations provide a powerful constraint on such linear combinations, which leads to a natural conjecture for any fishnet diagram as the determinant of a matrix of ladder integrals.
Random Young diagrams in a Rectangular Box
Beltoft, Dan; Boutillier, Cédric; Enriquez, Nathanaël
We exhibit the limit shape of random Young diagrams having a distribution proportional to the exponential of their area, and confined in a rectangular box. The Ornstein-Uhlenbeck bridge arises from the fluctuations around the limit shape.......We exhibit the limit shape of random Young diagrams having a distribution proportional to the exponential of their area, and confined in a rectangular box. The Ornstein-Uhlenbeck bridge arises from the fluctuations around the limit shape....
Reading fitness landscape diagrams through HSAB concepts
Vigneresse, Jean-Louis, E-mail: jean-louis.vigneresse@univ-lorraine.fr
2014-10-31
Highlights: • Qualitative information from HSAB descriptors. • 2D–3D diagrams using chemical descriptors (χ, η, ω, α) and principles (MHP, mEP, mPP). • Estimate of the energy exchange during reaction paths. • Examples from complex systems (geochemistry). - Abstract: Fitness landscapes are conceived as range of mountains, with local peaks and valleys. In terms of potential, such topographic variations indicate places of local instability or stability. The chemical potential, or electronegativity, its value changed of sign, carries similar information. In addition to chemical descriptors defined through hard-soft acid-base (HSAB) concepts and computed through density functional theory (DFT), the principles that rule chemical reactions allow the design of such landscape diagrams. The simplest diagram uses electrophilicity and hardness as coordinates. It allows examining the influence of maximum hardness or minimum electrophilicity principles. A third dimension is introduced within such a diagram by mapping the topography of electronegativity, polarizability or charge exchange. Introducing charge exchange during chemical reactions, or mapping a third parameter (f.i. polarizability) reinforces the information carried by a simple binary diagram. Examples of such diagrams are provided, using data from Earth Sciences, simple oxides or ligands.
The amplituhedron from momentum twistor diagrams
Bai, Yuntao; He, Song
2015-01-01
We propose a new diagrammatic formulation of the all-loop scattering amplitudes/Wilson loops in planar N=4 SYM, dubbed the “momentum-twistor diagrams”. These are on-shell-diagrams obtained by gluing trivalent black and white vertices in momentum twistor space, which, in the reduced diagram case, are known to be related to diagrams in the original twistor space. The new diagrams are manifestly Yangian invariant, and they naturally represent factorization and forward-limit contributions in the all-loop BCFW recursion relations in momentum twistor space, in a fashion that is completely different from those in momentum space. We show how to construct and evaluate momentum-twistor diagrams, and how to use them to obtain tree-level amplitudes and loop-level integrands; in particular the latter involve isolated bubble-structures for loop variables arising from forward limits, or the entangled removal of particles. From each diagram, the generalized “boundary measurement” directly gives the C, D matrices, thus a cell in the amplituhedron associated with the amplitude, and we expect that our diagrammatic representations of the amplitude provide triangulations of the amplituhedron. To demonstrate the computational power of the formalism, we give explicit results for general two-loop integrands, and the cells of the amplituhedron for two-loop MHV amplitudes.
Asymptotic laws for random knot diagrams
Chapman, Harrison
2017-06-01
We study random knotting by considering knot and link diagrams as decorated, (rooted) topological maps on spheres and pulling them uniformly from among sets of a given number of vertices n, as first established in recent work with Cantarella and Mastin. The knot diagram model is an exciting new model which captures both the random geometry of space curve models of knotting as well as the ease of computing invariants from diagrams. We prove that unknot diagrams are asymptotically exponentially rare, an analogue of Sumners and Whittington’s landmark result for self-avoiding polygons. Our proof uses the same key idea: we first show that knot diagrams obey a pattern theorem, which describes their fractal structure. We examine how quickly this behavior occurs in practice. As a consequence, almost all diagrams are asymmetric, simplifying sampling from this model. We conclude with experimental data on knotting in this model. This model of random knotting is similar to those studied by Diao et al, and Dunfield et al.
Bifurcation software in Matlab with applications in neuronal modeling.
Govaerts, Willy; Sautois, Bart
2005-02-01
Many biological phenomena, notably in neuroscience, can be modeled by dynamical systems. We describe a recent improvement of a Matlab software package for dynamical systems with applications to modeling single neurons and all-to-all connected networks of neurons. The new software features consist of an object-oriented approach to bifurcation computations and the partial inclusion of C-code to speed up the computation. As an application, we study the origin of the spiking behaviour of neurons when the equilibrium state is destabilized by an incoming current. We show that Class II behaviour, i.e. firing with a finite frequency, is possible even if the destabilization occurs through a saddle-node bifurcation. Furthermore, we show that synchronization of an all-to-all connected network of such neurons with only excitatory connections is also possible in this case.
Hybrid intravenous digital subtraction angiography of the carotid bifurcation
Burbank, F.H.; Enzmann, D.; Keyes, G.S.; Brody, W.R.
1984-01-01
A hybrid digital subtraction angiography technique and noise-reduction algorithm were used to evaluate the carotid bifurcation. Temporal, hybrid, and reduced-noise hybrid images were obtained in right and left anterior oblique projections, and both single- and multiple-frame images were created with each method. The resulting images were graded on a scale of 1 to 5 by three experienced neuroradiologists. Temporal images were preferred over hybrid images. The percentage of nondiagnostic examinations, as agreed upon by two readers, was higher for temporal alone than temporal + hybrid. In addition, also by agreement between two readers, temporal + hybrid images significantly increased the number of bifurcations seen in two views (87%) compared to temporal subtraction alone
Local bifurcations in differential equations with state-dependent delay.
Sieber, Jan
2017-11-01
A common task when analysing dynamical systems is the determination of normal forms near local bifurcations of equilibria. As most of these normal forms have been classified and analysed, finding which particular class of normal form one encounters in a numerical bifurcation study guides follow-up computations. This paper builds on normal form algorithms for equilibria of delay differential equations with constant delay that were developed and implemented in DDE-Biftool recently. We show how one can extend these methods to delay-differential equations with state-dependent delay (sd-DDEs). Since higher degrees of regularity of local center manifolds are still open for sd-DDEs, we give an independent (still only partial) argument which phenomena from the truncated normal must persist in the full sd-DDE. In particular, we show that all invariant manifolds with a sufficient degree of normal hyperbolicity predicted by the normal form exist also in the full sd-DDE.
A bifurcation analysis for the Lugiato-Lefever equation
Godey, Cyril
2017-05-01
The Lugiato-Lefever equation is a cubic nonlinear Schrödinger equation, including damping, detuning and driving, which arises as a model in nonlinear optics. We study the existence of stationary waves which are found as solutions of a four-dimensional reversible dynamical system in which the evolutionary variable is the space variable. Relying upon tools from bifurcation theory and normal forms theory, we discuss the codimension 1 bifurcations. We prove the existence of various types of steady solutions, including spatially localized, periodic, or quasi-periodic solutions. Contribution to the Topical Issue: "Theory and Applications of the Lugiato-Lefever Equation", edited by Yanne K. Chembo, Damia Gomila, Mustapha Tlidi, Curtis R. Menyuk.
Local bifurcations in differential equations with state-dependent delay
Sieber, Jan
2017-11-01
A common task when analysing dynamical systems is the determination of normal forms near local bifurcations of equilibria. As most of these normal forms have been classified and analysed, finding which particular class of normal form one encounters in a numerical bifurcation study guides follow-up computations. This paper builds on normal form algorithms for equilibria of delay differential equations with constant delay that were developed and implemented in DDE-Biftool recently. We show how one can extend these methods to delay-differential equations with state-dependent delay (sd-DDEs). Since higher degrees of regularity of local center manifolds are still open for sd-DDEs, we give an independent (still only partial) argument which phenomena from the truncated normal must persist in the full sd-DDE. In particular, we show that all invariant manifolds with a sufficient degree of normal hyperbolicity predicted by the normal form exist also in the full sd-DDE.
Model Reduction of Nonlinear Aeroelastic Systems Experiencing Hopf Bifurcation
Abdelkefi, Abdessattar
2013-06-18
In this paper, we employ the normal form to derive a reduced - order model that reproduces nonlinear dynamical behavior of aeroelastic systems that undergo Hopf bifurcation. As an example, we consider a rigid two - dimensional airfoil that is supported by nonlinear springs in the pitch and plunge directions and subjected to nonlinear aerodynamic loads. We apply the center manifold theorem on the governing equations to derive its normal form that constitutes a simplified representation of the aeroelastic sys tem near flutter onset (manifestation of Hopf bifurcation). Then, we use the normal form to identify a self - excited oscillator governed by a time - delay ordinary differential equation that approximates the dynamical behavior while reducing the dimension of the original system. Results obtained from this oscillator show a great capability to predict properly limit cycle oscillations that take place beyond and above flutter as compared with the original aeroelastic system.
Bifurcations and Crises in a Shape Memory Oscillator
Luciano G. Machado
2004-01-01
Full Text Available The remarkable properties of shape memory alloys have been motivating the interest in applications in different areas varying from biomedical to aerospace hardware. The dynamical response of systems composed by shape memory actuators presents nonlinear characteristics and a very rich behavior, showing periodic, quasi-periodic and chaotic responses. This contribution analyses some aspects related to bifurcation phenomenon in a shape memory oscillator where the restitution force is described by a polynomial constitutive model. The term bifurcation is used to describe qualitative changes that occur in the orbit structure of a system, as a consequence of parameter changes, being related to chaos. Numerical simulations show that the response of the shape memory oscillator presents period doubling cascades, direct and reverse, and crises.
Limit cycles bifurcating from a perturbed quartic center
Coll, Bartomeu, E-mail: dmitcv0@ps.uib.ca [Dept. de Matematiques i Informatica, Universitat de les Illes Balears, Facultat de ciencies, 07071 Palma de Mallorca (Spain); Llibre, Jaume, E-mail: jllibre@mat.uab.ca [Dept. de Matematiques, Universitat Autonoma de Barcelona, Edifici Cc 08193 Bellaterra, Barcelona, Catalonia (Spain); Prohens, Rafel, E-mail: dmirps3@ps.uib.ca [Dept. de Matematiques i Informatica, Universitat de les Illes Balears, Facultat de ciencies, 07071 Palma de Mallorca (Spain)
2011-04-15
Highlights: We study polynomial perturbations of a quartic center. We get simultaneous upper and lower bounds for the bifurcating limit cycles. A higher lower bound for the maximum number of limit cycles is obtained. We obtain more limit cycles than the number obtained in the cubic case. - Abstract: We consider the quartic center x{sup .}=-yf(x,y),y{sup .}=xf(x,y), with f(x, y) = (x + a) (y + b) (x + c) and abc {ne} 0. Here we study the maximum number {sigma} of limit cycles which can bifurcate from the periodic orbits of this quartic center when we perturb it inside the class of polynomial vector fields of degree n, using the averaging theory of first order. We prove that 4[(n - 1)/2] + 4 {<=} {sigma} {<=} 5[(n - 1)/2] + 14, where [{eta}] denotes the integer part function of {eta}.
Fold points and singularity induced bifurcation in inviscid transonic flow
Marszalek, Wieslaw
2012-01-01
Transonic inviscid flow equation of elliptic–hyperbolic type when written in terms of the velocity components and similarity variable results in a second order nonlinear ODE having several features typical of differential–algebraic equations rather than ODEs. These features include the fold singularities (e.g. folded nodes and saddles, forward and backward impasse points), singularity induced bifurcation behavior and singularity crossing phenomenon. We investigate the above properties and conclude that the quasilinear DAEs of transonic flow have interesting properties that do not occur in other known quasilinear DAEs, for example, in MHD. Several numerical examples are included. -- Highlights: ► A novel analysis of inviscid transonic flow and its similarity solutions. ► Singularity induced bifurcation, singular points of transonic flow. ► Projection method, index of transonic flow DAEs, linearization via matrix pencil.
Fully developed turbulence via Feigenbaum's period-doubling bifurcations
Duong-van, M.
1987-08-01
Since its publication in 1978, Feigenbaum's predictions of the onset of turbulence via period-doubling bifurcations have been thoroughly borne out experimentally. In this paper, Feigenbaum's theory is extended into the regime in which we expect to see fully developed turbulence. We develop a method of averaging that imposes correlations in the fluctuating system generated by this map. With this averaging method, the field variable is obtained by coarse-graining, while microscopic fluctuations are preserved in all averaging scales. Fully developed turbulence will be shown to be a result of microscopic fluctuations with proper averaging. Furthermore, this model preserves Feigenbaum's results on the physics of bifurcations at the onset of turbulence while yielding additional physics both at the onset of turbulence and in the fully developed turbulence regime
Structural bifurcation of microwave helium jet discharge at atmospheric pressure
Takamura, Shuichi; Kitoh, Masakazu; Soga, Tadasuke
2008-01-01
Structural bifurcation of microwave-sustained jet discharge at atmospheric gas pressure was found to produce a stable helium plasma jet, which may open the possibility of a new type of high-flux test plasma beam for plasma-wall interactions in fusion devices. The fundamental discharge properties are presented including hysteresis characteristics, imaging of discharge emissive structure, and stable ignition parameter area. (author)
Bifurcation analysis of magnetization dynamics driven by spin transfer
Bertotti, G.; Magni, A.; Bonin, R.; Mayergoyz, I.D.; Serpico, C.
2005-01-01
Nonlinear magnetization dynamics under spin-polarized currents is discussed by the methods of the theory of nonlinear dynamical systems. The fixed points of the dynamics are calculated. It is shown that there may exist 2, 4, or 6 fixed points depending on the values of the external field and of the spin-polarized current. The stability of the fixed points is analyzed and the conditions for the occurrence of saddle-node and Hopf bifurcations are determined
Bifurcation analysis of magnetization dynamics driven by spin transfer
Bertotti, G. [IEN Galileo Ferraris, Strada delle Cacce 91, 10135 Turin (Italy); Magni, A. [IEN Galileo Ferraris, Strada delle Cacce 91, 10135 Turin (Italy); Bonin, R. [Dipartimento di Fisica, Politecnico di Torino, Corso degli Abbruzzi, 10129 Turin (Italy)]. E-mail: bonin@ien.it; Mayergoyz, I.D. [Department of Electrical and Computer Engineering, University of Maryland, College Park, Maryland 20742 (United States); Serpico, C. [Department of Electrical Engineering, University of Napoli Federico II, via Claudio 21, 80125 Naples (Italy)
2005-04-15
Nonlinear magnetization dynamics under spin-polarized currents is discussed by the methods of the theory of nonlinear dynamical systems. The fixed points of the dynamics are calculated. It is shown that there may exist 2, 4, or 6 fixed points depending on the values of the external field and of the spin-polarized current. The stability of the fixed points is analyzed and the conditions for the occurrence of saddle-node and Hopf bifurcations are determined.
An alternative bifurcation analysis of the Rose-Hindmarsh model
Nikolov, Svetoslav
2005-01-01
The paper presents an alternative study of the bifurcation behavior of the Rose-Hindmarsh model using Lyapunov-Andronov's theory. This is done on the basis of the obtained analytical formula expressing the first Lyapunov's value (this is not Lyapunov exponent) at the boundary of stability. From the obtained results the following new conclusions are made: Transition to chaos and the occurrence of chaotic oscillations in the Rose-Hindmarsh system take place under hard stability loss
Stability and bifurcation of an SIS epidemic model with treatment
Li Xuezhi; Li Wensheng; Ghosh, Mini
2009-01-01
An SIS epidemic model with a limited resource for treatment is introduced and analyzed. It is assumed that treatment rate is proportional to the number of infectives below the capacity and is a constant when the number of infectives is greater than the capacity. It is found that a backward bifurcation occurs if the capacity is small. It is also found that there exist bistable endemic equilibria if the capacity is low.
Bifurcation in Z2-symmetry quadratic polynomial systems with delay
Zhang Chunrui; Zheng Baodong
2009-01-01
Z 2 -symmetry systems are considered. Firstly the general forms of Z 2 -symmetry quadratic polynomial system are given, and then a three-dimensional Z 2 equivariant system is considered, which describes the relations of two predator species for a single prey species. Finally, the explicit formulas for determining the Fold and Hopf bifurcations are obtained by using the normal form theory and center manifold argument.
Streamline topology: Patterns in fluid flows and their bifurcations
Brøns, Morten
2007-01-01
Using dynamical systems theory, we consider structures such as vortices and separation in the streamline patterns of fluid flows. Bifurcation of patterns under variation of external parameters is studied using simplifying normal form transformations. Flows away from boundaries, flows close to fix...... walls, and axisymmetric flows are analyzed in detail. We show how to apply the ideas from the theory to analyze numerical simulations of the vortex breakdown in a closed cylindrical container....
Application of the bifurcation method to the modified Boussinesq equation
Shaoyong Li
2014-08-01
Firstly, we give a property of the solutions of the equation, that is, if $1+u(x, t$ is a solution, so is $1-u(x, t$. Secondly, by using the bifurcation method of dynamical systems we obtain some explicit expressions of solutions for the equation, which include kink-shaped solutions, blow-up solutions, periodic blow-up solutions and solitary wave solutions. Some previous results are extended.
Spiral blood flow in aorta-renal bifurcation models.
Javadzadegan, Ashkan; Simmons, Anne; Barber, Tracie
2016-01-01
The presence of a spiral arterial blood flow pattern in humans has been widely accepted. It is believed that this spiral component of the blood flow alters arterial haemodynamics in both positive and negative ways. The purpose of this study was to determine the effect of spiral flow on haemodynamic changes in aorta-renal bifurcations. In this regard, a computational fluid dynamics analysis of pulsatile blood flow was performed in two idealised models of aorta-renal bifurcations with and without flow diverter. The results show that the spirality effect causes a substantial variation in blood velocity distribution, while causing only slight changes in fluid shear stress patterns. The dominant observed effect of spiral flow is on turbulent kinetic energy and flow recirculation zones. As spiral flow intensity increases, the rate of turbulent kinetic energy production decreases, reducing the region of potential damage to red blood cells and endothelial cells. Furthermore, the recirculation zones which form on the cranial sides of the aorta and renal artery shrink in size in the presence of spirality effect; this may lower the rate of atherosclerosis development and progression in the aorta-renal bifurcation. These results indicate that the spiral nature of blood flow has atheroprotective effects in renal arteries and should be taken into consideration in analyses of the aorta and renal arteries.
Bifurcation and category learning in network models of oscillating cortex
Baird, Bill
1990-06-01
A genetic model of oscillating cortex, which assumes “minimal” coupling justified by known anatomy, is shown to function as an associative memory, using previously developed theory. The network has explicit excitatory neurons with local inhibitory interneuron feedback that forms a set of nonlinear oscillators coupled only by long-range excitatory connections. Using a local Hebb-like learning rule for primary and higher-order synapses at the ends of the long-range connections, the system learns to store the kinds of oscillation amplitude patterns observed in olfactory and visual cortex. In olfaction, these patterns “emerge” during respiration by a pattern forming phase transition which we characterize in the model as a multiple Hopf bifurcation. We argue that these bifurcations play an important role in the operation of real digital computers and neural networks, and we use bifurcation theory to derive learning rules which analytically guarantee CAM storage of continuous periodic sequences-capacity: N/2 Fourier components for an N-node network-no “spurious” attractors.
Endodontic-periodontic bifurcation lesions: a novel treatment option.
Lin, Shaul; Tillinger, Gabriel; Zuckerman, Offer
2008-05-01
The purpose of this preliminary clinical report is to suggest a novel treatment modality for periodontal bifurcation lesions of endodontic origin. The study consisted of 11 consecutive patients who presented with periodontal bifurcation lesions of endodontic origin (endo-perio lesions). All patients were followed-up for at least 12 months. Treatment included calcium hydroxide with iodine-potassium iodide placed in the root canals for 90 days followed by canal sealing with gutta-percha and cement during a second stage. Dentin bonding was used to seal the furcation floor to prevent the ingress of bacteria and their by-products to the furcation root area through the accessory canals. A radiographic examination showed complete healing of the periradicular lesion in all patients. Probing periodontal pocket depths decreased to 2 to 4 mm (mean 3.5 mm), and resolution of the furcation involvement was observed in post-operative clinical evaluations. The suggested treatment of endo-perio lesions may result in complete healing. Further studies are warranted. This treatment method improves both the disinfection of the bifurcation area and the healing process in endodontically treated teeth considered to be hopeless.
Ternary choices in repeated games and border collision bifurcations
Dal Forno, Arianna; Gardini, Laura; Merlone, Ugo
2012-01-01
Highlights: ► We extend a model of binary choices with externalities to include more alternatives. ► Introducing one more option affects the complexity of the dynamics. ► We find bifurcation structures which where impossible to observe in binary choices. ► A ternary choice cannot simply be considered as a binary choice plus one. - Abstract: Several recent contributions formalize and analyze binary choices games with externalities as those described by Schelling. Nevertheless, in the real world choices are not always binary, and players have often to decide among more than two alternatives. These kinds of interactions are examined in game theory where, starting from the well known rock-paper-scissor game, several other kinds of strategic interactions involving more than two choices are examined. In this paper we investigate how the dynamics evolve introducing one more option in binary choice games with externalities. The dynamics we obtain are always in a stable regime, that is, the structurally stable dynamics are only attracting cycles, but of any possible positive integer as period. We show that, depending on the structure of the game, the dynamics can be quite different from those existing when considering binary choices. The bifurcation structure, due to border collisions, is explained, showing the existence of so-called big-bang bifurcation points.
Observation of bifurcation phenomena in an electron beam plasma system
Hayashi, N.; Tanaka, M.; Shinohara, S.; Kawai, Y.
1995-01-01
When an electron beam is injected into a plasma, unstable waves are excited spontaneously near the electron plasma frequency f pe by the electron beam plasma instability. The experiment on subharmonics in an electron beam plasma system was performed with a glow discharge tube. The bifurcation of unstable waves with the electron plasma frequency f pe and 1/2 f pe was observed using a double-plasma device. Furthermore, the period doubling route to chaos around the ion plasma frequency in an electron beam plasma system was reported. However, the physical mechanism of bifurcation phenomena in an electron beam plasma system has not been clarified so far. We have studied nonlinear behaviors of the electron beam plasma instability. It was found that there are some cases: the fundamental unstable waves and subharmonics of 2 period are excited by the electron beam plasma instability, the fundamental unstable waves and subharmonics of 3 period are excited. In this paper, we measured the energy distribution functions of electrons and the dispersion relation of test waves in order to examine the physical mechanism of bifurcation phenomena in an electron beam plasma system
Reverse bifurcation and fractal of the compound logistic map
Wang, Xingyuan; Liang, Qingyong
2008-07-01
The nature of the fixed points of the compound logistic map is researched and the boundary equation of the first bifurcation of the map in the parameter space is given out. Using the quantitative criterion and rule of chaotic system, the paper reveal the general features of the compound logistic map transforming from regularity to chaos, the following conclusions are shown: (1) chaotic patterns of the map may emerge out of double-periodic bifurcation and (2) the chaotic crisis phenomena and the reverse bifurcation are found. At the same time, we analyze the orbit of critical point of the compound logistic map and put forward the definition of Mandelbrot-Julia set of compound logistic map. We generalize the Welstead and Cromer's periodic scanning technology and using this technology construct a series of Mandelbrot-Julia sets of compound logistic map. We investigate the symmetry of Mandelbrot-Julia set and study the topological inflexibility of distributing of period region in the Mandelbrot set, and finds that Mandelbrot set contain abundant information of structure of Julia sets by founding the whole portray of Julia sets based on Mandelbrot set qualitatively.
Bifurcation in autonomous and nonautonomous differential equations with discontinuities
Akhmet, Marat
2017-01-01
This book is devoted to bifurcation theory for autonomous and nonautonomous differential equations with discontinuities of different types. That is, those with jumps present either in the right-hand-side or in trajectories or in the arguments of solutions of equations. The results obtained in this book can be applied to various fields such as neural networks, brain dynamics, mechanical systems, weather phenomena, population dynamics, etc. Without any doubt, bifurcation theory should be further developed to different types of differential equations. In this sense, the present book will be a leading one in this field. The reader will benefit from the recent results of the theory and will learn in the very concrete way how to apply this theory to differential equations with various types of discontinuity. Moreover, the reader will learn new ways to analyze nonautonomous bifurcation scenarios in these equations. The book will be of a big interest both for beginners and experts in the field. For the former group o...
Hopf Bifurcation Control of Subsynchronous Resonance Utilizing UPFC
Μ. Μ. Alomari
2017-06-01
Full Text Available The use of a unified power flow controller (UPFC to control the bifurcations of a subsynchronous resonance (SSR in a multi-machine power system is introduced in this study. UPFC is one of the flexible AC transmission systems (FACTS where a voltage source converter (VSC is used based on gate-turn-off (GTO thyristor valve technology. Furthermore, UPFC can be used as a stabilizer by means of a power system stabilizer (PSS. The considered system is a modified version of the second system of the IEEE second benchmark model of subsynchronous resonance where the UPFC is added to its transmission line. The dynamic effects of the machine components on SSR are considered. Time domain simulations based on the complete nonlinear dynamical mathematical model are used for numerical simulations. The results in case of including UPFC are compared to the case where the transmission line is conventionally compensated (without UPFC where two Hopf bifurcations are predicted with unstable operating point at wide range of compensation levels. For UPFC systems, it is worth to mention that the operating point of the system never loses stability at all realistic compensation degrees and therefore all power system bifurcations have been eliminated.
Nonlinear stability, bifurcation and resonance in granular plane Couette flow
Shukla, Priyanka; Alam, Meheboob
2010-11-01
A weakly nonlinear stability theory is developed to understand the effect of nonlinearities on various linear instability modes as well as to unveil the underlying bifurcation scenario in a two-dimensional granular plane Couette flow. The relevant order parameter equation, the Landau-Stuart equation, for the most unstable two-dimensional disturbance has been derived using the amplitude expansion method of our previous work on the shear-banding instability.ootnotetextShukla and Alam, Phys. Rev. Lett. 103, 068001 (2009). Shukla and Alam, J. Fluid Mech. (2010, accepted). Two types of bifurcations, Hopf and pitchfork, that result from travelling and stationary linear instabilities, respectively, are analysed using the first Landau coefficient. It is shown that the subcritical instability can appear in the linearly stable regime. The present bifurcation theory shows that the flow is subcritically unstable to disturbances of long wave-lengths (kx˜0) in the dilute limit, and both the supercritical and subcritical states are possible at moderate densities for the dominant stationary and traveling instabilities for which kx=O(1). We show that the granular plane Couette flow is prone to a plethora of resonances.ootnotetextShukla and Alam, J. Fluid Mech. (submitted, 2010)
Bifurcation-based approach reveals synergism and optimal combinatorial perturbation.
Liu, Yanwei; Li, Shanshan; Liu, Zengrong; Wang, Ruiqi
2016-06-01
Cells accomplish the process of fate decisions and form terminal lineages through a series of binary choices in which cells switch stable states from one branch to another as the interacting strengths of regulatory factors continuously vary. Various combinatorial effects may occur because almost all regulatory processes are managed in a combinatorial fashion. Combinatorial regulation is crucial for cell fate decisions because it may effectively integrate many different signaling pathways to meet the higher regulation demand during cell development. However, whether the contribution of combinatorial regulation to the state transition is better than that of a single one and if so, what the optimal combination strategy is, seem to be significant issue from the point of view of both biology and mathematics. Using the approaches of combinatorial perturbations and bifurcation analysis, we provide a general framework for the quantitative analysis of synergism in molecular networks. Different from the known methods, the bifurcation-based approach depends only on stable state responses to stimuli because the state transition induced by combinatorial perturbations occurs between stable states. More importantly, an optimal combinatorial perturbation strategy can be determined by investigating the relationship between the bifurcation curve of a synergistic perturbation pair and the level set of a specific objective function. The approach is applied to two models, i.e., a theoretical multistable decision model and a biologically realistic CREB model, to show its validity, although the approach holds for a general class of biological systems.
Ida, K.; Inagaki, S.; Yoshinuma, M.; Narushima, Y.; Itoh, K.; Kobuchi, T.; Watanabe, K. Y.; Funaba, H.; Sakakibara, S.; Morisaki, T.; LHD Experimental Group
2008-01-01
Three states of a magnetic island are observed when the magnetic shear at the rational surface is modified using inductive current associated with the neutral beam current drive in the Large Helical Device. One state is the healed magnetic island with a zero island width. The second state is the saturated magnetic island with partial flattening of the T e profile. The third state is characterized by the global flattening of the T e profile in the core region. As the plasma assumes each of the three states consecutively through a bifurcation process a clear hysteresis in the relation between the size of the magnetic island and the magnetic shear is observed
Bifurcating Particle Swarms in Smooth-Walled Fractures
Pyrak-Nolte, L. J.; Sun, H.
2010-12-01
Particle swarms can occur naturally or from industrial processes where small liquid drops containing thousands to millions of micron-size to colloidal-size particles are released over time from seepage or leaks into fractured rock. The behavior of these particle swarms as they fall under gravity are affected by particle interactions as well as interactions with the walls of the fractures. In this paper, we present experimental results on the effect of fractures on the cohesiveness of the swarm and the formation of bifurcation structures as they fall under gravity and interact with the fracture walls. A transparent cubic sample (100 mm x 100 mm x 100 mm) containing a synthetic fracture with uniform aperture distributions was optically imaged to quantify the effect of confinement within fractures on particle swarm formation, swarm velocity, and swarm geometry. A fracture with a uniform aperture distribution was fabricated from two polished rectangular prisms of acrylic. A series of experiments were performed to determine how swarm movement and geometry are affected as the walls of the fracture are brought closer together from 50 mm to 1 mm. During the experiments, the fracture was fully saturated with water. We created the swarms using two different particle sizes in dilute suspension (~ 1.0% by mass). The particles were 3 micron diameter fluorescent polymer beads and 25 micron diameter soda-lime glass beads. Experiments were performed using swarms that ranged in size from 5 µl to 60 µl. The swarm behavior was imaged using an optical fluorescent imaging system composed of a CCD camera illuminated by a 100 mW diode-pumped doubled YAG laser. As a swarm falls in an open-tank of water, it forms a torroidal shape that is stable as long as no ambient or background currents exist in the water tank. When a swarm is released into a fracture with an aperture less than 5 mm, the swarm forms the torroidal shape but it is distorted because of the presence of the walls. The
Modelling, singular perturbation and bifurcation analyses of bitrophic food chains.
Kooi, B W; Poggiale, J C
2018-04-20
Two predator-prey model formulations are studied: for the classical Rosenzweig-MacArthur (RM) model and the Mass Balance (MB) chemostat model. When the growth and loss rate of the predator is much smaller than that of the prey these models are slow-fast systems leading mathematically to singular perturbation problem. In contradiction to the RM-model, the resource for the prey are modelled explicitly in the MB-model but this comes with additional parameters. These parameter values are chosen such that the two models become easy to compare. In both models a transcritical bifurcation, a threshold above which invasion of predator into prey-only system occurs, and the Hopf bifurcation where the interior equilibrium becomes unstable leading to a stable limit cycle. The fast-slow limit cycles are called relaxation oscillations which for increasing differences in time scales leads to the well known degenerated trajectories being concatenations of slow parts of the trajectory and fast parts of the trajectory. In the fast-slow version of the RM-model a canard explosion of the stable limit cycles occurs in the oscillatory region of the parameter space. To our knowledge this type of dynamics has not been observed for the RM-model and not even for more complex ecosystem models. When a bifurcation parameter crosses the Hopf bifurcation point the amplitude of the emerging stable limit cycles increases. However, depending of the perturbation parameter the shape of this limit cycle changes abruptly from one consisting of two concatenated slow and fast episodes with small amplitude of the limit cycle, to a shape with large amplitude of which the shape is similar to the relaxation oscillation, the well known degenerated phase trajectories consisting of four episodes (concatenation of two slow and two fast). The canard explosion point is accurately predicted by using an extended asymptotic expansion technique in the perturbation and bifurcation parameter simultaneously where the small
Seitz, J.L.
2001-10-15
Global Issues is an introduction to the nature and background of some of the central issues - economic, social, political, environmental - of modern times. This new edition of this text has been fully updated throughout and features expanded sections on issues such as global warming, biotechnology, and energy. Fully updated throughout and features expanded sections on issues such as global warming, biotechnology, and energy. An introduction to the nature and background of some of the central issues - economic, social, political, environmental - of modern times. Covers a range of perspectives on a variety of societies, developed and developing. Extensively illustrated with diagrams and photographs, contains guides to further reading, media, and internet resources, and includes suggestions for discussion and studying the material. (author)
The Semiotic Structure of Geometry Diagrams: How Textbook Diagrams Convey Meaning
Dimmel, Justin K.; Herbst, Patricio G.
2015-01-01
Geometry diagrams use the visual features of specific drawn objects to convey meaning about generic mathematical entities. We examine the semiotic structure of these visual features in two parts. One, we conduct a semiotic inquiry to conceptualize geometry diagrams as mathematical texts that comprise choices from different semiotic systems. Two,…
Codimension-two bifurcation analysis on firing activities in Chay neuron model
Duan Lixia; Lu Qishao
2006-01-01
Using codimension-two bifurcation analysis in the Chay neuron model, the relationship between the electric activities and the parameters of neurons is revealed. The whole parameter space is divided into two parts, that is, the firing and silence regions of neurons. It is found that the transition sets between firing and silence regions are composed of the Hopf bifurcation curves of equilibrium states and the saddle-node bifurcation curves of limit cycles, with some codimension-two bifurcation points. The transitions from silence to firing in neurons are due to the Hopf bifurcation or the fold limit cycle bifurcation, but the codimension-two singularities lead to complexity in dynamical behaviour of neuronal firing
Codimension-two bifurcation analysis on firing activities in Chay neuron model
Duan Lixia [School of Science, Beijing University of Aeronautics and Astronautics, Beijing 100083 (China); Lu Qishao [School of Science, Beijing University of Aeronautics and Astronautics, Beijing 100083 (China)]. E-mail: qishaolu@hotmail.com
2006-12-15
Using codimension-two bifurcation analysis in the Chay neuron model, the relationship between the electric activities and the parameters of neurons is revealed. The whole parameter space is divided into two parts, that is, the firing and silence regions of neurons. It is found that the transition sets between firing and silence regions are composed of the Hopf bifurcation curves of equilibrium states and the saddle-node bifurcation curves of limit cycles, with some codimension-two bifurcation points. The transitions from silence to firing in neurons are due to the Hopf bifurcation or the fold limit cycle bifurcation, but the codimension-two singularities lead to complexity in dynamical behaviour of neuronal firing.
Fishbone Diagrams: Organize Reading Content with a "Bare Bones" Strategy
Clary, Renee; Wandersee, James
2010-01-01
Fishbone diagrams, also known as Ishikawa diagrams or cause-and-effect diagrams, are one of the many problem-solving tools created by Dr. Kaoru Ishikawa, a University of Tokyo professor. Part of the brilliance of Ishikawa's idea resides in the simplicity and practicality of the diagram's basic model--a fish's skeleton. This article describes how…
Visualizing Metrics on Areas of Interest in Software Architecture Diagrams
Byelas, Heorhiy; Telea, Alexandru; Eades, P; Ertl, T; Shen, HW
2009-01-01
We present a new method for the combined visualization of software architecture diagrams, Such as UML class diagrams or component diagrams, and software metrics defined on groups of diagram elements. Our method extends an existing rendering technique for the so-called areas of interest in system
Phase diagram of classical electronic bilayers
Ranganathan, S; Johnson, R E
2006-01-01
Extensive molecular dynamics calculations have been performed on classical, symmetric electronic bilayers at various values of the coupling strength Γ and interlayer separation d to delineate its phase diagram in the Γ-d plane. We studied the diffusion, the amplitude of the main peak of the intralayer static structure factor and the peak positions of the intralayer pair correlation function with the aim of defining equivalent signatures of freezing and constructing the resulting phase diagram. It is found that for Γ greater than 75, crystalline structures exist for a certain range of interlayer separations, while liquid phases are favoured at smaller and larger d. It is seen that there is good agreement between our phase diagram and previously published ones
Phase diagram of classical electronic bilayers
Ranganathan, S [Department of Physics, Royal Military College of Canada, Kingston, Ontario K7K 7B4 (Canada); Johnson, R E [Department of Mathematics and Computer Science, Royal Military College of Canada, Kingston, Ontario K7K 7B4 (Canada)
2006-04-28
Extensive molecular dynamics calculations have been performed on classical, symmetric electronic bilayers at various values of the coupling strength {gamma} and interlayer separation d to delineate its phase diagram in the {gamma}-d plane. We studied the diffusion, the amplitude of the main peak of the intralayer static structure factor and the peak positions of the intralayer pair correlation function with the aim of defining equivalent signatures of freezing and constructing the resulting phase diagram. It is found that for {gamma} greater than 75, crystalline structures exist for a certain range of interlayer separations, while liquid phases are favoured at smaller and larger d. It is seen that there is good agreement between our phase diagram and previously published ones.
The Butterfly diagram leopard skin pattern
Ternullo, Maurizio
2011-08-01
A time-latitude diagram where spotgroups are given proportional relevance to their area is presented. The diagram reveals that the spotted area distribution is higly dishomogeneous, most of it being concentrated in few, small portions (``knots'') of the Butterfly Diagram; because of this structure, the BD may be properly described as a cluster of knots. The description, assuming that spots scatter around the ``spot mean latitude'' steadily drifting equatorward, is challenged. Indeed, spots cluster around at as many latitudes as knots; a knot may appear at either lower or higher latitudes than previous ones, in a seemingly random way; accordingly, the spot mean latitude abruptly drifts equatorward or even poleward at any knot activation, in spite of any smoothing procedure. Preliminary analyses suggest that the activity splits, in any hemisphere, into two or more distinct ``activity waves'', drifting equatorward at a rate higher than the spot zone as a whole.
Phase diagrams of diluted transverse Ising nanowire
Bouhou, S.; Essaoudi, I. [Laboratoire de Physique des Matériaux et Modélisation, des Systèmes, (LP2MS), Unité Associée au CNRST-URAC 08, University of Moulay Ismail, Physics Department, Faculty of Sciences, B.P. 11201 Meknes (Morocco); Ainane, A., E-mail: ainane@pks.mpg.de [Laboratoire de Physique des Matériaux et Modélisation, des Systèmes, (LP2MS), Unité Associée au CNRST-URAC 08, University of Moulay Ismail, Physics Department, Faculty of Sciences, B.P. 11201 Meknes (Morocco); Max-Planck-Institut für Physik Complexer Systeme, Nöthnitzer Str. 38 D-01187 Dresden (Germany); Saber, M. [Laboratoire de Physique des Matériaux et Modélisation, des Systèmes, (LP2MS), Unité Associée au CNRST-URAC 08, University of Moulay Ismail, Physics Department, Faculty of Sciences, B.P. 11201 Meknes (Morocco); Max-Planck-Institut für Physik Complexer Systeme, Nöthnitzer Str. 38 D-01187 Dresden (Germany); Ahuja, R. [Condensed Matter Theory Group, Department of Physics and Astronomy, Uppsala University, 75120 Uppsala (Sweden); Dujardin, F. [Laboratoire de Chimie et Physique des Milieux Complexes (LCPMC), Institut de Chimie, Physique et Matériaux (ICPM), 1 Bd. Arago, 57070 Metz (France)
2013-06-15
In this paper, the phase diagrams of diluted Ising nanowire consisting of core and surface shell coupling by J{sub cs} exchange interaction are studied using the effective field theory with a probability distribution technique, in the presence of transverse fields in the core and in the surface shell. We find a number of characteristic phenomena. In particular, the effect of concentration c of magnetic atoms, the exchange interaction core/shell, the exchange in surface and the transverse fields in core and in surface shell of phase diagrams are investigated. - Highlights: ► We use the EFT to investigate the phase diagrams of Ising transverse nanowire. ► Ferrimagnetic and ferromagnetic cases are investigated. ► The effects of the dilution and the transverse fields in core and shell are studied. ► Behavior of the transition temperature with the exchange interaction is given.
Phase diagrams of diluted transverse Ising nanowire
Bouhou, S.; Essaoudi, I.; Ainane, A.; Saber, M.; Ahuja, R.; Dujardin, F.
2013-01-01
In this paper, the phase diagrams of diluted Ising nanowire consisting of core and surface shell coupling by J cs exchange interaction are studied using the effective field theory with a probability distribution technique, in the presence of transverse fields in the core and in the surface shell. We find a number of characteristic phenomena. In particular, the effect of concentration c of magnetic atoms, the exchange interaction core/shell, the exchange in surface and the transverse fields in core and in surface shell of phase diagrams are investigated. - Highlights: ► We use the EFT to investigate the phase diagrams of Ising transverse nanowire. ► Ferrimagnetic and ferromagnetic cases are investigated. ► The effects of the dilution and the transverse fields in core and shell are studied. ► Behavior of the transition temperature with the exchange interaction is given
Repair of Partly Misspecified Causal Diagrams.
Oates, Chris J; Kasza, Jessica; Simpson, Julie A; Forbes, Andrew B
2017-07-01
Errors in causal diagrams elicited from experts can lead to the omission of important confounding variables from adjustment sets and render causal inferences invalid. In this report, a novel method is presented that repairs a misspecified causal diagram through the addition of edges. These edges are determined using a data-driven approach designed to provide improved statistical efficiency relative to de novo structure learning methods. Our main assumption is that the expert is "directionally informed," meaning that "false" edges provided by the expert would not create cycles if added to the "true" causal diagram. The overall procedure is cast as a preprocessing technique that is agnostic to subsequent causal inferences. Results based on simulated data and data derived from an observational cohort illustrate the potential for data-assisted elicitation in epidemiologic applications. See video abstract at, http://links.lww.com/EDE/B208.
A Critical Appraisal of the "Day" Diagram
Roberts, Andrew P.; Tauxe, Lisa; Heslop, David; Zhao, Xiang; Jiang, Zhaoxia
2018-04-01
The "Day" diagram (Day et al., 1977, https://doi.org/10.1016/0031-9201(77)90108-X) is used widely to make inferences about the domain state of magnetic mineral assemblages. Based on theoretical and empirical arguments, the Day diagram is demarcated into stable "single domain" (SD), "pseudo single domain" ("PSD"), and "multidomain" (MD) zones. It is straightforward to make the necessary measurements for a sample and to plot results within the "domain state" framework based on the boundaries defined by Day et al. (1977, https://doi.org/10.1016/0031-9201(77)90108-X). We discuss 10 issues that limit Day diagram interpretation, including (1) magnetic mineralogy, (2) the associated magnetocrystalline anisotropy type, (3) mineral stoichiometry, (4) stress state, (5) surface oxidation, (6) magnetostatic interactions, (7) particle shape, (8) thermal relaxation, (9) magnetic particle mixtures, and (10) definitional/measurement issues. In most studies, these variables are unknowns and cannot be controlled for, so that hysteresis parameters for single bulk samples are nonunique and any data point in a Day diagram could result from infinite combinations of relevant variables. From this critical appraisal, we argue that the Day diagram is fundamentally ambiguous for domain state diagnosis. Widespread use of the Day diagram has also contributed significantly to prevalent but questionable views, including underrecognition of the importance of stable SD particles in the geological record and reinforcement of the unhelpful PSD concept and of its geological importance. Adoption of approaches that enable correct domain state diagnosis should be an urgent priority for component-specific understanding of magnetic mineral assemblages and for quantitative rock magnetic interpretation.
Sliding bifurcations and chaos induced by dry friction in a braking system
Yang, F.H.; Zhang, W.; Wang, J.
2009-01-01
In this paper, non-smooth bifurcations and chaotic dynamics are investigated for a braking system. A three-degree-of-freedom model is considered to capture the complicated nonlinear characteristics, in particular, non-smooth bifurcations in the braking system. The stick-slip transition is analyzed for the braking system. From the results of numerical simulation, it is observed that there also exist the grazing-sliding bifurcation and stick-slip chaos in the braking system.
Stability and Hopf Bifurcation in a Delayed SEIRS Worm Model in Computer Network
Zizhen Zhang
2013-01-01
Full Text Available A delayed SEIRS epidemic model with vertical transmission in computer network is considered. Sufficient conditions for local stability of the positive equilibrium and existence of local Hopf bifurcation are obtained by analyzing distribution of the roots of the associated characteristic equation. Furthermore, the direction of the local Hopf bifurcation and the stability of the bifurcating periodic solutions are determined by using the normal form theory and center manifold theorem. Finally, a numerical example is presented to verify the theoretical analysis.
Bifurcation Analysis of the QI 3-D Four-Wing Chaotic System
Sun, Y.; Qi, G.; Wang, Z.; Wyk, B.J. van
2010-01-01
This paper analyzes the pitchfork and Hopf bifurcations of a new 3-D four-wing quadratic autonomous system proposed by Qi et al. The center manifold technique is used to reduce the dimensions of this system. The pitchfork and Hopf bifurcations of the system are theoretically analyzed. The influence of system parameters on other bifurcations are also investigated. The theoretical analysis and simulations demonstrate the rich dynamics of the system. (authors)
Period-doubling bifurcation and chaos control in a discrete-time mosquito model
Qamar Din
2017-12-01
Full Text Available This article deals with the study of some qualitative properties of a discrete-time mosquito Model. It is shown that there exists period-doubling bifurcation for wide range of bifurcation parameter for the unique positive steady-state of given system. In order to control the bifurcation we introduced a feedback strategy. For further confirmation of complexity and chaotic behavior largest Lyapunov exponents are plotted.
Stability and bifurcation of a discrete BAM neural network model with delays
Zheng Baodong; Zhang Yang; Zhang Chunrui
2008-01-01
A map modelling a discrete bidirectional associative memory neural network with delays is investigated. Its dynamics is studied in terms of local analysis and Hopf bifurcation analysis. By analyzing the associated characteristic equation, its linear stability is investigated and Hopf bifurcations are demonstrated. It is found that there exist Hopf bifurcations when the delay passes a sequence of critical values. Numerical simulation is performed to verify the analytical results
Karaoglu, Esra; Merdan, Huseyin
2014-01-01
Highlights: • A ratio-dependent predator–prey system involving two discrete maturation time delays is studied. • Hopf bifurcations are analyzed by choosing delay parameters as bifurcation parameters. • When a delay parameter passes through a critical value, Hopf bifurcations occur. • The direction of bifurcation, the period and the stability of periodic solution are also obtained. - Abstract: In this paper we give a detailed Hopf bifurcation analysis of a ratio-dependent predator–prey system involving two different discrete delays. By analyzing the characteristic equation associated with the model, its linear stability is investigated. Choosing delay terms as bifurcation parameters the existence of Hopf bifurcations is demonstrated. Stability of the bifurcating periodic solutions is determined by using the center manifold theorem and the normal form theory introduced by Hassard et al. Furthermore, some of the bifurcation properties including direction, stability and period are given. Finally, theoretical results are supported by some numerical simulations
Formal Analysis Of Use Case Diagrams
Radosław Klimek
2010-01-01
Full Text Available Use case diagrams play an important role in modeling with UML. Careful modeling is crucialin obtaining a correct and efficient system architecture. The paper refers to the formalanalysis of the use case diagrams. A formal model of use cases is proposed and its constructionfor typical relationships between use cases is described. Two methods of formal analysis andverification are presented. The first one based on a states’ exploration represents a modelchecking approach. The second one refers to the symbolic reasoning using formal methodsof temporal logic. Simple but representative example of the use case scenario verification isdiscussed.
Abulkhaev, V.L.; Ganiev, I.N.
1994-01-01
By means of thermal differential analysis, X-ray and microstructural analysis the state diagram of Pr-Bi system was studied. Following intermetallic compounds were defined in the system: Pr 2 Bi, Pr 5 Bi 3 , Pr 4 Bi 3 , Pr Bi, PrBi 2 , Pr 2 Bi, Pr 5 Bi 3 , Pr 4 Bi 3 and PrBi 2 . The data analysis on Ln-Bi diagram allowed to determine the regularity of change of properties of intermetallic compounds in the line of rare earth elements of cerium subgroup.
Fusion Diagrams in the - and - Systems
Asadov, M. M.; Akhmedova, N. A.
2014-10-01
A calculation model of the Gibbs energy of ternary oxide compounds from the binary components was used. Thermodynamic properties of -- ternary systems in the condensed state were calculated. Thermodynamic data of binary and ternary compounds were used to determine the stable sections. The probability of reactions between the corresponding components in the -- system was estimated. Fusibility diagrams of systems - and - were studied by physical-chemical analysis. The isothermal section of the phase diagram of -- at 298 K is built, as well as the projection of the liquid surface of --.
Analysis of stability and Hopf bifurcation for a viral infectious model with delay
Sun Chengjun; Cao Zhijie; Lin Yiping
2007-01-01
In this paper, a four-dimensional viral infectious model with delay is considered. The stability of the two equilibria and the existence of Hopf bifurcation are investigated. It is found that there are stability switches and Hopf bifurcations occur when the delay τ passes through a sequence of critical values. Using the normal form theory and center manifold argument [Hassard B, Kazarino D, Wan Y. Theory and applications of Hopf bifurcation. Cambridge: Cambridge University Press; 1981], the explicit formulaes which determine the stability, the direction and the period of bifurcating periodic solutions are derived. Numerical simulations are carried out to illustrate the validity of the main results
Bifurcation structure of localized states in the Lugiato-Lefever equation with anomalous dispersion
Parra-Rivas, P.; Gomila, D.; Gelens, L.; Knobloch, E.
2018-04-01
The origin, stability, and bifurcation structure of different types of bright localized structures described by the Lugiato-Lefever equation are studied. This mean field model describes the nonlinear dynamics of light circulating in fiber cavities and microresonators. In the case of anomalous group velocity dispersion and low values of the intracavity phase detuning these bright states are organized in a homoclinic snaking bifurcation structure. We describe how this bifurcation structure is destroyed when the detuning is increased across a critical value, and determine how a bifurcation structure known as foliated snaking emerges.
Hopf bifurcation in a delayed reaction-diffusion-advection population model
Chen, Shanshan; Lou, Yuan; Wei, Junjie
2018-04-01
In this paper, we investigate a reaction-diffusion-advection model with time delay effect. The stability/instability of the spatially nonhomogeneous positive steady state and the associated Hopf bifurcation are investigated when the given parameter of the model is near the principle eigenvalue of an elliptic operator. Our results imply that time delay can make the spatially nonhomogeneous positive steady state unstable for a reaction-diffusion-advection model, and the model can exhibit oscillatory pattern through Hopf bifurcation. The effect of advection on Hopf bifurcation values is also considered, and our results suggest that Hopf bifurcation is more likely to occur when the advection rate increases.
Numerical Hopf bifurcation of Runge-Kutta methods for a class of delay differential equations
Wang Qiubao; Li Dongsong; Liu, M.Z.
2009-01-01
In this paper, we consider the discretization of parameter-dependent delay differential equation of the form y ' (t)=f(y(t),y(t-1),τ),τ≥0,y element of R d . It is shown that if the delay differential equation undergoes a Hopf bifurcation at τ=τ * , then the discrete scheme undergoes a Hopf bifurcation at τ(h)=τ * +O(h p ) for sufficiently small step size h, where p≥1 is the order of the Runge-Kutta method applied. The direction of numerical Hopf bifurcation and stability of bifurcating invariant curve are the same as that of delay differential equation.
Stability, bifurcation and a new chaos in the logistic differential equation with delay
Jiang Minghui; Shen Yi; Jian Jigui; Liao Xiaoxin
2006-01-01
This Letter is concerned with bifurcation and chaos in the logistic delay differential equation with a parameter r. The linear stability of the logistic equation is investigated by analyzing the associated characteristic transcendental equation. Based on the normal form approach and the center manifold theory, the formula for determining the direction of Hopf bifurcation and the stability of bifurcation periodic solution in the first bifurcation values is obtained. By theoretical analysis and numerical simulation, we found a new chaos in the logistic delay differential equation
Delay Induced Hopf Bifurcation of an Epidemic Model with Graded Infection Rates for Internet Worms
Tao Zhao
2017-01-01
Full Text Available A delayed SEIQRS worm propagation model with different infection rates for the exposed computers and the infectious computers is investigated in this paper. The results are given in terms of the local stability and Hopf bifurcation. Sufficient conditions for the local stability and the existence of Hopf bifurcation are obtained by using eigenvalue method and choosing the delay as the bifurcation parameter. In particular, the direction and the stability of the Hopf bifurcation are investigated by means of the normal form theory and center manifold theorem. Finally, a numerical example is also presented to support the obtained theoretical results.
Bifurcation of the Kuroshio Extension at the Shatsky Rise
Hurlburt, Harley E.; Metzger, E. Joseph
1998-04-01
A 1/16° six-layer Pacific Ocean model north of 20°S is used to investigate the bifurcation of the Kuroshio Extension at the main Shatsky Rise and the pathway of the northern branch from the bifurcation to the subarctic front. Upper ocean-topographic coupling via a mixed barotropic-baroclinic instability is essential to this bifurcation and to the formation and mean pathway of the northern branch as are several aspects of the Shatsky Rise complex of topography and the latitude of the Kuroshio Extension in relation to the topography. The flow instabilities transfer energy to the abyssal layer where it is constrained by geostrophic contours of the bottom topography. The topographically constrained abyssal currents in turn steer upper ocean currents, which do not directly impinge on the bottom topography. This includes steering of mean pathways. Obtaining sufficient coupling requires very fine resolution of mesoscale variability and sufficient eastward penetration of the Kuroshio as an unstable inertial jet. Resolution of 1/8° for each variable was not sufficient in this case. The latitudinal extent of the main Shatsky Rise (31°N-36°N) and the shape of the downward slope on the north side are crucial to the bifurcation at the main Shatsky Rise, with both branches passing north of the peak. The well-defined, relatively steep and straight eastern edge of the Shatsky Rise topographic complex (30°N-42°N) and the southwestward abyssal flow along it play a critical role in forming the rest of the Kuroshio northern branch which flows in the opposite direction. A deep pass between the main Shatsky Rise and the rest of the ridge to the northeast helps to link the northern fork of the bifurcation at the main rise to the rest of the northern branch. Two 1/16° "identical twin" interannual simulations forced by daily winds 1981-1995 show that the variability in this region is mostly nondeterministic on all timescales that could be examined (up to 7 years in these 15-year
Dynamical Regimes and the Dynamo Bifurcation in Geodynamo Simulations
Petitdemange, L.
2017-12-01
We investigate the nature of the dynamo bifurcation in a configuration applicable to the Earth's liquid outer core : in a rotating spherical shell with thermally driven motions with no-slip boundaries. Unlike previous studies on dynamo bifurcations, the control parameters have been varied significantly in order to deduce general tendencies. Numerical studies on the stability domain of dipolar magnetic fields found a dichotomy between non-reversing dipole-dominated dynamos and the reversing non-dipole-dominated multipolar solutions. We show that, by considering weak initial fields, the above transition is replaced by a region of bistability for which dipolar and multipolar dynamos coexist. Such a result was also observed in models with free-slip boundaries in which the strong shear of geostrophic zonal flows can develop and gives rise to non-dipolar fields. We show that a similar process develops in no-slip models when viscous effects are reduced sufficiently.Close to the onset of convection (Rac), the axial dipole grows exponentially in the kinematic phase and saturation occurs by marginally changing the flow structure close to the dynamo threshold Rmc. The resulting bifurcation is then supercritical.In the range 3RacIf (Ra/Ra_c>10), important zonal flows develop in non-magnetic models with low viscosity. The field topology depends on the initial magnetic field. The dipolar branch has a subcritical behaviour whereas the multipolar branch is supercritical. By approaching more realistic parameters, the extension of this bistable regime increases (lower Rossby numbers). An hysteretic behaviour questions the common interpretation for geomagnetic reversals. Far above Rm_c$, the Lorentz force becomes dominant, as it is expected in planetary cores.
Dynamic stability and bifurcation analysis in fractional thermodynamics
Béda, Péter B.
2018-02-01
In mechanics, viscoelasticity was the first field of applications in studying geomaterials. Further possibilities arise in spatial non-locality. Non-local materials were already studied in the 1960s by several authors as a part of continuum mechanics and are still in focus of interest because of the rising importance of materials with internal micro- and nano-structure. When material instability gained more interest, non-local behavior appeared in a different aspect. The problem was concerned to numerical analysis, because then instability zones exhibited singular properties for local constitutive equations. In dynamic stability analysis, mathematical aspects of non-locality were studied by using the theory of dynamic systems. There the basic set of equations describing the behavior of continua was transformed to an abstract dynamic system consisting of differential operators acting on the perturbation field variables. Such functions should satisfy homogeneous boundary conditions and act as indicators of stability of a selected state of the body under consideration. Dynamic systems approach results in conditions for cases, when the differential operators have critical eigenvalues of zero real parts (dynamic stability or instability conditions). When the critical eigenvalues have non-trivial eigenspace, the way of loss of stability is classified as a typical (or generic) bifurcation. Our experiences show that material non-locality and the generic nature of bifurcation at instability are connected, and the basic functions of the non-trivial eigenspace can be used to determine internal length quantities of non-local mechanics. Fractional calculus is already successfully used in thermo-elasticity. In the paper, non-locality is introduced via fractional strain into the constitutive relations of various conventional types. Then, by defining dynamic systems, stability and bifurcation are studied for states of thermo-mechanical solids. Stability conditions and genericity
Technique and results of femoral bifurcation endarterectomy by eversion.
Dufranc, Julie; Palcau, Laura; Heyndrickx, Maxime; Gouicem, Djelloul; Coffin, Olivier; Felisaz, Aurélien; Berger, Ludovic
2015-03-01
This study evaluated, in a contemporary prospective series, the safety and efficacy of femoral endarterectomy using the eversion technique and compared our results with results obtained in the literature for the standard endarterectomy with patch closure. Between 2010 and 2012, 121 patients (76% male; mean age, 68.7 years; diabetes, 28%; renal insufficiency, 20%) underwent 147 consecutive femoral bifurcation endarterectomies using the eversion technique, associating or not inflow or outflow concomitant revascularization. The indications were claudication in 89 procedures (60%) and critical limb ischemia in 58 (40%). Primary, primary assisted, and secondary patency of the femoral bifurcation, clinical improvement, limb salvage, and survival were assessed using Kaplan-Meier life-table analysis. Factors associated with those primary end-points were evaluated with univariate analysis. The technical success of eversion was of 93.2%. The 30-day mortality was 0%, and the complication rate was 8.2%; of which, half were local and benign. Median follow-up was 16 months (range, 1.6-31.2 months). Primary, primary assisted, and secondary patencies were, respectively, 93.2%, 97.2%, and 98.6% at 2 years. Primary, primary assisted, and secondary maintenance of clinical improvement were, respectively, 79.9%, 94.6%, and 98.6% at 2 years. The predictive factors for clinical degradation were clinical stage (Rutherford category 5 or 6, P = .024), platelet aggregation inhibitor treatment other than clopidogrel (P = .005), malnutrition (P = .025), and bad tibial runoff (P = .0016). A reintervention was necessary in 18.3% of limbs at 2 years: 2% involving femoral bifurcation, 6.1% inflow improvement, and 9.5% outflow improvement. The risk factors of reintervention were platelet aggregation inhibitor (other than clopidogrel, P = .049) and cancer (P = .011). Limb preservation at 2 years was 100% in the claudicant population. Limb salvage was 88.6% in the critical limb ischemia population
One-dimensional map lattices: Synchronization, bifurcations, and chaotic structures
Belykh, Vladimir N.; Mosekilde, Erik
1996-01-01
The paper presents a qualitative analysis of coupled map lattices (CMLs) for the case of arbitrary nonlinearity of the local map and with space-shift as well as diffusion coupling. The effect of synchronization where, independently of the initial conditions, all elements of a CML acquire uniform...... dynamics is investigated and stable chaotic time behaviors, steady structures, and traveling waves are described. Finally, the bifurcations occurring under the transition from spatiotemporal chaos to chaotic synchronization and the peculiarities of CMLs with specific symmetries are discussed....
Stochastic Calculus: Application to Dynamic Bifurcations and Threshold Crossings
Jansons, Kalvis M.; Lythe, G. D.
1998-01-01
For the dynamic pitchfork bifurcation in the presence of white noise, the statistics of the last time at zero are calculated as a function of the noise level ∈ and the rate of change of the parameter μ. The threshold crossing problem used, for example, to model the firing of a single cortical neuron is considered, concentrating on quantities that may be experimentally measurable but have so far received little attention. Expressions for the statistics of pre-threshold excursions, occupation density, and last crossing time of zero are compared with results from numerical generation of paths.
Square-lattice random Potts model: criticality and pitchfork bifurcation
Costa, U.M.S.; Tsallis, C.
1983-01-01
Within a real space renormalization group framework based on self-dual clusters, the criticality of the quenched bond-mixed q-state Potts ferromagnet on square lattice is discussed. On qualitative grounds it is exhibited that the crossover from the pure fixed point to the random one occurs, while q increases, through a pitchfork bifurcation; the relationship with Harris criterion is analyzed. On quantitative grounds high precision numerical values are presented for the critical temperatures corresponding to various concentrations of the coupling constants J 1 and J 2 , and various ratios J 1 /J 2 . The pure, random and crossover critical exponents are discussed as well. (Author) [pt
Bifurcation analysis of dengue transmission model in Baguio City, Philippines
Libatique, Criselda P.; Pajimola, Aprimelle Kris J.; Addawe, Joel M.
2017-11-01
In this study, we formulate a deterministic model for the transmission dynamics of dengue fever in Baguio City, Philippines. We analyzed the existence of the equilibria of the dengue model. We computed and obtained conditions for the existence of the equilibrium states. Stability analysis for the system is carried out for disease free equilibrium. We showed that the system becomes stable under certain conditions of the parameters. A particular parameter is taken and with the use of the Theory of Centre Manifold, the proposed model demonstrates a bifurcation phenomenon. We performed numerical simulation to verify the analytical results.
Enumeration of diagonally colored Young diagrams
Gyenge, Ádám
2015-01-01
In this note we give a new proof of a closed formula for the multivariable generating series of diagonally colored Young diagrams. This series also describes the Euler characteristics of certain Nakajima quiver varieties. Our proof is a direct combinatorial argument, based on Andrews' work on generalized Frobenius partitions. We also obtain representations of these series in some particular cases as infinite products.
Partial chord diagrams and matrix models
Andersen, Jørgen Ellegaard; Fuji, Hiroyuki; Manabe, Masahide
In this article, the enumeration of partial chord diagrams is discussed via matrix model techniques. In addition to the basic data such as the number of backbones and chords, we also consider the Euler characteristic, the backbone spectrum, the boundary point spectrum, and the boundary length spe...
Characteristic Dynkin diagrams and W algebras
Ragoucy, E.
1993-01-01
We present a classification of characteristic Dynkin diagrams for the A N , B N , C N and D N algebras. This classification is related to the classification of W(G, K) algebras arising from non-abelian Toda models, and we argue that it can give new insight on the structure of W algebras. (orig.)
Diagram of a LEP superconducting cavity
1991-01-01
This diagram gives a schematic representation of the superconducting radio-frequency cavities at LEP. Liquid helium is used to cool the cavity to 4.5 degrees above absolute zero so that very high electric fields can be produced, increasing the operating energy of the accelerator. Superconducting cavities were used only in the LEP-2 phase of the accelerator, from 1996 to 2000.
Extended sequence diagram for human system interaction
Hwang, Jong Rok; Choi, Sun Woo; Ko, Hee Ran; Kim, Jong Hyun
2012-01-01
Unified Modeling Language (UML) is a modeling language in the field of object oriented software engineering. The sequence diagram is a kind of interaction diagram that shows how processes operate with one another and in what order. It is a construct of a message sequence chart. It depicts the objects and classes involved in the scenario and the sequence of messages exchanged between the objects needed to carry out the functionality of the scenario. This paper proposes the Extended Sequence Diagram (ESD), which is capable of depicting human system interaction for nuclear power plants, as well as cognitive process of operators analysis. In the conventional sequence diagram, there is a limit to only identify the activities of human and systems interactions. The ESD is extended to describe operators' cognitive process in more detail. The ESD is expected to be used as a task analysis method for describing human system interaction. The ESD can also present key steps causing abnormal operations or failures and diverse human errors based on cognitive condition
Kelp diagrams : Point set membership visualization
Dinkla, K.; Kreveld, van M.J.; Speckmann, B.; Westenberg, M.A.
2012-01-01
We present Kelp Diagrams, a novel method to depict set relations over points, i.e., elements with predefined positions. Our method creates schematic drawings and has been designed to take aesthetic quality, efficiency, and effectiveness into account. This is achieved by a routing algorithm, which
Mixed wasted integrated program: Logic diagram
Mayberry, J.; Stelle, S.; O'Brien, M.; Rudin, M.; Ferguson, J.; McFee, J.
1994-01-01
The Mixed Waste Integrated Program Logic Diagram was developed to provide technical alternative for mixed wastes projects for the Office of Technology Development's Mixed Waste Integrated Program (MWIP). Technical solutions in the areas of characterization, treatment, and disposal were matched to a select number of US Department of Energy (DOE) treatability groups represented by waste streams found in the Mixed Waste Inventory Report (MWIR)
Phase Diagrams of Strongly Interacting Theories
Sannino, Francesco
2010-01-01
We summarize the phase diagrams of SU, SO and Sp gauge theories as function of the number of flavors, colors, and matter representation as well as the ones of phenomenologically relevant chiral gauge theories such as the Bars-Yankielowicz and the generalized Georgi-Glashow models. We finally report...
Spin wave Feynman diagram vertex computation package
Price, Alexander; Javernick, Philip; Datta, Trinanjan
Spin wave theory is a well-established theoretical technique that can correctly predict the physical behavior of ordered magnetic states. However, computing the effects of an interacting spin wave theory incorporating magnons involve a laborious by hand derivation of Feynman diagram vertices. The process is tedious and time consuming. Hence, to improve productivity and have another means to check the analytical calculations, we have devised a Feynman Diagram Vertex Computation package. In this talk, we will describe our research group's effort to implement a Mathematica based symbolic Feynman diagram vertex computation package that computes spin wave vertices. Utilizing the non-commutative algebra package NCAlgebra as an add-on to Mathematica, symbolic expressions for the Feynman diagram vertices of a Heisenberg quantum antiferromagnet are obtained. Our existing code reproduces the well-known expressions of a nearest neighbor square lattice Heisenberg model. We also discuss the case of a triangular lattice Heisenberg model where non collinear terms contribute to the vertex interactions.
Phase diagram distortion from traffic parameter averaging.
Stipdonk, H. Toorenburg, J. van & Postema, M.
2010-01-01
Motorway traffic congestion is a major bottleneck for economic growth. Therefore, research of traffic behaviour is carried out in many countries. Although well describing the undersaturated free flow phase as an almost straight line in a (k,q)-phase diagram, congested traffic observations and
A Generalized Wave Diagram for Moving Sources
Alt, Robert; Wiley, Sam
2004-12-01
Many introductory physics texts1-5 accompany the discussion of the Doppler effect and the formation of shock waves with diagrams illustrating the effect of a source moving through an elastic medium. Typically these diagrams consist of a series of equally spaced dots, representing the location of the source at different times. These are surrounded by a series of successively smaller circles representing wave fronts (see Fig. 1). While such a diagram provides a clear illustration of the shock wave produced by a source moving at a speed greater than the wave speed, and also the resultant pattern when the source speed is less than the wave speed (the Doppler effect), the texts do not often show the details of the construction. As a result, the key connection between the relative distance traveled by the source and the distance traveled by the wave is not explicitly made. In this paper we describe an approach emphasizing this connection that we have found to be a useful classroom supplement to the usual text presentation. As shown in Fig. 2 and Fig. 3, the Doppler effect and the shock wave can be illustrated by diagrams generated by the construction that follows.
Planar quark diagrams and binary spin processes
Grigoryan, A.A.; Ivanov, N.Ya.
1986-01-01
Contributions of planar diagrams to the binary scattering processes are analyzed. The analysis is based on the predictions of quark-gluon picture of strong interactions for the coupling of reggeons with quarks as well as on the SU(6)-classification of hadrons. The dependence of contributions of nonplanar corrections on spins and quark composition of interacting particles is discussed
Phase diagram of spiking neural networks.
Seyed-Allaei, Hamed
2015-01-01
In computer simulations of spiking neural networks, often it is assumed that every two neurons of the network are connected by a probability of 2%, 20% of neurons are inhibitory and 80% are excitatory. These common values are based on experiments, observations, and trials and errors, but here, I take a different perspective, inspired by evolution, I systematically simulate many networks, each with a different set of parameters, and then I try to figure out what makes the common values desirable. I stimulate networks with pulses and then measure their: dynamic range, dominant frequency of population activities, total duration of activities, maximum rate of population and the occurrence time of maximum rate. The results are organized in phase diagram. This phase diagram gives an insight into the space of parameters - excitatory to inhibitory ratio, sparseness of connections and synaptic weights. This phase diagram can be used to decide the parameters of a model. The phase diagrams show that networks which are configured according to the common values, have a good dynamic range in response to an impulse and their dynamic range is robust in respect to synaptic weights, and for some synaptic weights they oscillates in α or β frequencies, independent of external stimuli.