Adaptive function projective synchronization of two-cell Quantum-CNN chaotic oscillators with uncertain parameters

International Nuclear Information System (INIS)

Sudheer, K. Sebastian; Sabir, M.

2009-01-01

This work investigates function projective synchronization of two-cell Quantum-CNN chaotic oscillators using adaptive method. Quantum-CNN oscillators produce nano scale chaotic oscillations under certain conditions. By Lyapunove stability theory, the adaptive control law and the parameter update law are derived to make the state of two chaotic systems function projective synchronized. Numerical simulations are presented to demonstrate the effectiveness of the proposed adaptive controllers.

EEG simulation by 2D interconnected chaotic oscillators

Energy Technology Data Exchange (ETDEWEB)

Kubany, Adam, E-mail: adamku@bgu.ac.i [Department of Industrial Engineering and Management, Ben-Gurion University of the Negev, P.O. Box 653, Beer-Sheva 84105 (Israel); Mhabary, Ziv; Gontar, Vladimir [Department of Industrial Engineering and Management, Ben-Gurion University of the Negev, P.O. Box 653, Beer-Sheva 84105 (Israel)

2011-01-15

Research highlights: ANN of 2D interconnected chaotic oscillators is explored for EEG simulation. An inverse problem solution (PRCGA) is proposed. Good matching between the simulated and experimental EEG signals has been achieved. - Abstract: An artificial neuronal network composed by 2D interconnected chaotic oscillators is explored for brain waves (EEG) simulation. For the inverse problem solution a parallel real-coded genetic algorithm (PRCGA) is proposed. In order to conduct thorough comparison between the simulated and target signal characteristics, a spectrum analysis of the signals is undertaken. A good matching between the theoretical and experimental EEG signals has been achieved. Numerical results of calculations are presented and discussed.

EEG simulation by 2D interconnected chaotic oscillators

International Nuclear Information System (INIS)

Kubany, Adam; Mhabary, Ziv; Gontar, Vladimir

2011-01-01

Research highlights: → ANN of 2D interconnected chaotic oscillators is explored for EEG simulation. → An inverse problem solution (PRCGA) is proposed. → Good matching between the simulated and experimental EEG signals has been achieved. - Abstract: An artificial neuronal network composed by 2D interconnected chaotic oscillators is explored for brain waves (EEG) simulation. For the inverse problem solution a parallel real-coded genetic algorithm (PRCGA) is proposed. In order to conduct thorough comparison between the simulated and target signal characteristics, a spectrum analysis of the signals is undertaken. A good matching between the theoretical and experimental EEG signals has been achieved. Numerical results of calculations are presented and discussed.

A survey of Wien bridge-based chaotic oscillators: Design and experimental issues

Energy Technology Data Exchange (ETDEWEB)

Kilic, Recai [Erciyes University, Department of Electrical and Electronic Engineering, 38039 Kayseri (Turkey)], E-mail: kilic@erciyes.edu.tr; Yildirim, Fatma [Erciyes University, Civil Aviation School, 38039 Kayseri (Turkey)

2008-12-15

This paper presents a comparative study on design and implementation of Wien type chaotic oscillators. By making a collection of almost all Wien bridge-based chaotic circuits, we have investigated these oscillators in terms of chaotic dynamics, circuit structures, active building blocks, nonlinear element structures and operating frequency by using PSpice simulations and laboratory experiments. In addition to this comparative investigation, we present our two basic experimental contributions to referred implementations. While the first of our experimental contributions consists of the experimentally implementation of CFOA-based Chua's circuit modified for very high chaotic oscillations, the scope of the second is to experimentally implement a Wien type high frequency chaos generator, which has the diode-inductor composite, in the inductorless form by using CFOA-based synthetic inductor.

Study of chaotic oscillations in practical work on radio physics

International Nuclear Information System (INIS)

Ezdov, A.A.; Il'in, V.A.; Petrova, E.B.

1995-01-01

A description is given of a laboratory study of chaotic oscillations in deterministic dynamical systems. This work utilizes mathematical modeling and a computer experiment, as well as a direct study of the chaotic behavior of nonlinear electrical circuits

Application of fixed point theory to chaotic attractors of forced oscillators

International Nuclear Information System (INIS)

Stewart, H.B.

1990-11-01

A review of the structure of chaotic attractors of periodically forced second order nonlinear oscillators suggests that the theory of fixed points of transformations gives information about the fundamental topological structure of attractors. First a simple extension of the Levinson index formula is proved. Then numerical evidence is used to formulate plausible conjectures about absorbing regions containing chaotic attractors in forced oscillators. Applying the Levinson formula suggests a fundamental relation between the number of fixed points or periodic points in a section of the chaotic attractor on the one hand, and a topological invariant of an absorbing region on the other hand. (author)

A New Method for Suppressing Periodic Narrowband Interference Based on the Chaotic van der Pol Oscillator

Science.gov (United States)

Lu, Jia; Zhang, Xiaoxing; Xiong, Hao

The chaotic van der Pol oscillator is a powerful tool for detecting defects in electric systems by using online partial discharge (PD) monitoring. This paper focuses on realizing weak PD signal detection in the strong periodic narrowband interference by using high sensitivity to the periodic narrowband interference signals and immunity to white noise and PD signals of chaotic systems. A new approach to removing the periodic narrowband interference by using a van der Pol chaotic oscillator is described by analyzing the motion characteristic of the chaotic oscillator on the basis of the van der Pol equation. Furthermore, the Floquet index for measuring the amplitude of periodic narrowband signals is redefined. The denoising signal processed by the chaotic van der Pol oscillators is further processed by wavelet analysis. Finally, the denoising results verify that the periodic narrowband and white noise interference can be removed efficiently by combining the theory of the chaotic van der Pol oscillator and wavelet analysis.

Dynamic synchronization of a time-evolving optical network of chaotic oscillators.

Science.gov (United States)

Cohen, Adam B; Ravoori, Bhargava; Sorrentino, Francesco; Murphy, Thomas E; Ott, Edward; Roy, Rajarshi

2010-12-01

We present and experimentally demonstrate a technique for achieving and maintaining a global state of identical synchrony of an arbitrary network of chaotic oscillators even when the coupling strengths are unknown and time-varying. At each node an adaptive synchronization algorithm dynamically estimates the current strength of the net coupling signal to that node. We experimentally demonstrate this scheme in a network of three bidirectionally coupled chaotic optoelectronic feedback loops and we present numerical simulations showing its application in larger networks. The stability of the synchronous state for arbitrary coupling topologies is analyzed via a master stability function approach. © 2010 American Institute of Physics.

Determining the Lyapunov Spectrum of Continuous-Time 1D and 2D Multiscroll Chaotic Oscillators via the Solution of m-PWL Variational Equations

Directory of Open Access Journals (Sweden)

Jesus Manuel Munoz-Pacheco

2013-01-01

Full Text Available An algorithm to compute the Lyapunov exponents of piecewise linear function-based multidirectional multiscroll chaotic oscillators is reported. Based on the m regions in the piecewise linear functions, the suggested algorithm determines the individual expansion rate of Lyapunov exponents from m-piecewise linear variational equations and their associated m-Jacobian matrices whose entries remain constant during all computation cycles. Additionally, by considering OpAmp-based chaotic oscillators, we study the impact of two analog design procedures on the magnitude of Lyapunov exponents. We focus on analyzing variations of both frequency bandwidth and voltage/current dynamic range of the chaotic signals at electronic system level. As a function of the design parameters, a renormalization factor is proposed to estimate correctly the Lyapunov spectrum. Numerical simulation results in a double-scroll type chaotic oscillator and complex chaotic oscillators generating multidirectional multiscroll chaotic attractors on phase space confirm the usefulness of the reported algorithm.

Regular and chaotic behaviors of plasma oscillations modeled by a modified Duffing equation

International Nuclear Information System (INIS)

Enjieu Kadji, H.G.; Chabi Orou, J.B.; Woafo, P.; Abdus Salam International Centre for Theoretical Physics, Trieste

2005-07-01

The regular and chaotic behavior of plasma oscillations governed by a modified Duffing equation is studied. The plasma oscillations are described by a nonlinear differential equation of the form x + w 0 2 x + βx 2 + αx 3 = 0 which is similar to a Duffing equation. By focusing on the quadratic term, which is mainly the term modifying the Duffing equation, the harmonic balance method and the fourth order Runge-Kutta algorithm are used to derive regular and chaotic motions respectively. A strong chaotic behavior exhibited by the system in that event when the system is subjected to an external periodic forcing oscillation is reported as β varies. (author)

Chaotic Dynamics and Application of LCR Oscillators Sharing Common Nonlinearity

Science.gov (United States)

Jeevarekha, A.; Paul Asir, M.; Philominathan, P.

2016-06-01

This paper addresses the problem of sharing common nonlinearity among nonautonomous and autonomous oscillators. By choosing a suitable common nonlinear element with the driving point characteristics capable of bringing out chaotic motion in a combined system, we obtain identical chaotic states. The dynamics of the coupled system is explored through numerical and experimental studies. Employing the concept of common nonlinearity, a simple chaotic communication system is modeled and its performance is verified through Multisim simulation.

Intermittent and sustained periodic windows in networked chaotic Rössler oscillators

International Nuclear Information System (INIS)

He, Zhiwei; Sun, Yong; Zhan, Meng

2013-01-01

Route to chaos (or periodicity) in dynamical systems is one of fundamental problems. Here, dynamical behaviors of coupled chaotic Rössler oscillators on complex networks are investigated and two different types of periodic windows with the variation of coupling strength are found. Under a moderate coupling, the periodic window is intermittent, and the attractors within the window extremely sensitively depend on the initial conditions, coupling parameter, and topology of the network. Therefore, after adding or removing one edge of network, the periodic attractor can be destroyed and substituted by a chaotic one, or vice versa. In contrast, under an extremely weak coupling, another type of periodic window appears, which insensitively depends on the initial conditions, coupling parameter, and network. It is sustained and unchanged for different types of network structure. It is also found that the phase differences of the oscillators are almost discrete and randomly distributed except that directly linked oscillators more likely have different phases. These dynamical behaviors have also been generally observed in other networked chaotic oscillators

Multisynchronization of Chaotic Oscillators via Nonlinear Observer Approach

Directory of Open Access Journals (Sweden)

Ricardo Aguilar-López

2014-01-01

Full Text Available The goal of this work is to synchronize a class of chaotic oscillators in a master-slave scheme, under different initial conditions, considering several slaves systems. The Chen oscillator is employed as a benchmark model and a nonlinear observer is proposed to reach synchronicity between the master and the slaves’ oscillators. The proposed observer contains a proportional and integral form of a bounded function of the synchronization error in order to provide asymptotic synchronization with a satisfactory performance. Numerical experiments were carried out to show the operation of the considered methodology.

Multisynchronization of chaotic oscillators via nonlinear observer approach.

Science.gov (United States)

Aguilar-López, Ricardo; Martínez-Guerra, Rafael; Mata-Machuca, Juan L

2014-01-01

The goal of this work is to synchronize a class of chaotic oscillators in a master-slave scheme, under different initial conditions, considering several slaves systems. The Chen oscillator is employed as a benchmark model and a nonlinear observer is proposed to reach synchronicity between the master and the slaves' oscillators. The proposed observer contains a proportional and integral form of a bounded function of the synchronization error in order to provide asymptotic synchronization with a satisfactory performance. Numerical experiments were carried out to show the operation of the considered methodology.

Raby chaotic vacuum oscillations in resonator quantum electrodynamics

International Nuclear Information System (INIS)

Kon'kov, L.E.; Prants, S.V.

1997-01-01

It is shown in numerical experiments with two-level atoms, moving through a single-mode high-quality resonator, that a new type of spontaneous radiation - the Raby chaotic vacuum oscillation - originates in the mode of strong atom-field bonds

Autonomous third-order duffing-holmes type chaotic oscillator

DEFF Research Database (Denmark)

Lindberg, Erik; Tamaseviciute, E; Mykolaitis, G

2009-01-01

feedback loop. In contrast to many other autonomous chaotic oscillators, including linear unstable resonators and nonlinear damping loops, the novel circuit is based on nonlinear resonator and linear damping loop in the negative feedback. SPICE simulation and hardware experimental investigations...

A new kind of metal detector based on chaotic oscillator

Science.gov (United States)

Hu, Wenjing

2017-12-01

The sensitivity of a metal detector greatly depends on the identification ability to weak signals from the probe. In order to improve the sensitivity of metal detectors, this paper applies the Duffing chaotic oscillator to metal detectors based on its characteristic which is very sensitive to weak periodic signals. To make a suitable Duffing system for detectors, this paper computes two Lyapunov characteristics exponents of the Duffing oscillator, which help to obtain the threshold of the Duffing system in the critical state accurately and give quantitative criteria for chaos. Meanwhile, a corresponding simulation model of the chaotic oscillator is made by the Simulink tool box of Matlab. Simulation results shows that Duffing oscillator is very sensitive to sinusoidal signals in high frequency cases. And experimental results show that the measurable diameter of metal particles is about 1.5mm. It indicates that this new method can feasibly and effectively improve the metal detector sensitivity.

CHAOTIC DUFFING TYPE OSCILLATOR WITH INERTIAL DAMPING

DEFF Research Database (Denmark)

Tamaševicius, Arunas; Mykolaitis, Gytis; Kirvaitis, Raimundas

2009-01-01

A novel Duffing-Holmes type autonomous chaotic oscillator is described. In comparison with the well-known non-autonomous Duffing-Holmes circuit it lacks the external periodic drive, but includes two extra linear feedback sub-circuits, namely a direct positive feedback loop, and an inertial negati...... feedback loop. SPICE simulation and hardware experimental results are presented....

Experimental Observation of Chaotic Beats in Oscillators Sharing Nonlinearity

Science.gov (United States)

Paul Asir, M.; Jeevarekha, A.; Philominathan, P.

This paper deals with the generation of chaotic beats in a system of two forced dissipative LCR oscillators sharing a nonlinear element. The presence of two external periodic excitations and a common nonlinear element in the chosen system enables the facile generation of chaotic beats. Thus rendered chaotic beats were characterized in both time domain and phase space. Lyapunov exponents and envelope of the beats were computed to diagnose the chaotic nature of the signals. The role of common nonlinearity on the complexity of the generated beats is discussed. Real-time experimental hardware implementation has also been done to confirm the subsistence of the phenomenon, for the first time. Extensive Multisim simulations were carried out to understand, a bit more about the shrinkage and revivals of state variables in phase space.

Chaotic oscillator containing memcapacitor and meminductor and its dimensionality reduction analysis.

Science.gov (United States)

Yuan, Fang; Wang, Guangyi; Wang, Xiaowei

2017-03-01

In this paper, smooth curve models of meminductor and memcapacitor are designed, which are generalized from a memristor. Based on these models, a new five-dimensional chaotic oscillator that contains a meminductor and memcapacitor is proposed. By dimensionality reducing, this five-dimensional system can be transformed into a three-dimensional system. The main work of this paper is to give the comparisons between the five-dimensional system and its dimensionality reduction model. To investigate dynamics behaviors of the two systems, equilibrium points and stabilities are analyzed. And the bifurcation diagrams and Lyapunov exponent spectrums are used to explore their properties. In addition, digital signal processing technologies are used to realize this chaotic oscillator, and chaotic sequences are generated by the experimental device, which can be used in encryption applications.

Chaotic weak chimeras and their persistence in coupled populations of phase oscillators

International Nuclear Information System (INIS)

Bick, Christian; Ashwin, Peter

2016-01-01

Nontrivial collective behavior may emerge from the interactive dynamics of many oscillatory units. Chimera states are chaotic patterns of spatially localized coherent and incoherent oscillations. The recently-introduced notion of a weak chimera gives a rigorously testable characterization of chimera states for finite-dimensional phase oscillator networks. In this paper we give some persistence results for dynamically invariant sets under perturbations and apply them to coupled populations of phase oscillators with generalized coupling. In contrast to the weak chimeras with nonpositive maximal Lyapunov exponents constructed so far, we show that weak chimeras that are chaotic can exist in the limit of vanishing coupling between coupled populations of phase oscillators. We present numerical evidence that positive Lyapunov exponents can persist for a positive measure set of this inter-population coupling strength. (paper)

Experimental dynamical characterization of five autonomous chaotic oscillators with tunable series resistance

Energy Technology Data Exchange (ETDEWEB)

Minati, Ludovico, E-mail: lminati@ieee.org, E-mail: ludovico.minati@unitn.it [MR-Lab, Center for Mind/Brain Science, University of Trento, Trento, Italy and Scientific Department, Fondazione IRCCS Istituto Neurologico Carlo Besta, Milan (Italy)

2014-09-01

In this paper, an experimental characterization of the dynamical properties of five autonomous chaotic oscillators, based on bipolar-junction transistors and obtained de-novo through a genetic algorithm in a previous study, is presented. In these circuits, a variable resistor connected in series to the DC voltage source acts as control parameter, for a range of which the largest Lyapunov exponent, correlation dimension, approximate entropy, and amplitude variance asymmetry are calculated, alongside bifurcation diagrams and spectrograms. Numerical simulations are compared to experimental measurements. The oscillators can generate a considerable variety of regular and chaotic sine-like and spike-like signals.

Cluster synchronization modes in an ensemble of coupled chaotic oscillators

DEFF Research Database (Denmark)

Belykh, Vladimir N.; Belykh, Igor V.; Mosekilde, Erik

2001-01-01

Considering systems of diffusively coupled identical chaotic oscillators, an effective method to determine the possible states of cluster synchronization and ensure their stability is presented. The method, which may find applications in communication engineering and other fields of science...

A Chaotic Oscillator Based on HP Memristor Model

Directory of Open Access Journals (Sweden)

Guangyi Wang

2015-01-01

Full Text Available This paper proposes a simple autonomous memristor-based oscillator for generating periodic signals. Applying an external sinusoidal excitation to the autonomous system, a nonautonomous oscillator is obtained, which contains HP memristor model and four linear circuit elements. This memristor-based oscillator can generate periodic, chaotic, and hyperchaotic signals under the periodic excitation and an appropriate set of circuit parameters. It also shows that the system exhibits alternately a hidden attractor with no equilibrium and a self-excited attractor with a line equilibrium as time goes on. Furthermore, some specialties including burst chaos, irregular periodic bifurcations, and nonintermittence chaos of the circuit are found by theoretical analysis and numerical simulations. Finally, a discrete model for the HP memristor is given and the main statistical properties of this memristor-based oscillator are verified via DSP chip experiments and NIST (National Institute of Standards and Technology tests.

Adaptive synchronization of uncertain chaotic colpitts oscillators based on parameter identification

International Nuclear Information System (INIS)

Fotsin, H.B.; Daafouz, J.

2005-01-01

This Letter uses systematic tools from recent papers to design non-linear observers for synchronization of a chaotic colpitts oscillator both in the non adaptive and adaptive cases. It is shown that all parameters of a totally uncertain model of the oscillator can be estimated through adaptive synchronization. A strategy for practical implementation of a secure communication strategy is also discussed

Dynamics of chaotic oscillations in mutually coupled microchip lasers

CERN Document Server

Uchida, A; Kinugawa, S; Yoshimori, S

2003-01-01

We have numerically and experimentally investigated the dynamics of mutually coupled microchip lasers. Chaotic oscillations are observed in the vicinity of the boundary of the injection-locking range when the coupling strength and the difference of the optical frequencies are varied. Synchronization of chaos is always achieved under the condition to generate chaos.

Chaotic synchronization of three coupled oscillators with ring connection

International Nuclear Information System (INIS)

Kyprianidis, I.M.; Stouboulos, I.N.

2003-01-01

We study the evolution of three identical, resistively coupled with ring connection, nonlinear and nonautonomous electric circuits from nonsynchronized oscillations to synchronized ones, when they exhibit chaotic behavior. Phase-locked states are also observed, as the coupling parameter is varied. The system's dynamics depends on the way of coupling (unidirectional or bidirectional)

Chaotic synchronization of three coupled oscillators with ring connection

CERN Document Server

Kyprianidis, I M

2003-01-01

We study the evolution of three identical, resistively coupled with ring connection, nonlinear and nonautonomous electric circuits from nonsynchronized oscillations to synchronized ones, when they exhibit chaotic behavior. Phase-locked states are also observed, as the coupling parameter is varied. The system's dynamics depends on the way of coupling (unidirectional or bidirectional).

Feedback control and adaptive synchronization of chaotic forced Bonhoeffer-van der Pol oscillators

Energy Technology Data Exchange (ETDEWEB)

Kontchou, E W Chimi; Fotsin, H B [Laboratoire d' Electronique, Departement de Physique, Faculte des Sciences, Universite de Dschang, B P 67 Dschang (Cameroon); Woafo, P [Laboratory of Modelling and Simulation in Engineering and Biological Physics, Faculty of Science, University of Yaounde I, Box 812, Yaounde (Cameroon)], E-mail: hbfotsin@yahoo.fr

2008-04-15

This paper deals with chaos control and synchronization in forced Bonhoeffer-van der Pol (FBVP) oscillators. The state equations of the model are first established and the stability is analysed. A feedback control strategy for stabilizing the chaotic dynamics on a periodic orbit of the phase space is investigated. Adaptive synchronization of two FBVP oscillators, based on parameter estimation and a nonlinear observer approach, is also investigated. It appears that a particular unknown parameter of the model can be estimated, which gives the possibility of recovering information through chaotic masking. An application in secure communications is presented.

Feedback control and adaptive synchronization of chaotic forced Bonhoeffer-van der Pol oscillators

International Nuclear Information System (INIS)

Kontchou, E W Chimi; Fotsin, H B; Woafo, P

2008-01-01

This paper deals with chaos control and synchronization in forced Bonhoeffer-van der Pol (FBVP) oscillators. The state equations of the model are first established and the stability is analysed. A feedback control strategy for stabilizing the chaotic dynamics on a periodic orbit of the phase space is investigated. Adaptive synchronization of two FBVP oscillators, based on parameter estimation and a nonlinear observer approach, is also investigated. It appears that a particular unknown parameter of the model can be estimated, which gives the possibility of recovering information through chaotic masking. An application in secure communications is presented

ELMy-H mode as limit cycle and chaotic oscillations in tokamak plasmas

International Nuclear Information System (INIS)

Itoh, Sanae; Itoh, Kimitaka; Fukuyama, Atsushi.

1991-06-01

A model of Edge Localized Modes (ELMs) in tokamaks is presented. A limit cycle solution is found in time-dependent Ginzburg Landau type model equation of L/H transition, which has a hysteresis curve between the plasma gradient and flux. The oscillation of edge density appears near the L/H transition boundary. Spatial structure of the intermediate state (mesophase) is obtained in the edge region. Chaotic oscillation is predicted due to random neutrals and external oscillations. (author)

Output-Feedback Control of a Chaotic MEMS Resonator for Oscillation Amplitude Enhancement

Directory of Open Access Journals (Sweden)

Alexander Jimenez-Triana

2014-01-01

Full Text Available The present work addresses the problem of chaos control in an electrostatic MEMS resonator by using an output-feedback control scheme. One of the unstable orbits immersed in the chaotic attractor is stabilized in order to produce a sustained oscillation of the movable plate composing the microstructure. The orbit is carefully chosen so as to produce a high amplitude oscillation. This approach allows the enhancement of oscillation amplitude of the resonator at a reduced control effort, since the unstable orbit already exists in the system and it is not necessary to spend energy to create it. Realistic operational conditions of the MEMS are considered including parametric uncertainties in the model and constraints due to the difficulty in measuring the speed of the plates of the microstructure. A control law is constructed recursively by using the technique of backstepping. Finally, numerical simulations are carried out to confirm the validity of the developed control scheme and to demonstrate the effect of controlling orbits immersed in the chaotic attractor.

ELMy-H mode as limit cycle and chaotic oscillations in tokamak plasmas

International Nuclear Information System (INIS)

Itoh Sanae, I.; Itoh, Kimitaka; Fukuyama, Atsushi; Miura, Yukitoshi.

1991-05-01

A model of Edge Localized Modes (ELMs) in tokamak plasmas is presented. A limit cycle solution is found in the transport equation (time-dependent Ginzburg-Landau type), which a has hysteresis curve between the gradient and flux. Periodic oscillation of the particle outflux and L/H intermediate state are predicted near the L/H transition boundary. A mesophase in spatial structure appears near edge. Chaotic oscillation is also predicted. (author)

Regular self-oscillating and chaotic behaviour of a PID controlled gimbal suspension gyro

International Nuclear Information System (INIS)

Perez Polo, Manuel F.; Perez Molina, Manuel

2004-01-01

The dynamics of a gyro in gimbal with a PID controller to obtain steady state, self-oscillating and chaotic motion is considered in this paper. The mathematical model of the whole system is deduced from the gyroscope nutation theory and from a feedback control system formed by a PID controller with constrained integral action. The paper shows that the gyro and the associated PID feedback control system have multiple equilibrium points, and from the analysis of a Poincare-Andronov-Hopf bifurcation at the equilibrium points, it is possible to deduce the conditions, which give regular and self-oscillating behaviour. The calculation of the first Lyapunov value is used to predict the motion of the gyro in order to obtain a desired equilibrium point or self-oscillating behaviour. The mechanism of the stability loss of the gyro under small vibrations of the gyro platform and the appearance of chaotic motion is also presented. Numerical simulations are performed to verify the analytical results

Least Squares Shadowing sensitivity analysis of chaotic limit cycle oscillations

Energy Technology Data Exchange (ETDEWEB)

Wang, Qiqi, E-mail: qiqi@mit.edu; Hu, Rui, E-mail: hurui@mit.edu; Blonigan, Patrick, E-mail: blonigan@mit.edu

2014-06-15

The adjoint method, among other sensitivity analysis methods, can fail in chaotic dynamical systems. The result from these methods can be too large, often by orders of magnitude, when the result is the derivative of a long time averaged quantity. This failure is known to be caused by ill-conditioned initial value problems. This paper overcomes this failure by replacing the initial value problem with the well-conditioned “least squares shadowing (LSS) problem”. The LSS problem is then linearized in our sensitivity analysis algorithm, which computes a derivative that converges to the derivative of the infinitely long time average. We demonstrate our algorithm in several dynamical systems exhibiting both periodic and chaotic oscillations.

Atypical transistor-based chaotic oscillators: Design, realization, and diversity

Science.gov (United States)

Minati, Ludovico; Frasca, Mattia; OświÈ©cimka, Paweł; Faes, Luca; DroŻdŻ, Stanisław

2017-07-01

In this paper, we show that novel autonomous chaotic oscillators based on one or two bipolar junction transistors and a limited number of passive components can be obtained via random search with suitable heuristics. Chaos is a pervasive occurrence in these circuits, particularly after manual adjustment of a variable resistor placed in series with the supply voltage source. Following this approach, 49 unique circuits generating chaotic signals when physically realized were designed, representing the largest collection of circuits of this kind to date. These circuits are atypical as they do not trivially map onto known topologies or variations thereof. They feature diverse spectra and predominantly anti-persistent monofractal dynamics. Notably, we recurrently found a circuit comprising one resistor, one transistor, two inductors, and one capacitor, which generates a range of attractors depending on the parameter values. We also found a circuit yielding an irregular quantized spike-train resembling some aspects of neural discharge and another one generating a double-scroll attractor, which represent the smallest known transistor-based embodiments of these behaviors. Through three representative examples, we additionally show that diffusive coupling of heterogeneous oscillators of this kind may give rise to complex entrainment, such as lag synchronization with directed information transfer and generalized synchronization. The replicability and reproducibility of the experimental findings are good.

Impact of hyperbolicity on chimera states in ensembles of nonlocally coupled chaotic oscillators

Energy Technology Data Exchange (ETDEWEB)

Semenova, N.; Anishchenko, V. [Department of Physics, Saratov State University, Astrakhanskaya Str. 83, 410012 Saratov (Russian Federation); Zakharova, A.; Schöll, E. [Institut für Theoretische Physik, TU Berlin, Hardenbergstraße 36, 10623 Berlin (Germany)

2016-06-08

In this work we analyse nonlocally coupled networks of identical chaotic oscillators. We study both time-discrete and time-continuous systems (Henon map, Lozi map, Lorenz system). We hypothesize that chimera states, in which spatial domains of coherent (synchronous) and incoherent (desynchronized) dynamics coexist, can be obtained only in networks of chaotic non-hyperbolic systems and cannot be found in networks of hyperbolic systems. This hypothesis is supported by numerical simulations for hyperbolic and non-hyperbolic cases.

Acoustically levitated dancing drops: Self-excited oscillation to chaotic shedding

Science.gov (United States)

Lin, Po-Cheng; I, Lin

2016-02-01

We experimentally demonstrate self-excited oscillation and shedding of millimeter-sized water drops, acoustically levitated in a single-node standing waves cavity, by decreasing the steady acoustic wave intensity below a threshold. The perturbation of the acoustic field by drop motion is a possible source for providing an effective negative damping for sustaining the growing amplitude of the self-excited motion. Its further interplay with surface tension, drop inertia, gravity and acoustic intensities, select various self-excited modes for different size of drops and acoustic intensity. The large drop exhibits quasiperiodic motion from a vertical mode and a zonal mode with growing coupling, as oscillation amplitudes grow, until falling on the floor. For small drops, chaotic oscillations constituted by several broadened sectorial modes and corresponding zonal modes are self-excited. The growing oscillation amplitude leads to droplet shedding from the edges of highly stretched lobes, where surface tension no longer holds the rapid expanding flow.

Chaotic behavior in Casimir oscillators: A case study for phase-change materials.

Science.gov (United States)

Tajik, Fatemeh; Sedighi, Mehdi; Khorrami, Mohammad; Masoudi, Amir Ali; Palasantzas, George

2017-10-01

Casimir forces between material surfaces at close proximity of less than 200 nm can lead to increased chaotic behavior of actuating devices depending on the strength of the Casimir interaction. We investigate these phenomena for phase-change materials in torsional oscillators, where the amorphous to crystalline phase transitions lead to transitions between high and low Casimir force and torque states, respectively, without material compositions. For a conservative system bifurcation curve and Poincare maps analysis show the absence of chaotic behavior but with the crystalline phase (high force-torque state) favoring more unstable behavior and stiction. However, for a nonconservative system chaotic behavior can take place introducing significant risk for stiction, which is again more pronounced for the crystalline phase. The latter illustrates the more general scenario that stronger Casimir forces and torques increase the possibility for chaotic behavior. The latter is making it impossible to predict whether stiction or stable actuation will occur on a long-term basis, and it is setting limitations in the design of micronano devices operating at short-range nanoscale separations.

Chaotic oscillation and random-number generation based on nanoscale optical-energy transfer.

Science.gov (United States)

Naruse, Makoto; Kim, Song-Ju; Aono, Masashi; Hori, Hirokazu; Ohtsu, Motoichi

2014-08-12

By using nanoscale energy-transfer dynamics and density matrix formalism, we demonstrate theoretically and numerically that chaotic oscillation and random-number generation occur in a nanoscale system. The physical system consists of a pair of quantum dots (QDs), with one QD smaller than the other, between which energy transfers via optical near-field interactions. When the system is pumped by continuous-wave radiation and incorporates a timing delay between two energy transfers within the system, it emits optical pulses. We refer to such QD pairs as nano-optical pulsers (NOPs). Irradiating an NOP with external periodic optical pulses causes the oscillating frequency of the NOP to synchronize with the external stimulus. We find that chaotic oscillation occurs in the NOP population when they are connected by an external time delay. Moreover, by evaluating the time-domain signals by statistical-test suites, we confirm that the signals are sufficiently random to qualify the system as a random-number generator (RNG). This study reveals that even relatively simple nanodevices that interact locally with each other through optical energy transfer at scales far below the wavelength of irradiating light can exhibit complex oscillatory dynamics. These findings are significant for applications such as ultrasmall RNGs.

Numerical study of chaotic oscillations in the electron beam with virtual cathode in the external non-uniform magnetic fields

Energy Technology Data Exchange (ETDEWEB)

Hramov, Alexander E., E-mail: aeh@nonlin.sgu.r [Faculty of Nonlinear Processes, Saratov State University, 83, Astrakhanskaya, Saratov, 410012 (Russian Federation); Koronovskii, Alexey A., E-mail: alkor@nonlin.sgu.r [Faculty of Nonlinear Processes, Saratov State University, 83, Astrakhanskaya, Saratov, 410012 (Russian Federation); Kurkin, Semen, E-mail: KurkinSA@nonlin.sgu.r [Faculty of Nonlinear Processes, Saratov State University, 83, Astrakhanskaya, Saratov, 410012 (Russian Federation)

2010-07-05

In this Letter the results of theoretical investigations of the chaotic microwave oscillator based on the electron beam with a virtual cathode are presented. Nonlinear non-stationary processes in these electron systems are studied by means of numerical analysis of 2.5D model. It was discovered that the non-uniform external magnetic field value controls the dynamical regime of oscillations in the virtual cathode oscillator. The processes of the chaotization of output microwave radiation are described and interpreted from the point of view of the formation and interaction of electron structures (bunches) in the electron beams. The numerical results have shown that the investigated electron system with virtual cathode could be considered as a promising controlled source of wideband chaotic oscillations in the microwave range.

Chaotic phase oscillation of a proton beam in a synchrotron

International Nuclear Information System (INIS)

Li Fei; Hai Wenhua; Ren Zhongzhou; Shu Weixing

2006-01-01

We investigate the chaotic phase oscillation of a proton beam in a cooler synchrotron. By using direct perturbation method, we construct the general solution of the 1st-order equation. It is demonstrated that the general solution is bounded under some initial and parameter conditions. From these conditions, we get a Melnikov function which predicts the existence of Smale-horseshoe chaos iff it has simple zeros. Our result under the 1st-order approximation is in good agreement with that in [H. Huang et al., Phys. Rev. E 48 (1993) 4678]. When the perturbation method is not suitable for the system, numerical simulation shows the system may present transient chaos before it goes into periodical oscillation; changing the damping parameter can result in or suppress stationary chaos

Modulation response, mixed-mode oscillations and chaotic spiking in quantum dot light emitting diode

International Nuclear Information System (INIS)

Al Husseini, Hussein B.; Al Naimee, Kais A.; Al Khursan, Amin H.; Abdalah, Sora F.; Khedir, Ali H.; Meucci, Riccardo; Arecchi, F. Tito

2015-01-01

In this work quantum dot light emitting diode (QD-LED) was modeled in a dimensionless rate equations system where it is not done earlier. The model was examined first under bias current without any external perturbation where it exhibits chaotic phenomena since the model has multi-degrees of freedom. Then, it is perturbed by both small signal and direct current modulations (DCM), separately. The system exhibits mixed-mode oscillations (MMOs) under DCM. This behavior was reasoned to continuous states of two dimensional wetting layer (WL) which works as a reservoir to quantum dot (QD) states. QD capture was the dominant rate controlling the dynamic behavior in QD-LED. The nonlinear dynamic behavior of our model is compared very well to the experimental observations in the QD-LED

Chaotic oscillations in a low pressure two-phase natural circulation loop under low power and high inlet subcooling conditions

International Nuclear Information System (INIS)

Wu, C.Y.; Wang, S.B.; Pan, C.

1996-01-01

The oscillation characteristics of a low pressure two-phase natural circulation loop have been investigated experimentally in this study. Experimental results indicate that the characteristics of the thermal hydraulic oscillations can be periodic, with 2-5 fundamental frequencies, or chaotic, depending on the heating power and inlet subcooling. The number of fundamental frequencies of oscillation increases if the inlet subcooling is increased at a given heating power or the heating power is decreased at a given inlet subcooling; chaotic oscillations appear if the inlet subcooling is further increased and/or the heating power is further decreased. A map of the oscillation characteristics is thus established. The change in oscillation characteristics is evident from the time evolution and power spectrum of a thermal hydraulic parameter and the phase portraits of two thermal hydraulic parameters. These results reveal that a strange attractor exists in a low pressure two-phase natural circulation loop with low power and very high inlet subcooling. (orig.)

Time delay induced different synchronization patterns in repulsively coupled chaotic oscillators

Science.gov (United States)

Yao, Chenggui; Yi, Ming; Shuai, Jianwei

2013-09-01

Time delayed coupling plays a crucial role in determining the system's dynamics. We here report that the time delay induces transition from the asynchronous state to the complete synchronization (CS) state in the repulsively coupled chaotic oscillators. In particular, by changing the coupling strength or time delay, various types of synchronous patterns, including CS, antiphase CS, antiphase synchronization (ANS), and phase synchronization, can be generated. In the transition regions between different synchronous patterns, bistable synchronous oscillators can be observed. Furthermore, we show that the time-delay-induced phase flip bifurcation is of key importance for the emergence of CS. All these findings may light on our understanding of neuronal synchronization and information processing in the brain.

Chaotic itinerancy within the coupled dynamics between a physical body and neural oscillator networks.

Science.gov (United States)

Park, Jihoon; Mori, Hiroki; Okuyama, Yuji; Asada, Minoru

2017-01-01

Chaotic itinerancy is a phenomenon in which the state of a nonlinear dynamical system spontaneously explores and attracts certain states in a state space. From this perspective, the diverse behavior of animals and its spontaneous transitions lead to a complex coupled dynamical system, including a physical body and a brain. Herein, a series of simulations using different types of non-linear oscillator networks (i.e., regular, small-world, scale-free, random) with a musculoskeletal model (i.e., a snake-like robot) as a physical body are conducted to understand how the chaotic itinerancy of bodily behavior emerges from the coupled dynamics between the body and the brain. A behavior analysis (behavior clustering) and network analysis for the classified behavior are then applied. The former consists of feature vector extraction from the motions and classification of the movement patterns that emerged from the coupled dynamics. The network structures behind the classified movement patterns are revealed by estimating the "information networks" different from the given non-linear oscillator networks based on the transfer entropy which finds the information flow among neurons. The experimental results show that: (1) the number of movement patterns and their duration depend on the sensor ratio to control the balance of strength between the body and the brain dynamics and on the type of the given non-linear oscillator networks; and (2) two kinds of information networks are found behind two kinds movement patterns with different durations by utilizing the complex network measures, clustering coefficient and the shortest path length with a negative and a positive relationship with the duration periods of movement patterns. The current results seem promising for a future extension of the method to a more complicated body and environment. Several requirements are also discussed.

Chaotic itinerancy within the coupled dynamics between a physical body and neural oscillator networks.

Directory of Open Access Journals (Sweden)

Jihoon Park

Full Text Available Chaotic itinerancy is a phenomenon in which the state of a nonlinear dynamical system spontaneously explores and attracts certain states in a state space. From this perspective, the diverse behavior of animals and its spontaneous transitions lead to a complex coupled dynamical system, including a physical body and a brain. Herein, a series of simulations using different types of non-linear oscillator networks (i.e., regular, small-world, scale-free, random with a musculoskeletal model (i.e., a snake-like robot as a physical body are conducted to understand how the chaotic itinerancy of bodily behavior emerges from the coupled dynamics between the body and the brain. A behavior analysis (behavior clustering and network analysis for the classified behavior are then applied. The former consists of feature vector extraction from the motions and classification of the movement patterns that emerged from the coupled dynamics. The network structures behind the classified movement patterns are revealed by estimating the "information networks" different from the given non-linear oscillator networks based on the transfer entropy which finds the information flow among neurons. The experimental results show that: (1 the number of movement patterns and their duration depend on the sensor ratio to control the balance of strength between the body and the brain dynamics and on the type of the given non-linear oscillator networks; and (2 two kinds of information networks are found behind two kinds movement patterns with different durations by utilizing the complex network measures, clustering coefficient and the shortest path length with a negative and a positive relationship with the duration periods of movement patterns. The current results seem promising for a future extension of the method to a more complicated body and environment. Several requirements are also discussed.

Synchronisation phenomenon in three blades rotor driven by regular or chaotic oscillations

Directory of Open Access Journals (Sweden)

Szmit Zofia

2018-01-01

Full Text Available The goal of the paper is to analysed the influence of the different types of excitation on the synchronisation phenomenon in case of the rotating system composed of a rigid hub and three flexible composite beams. In the model is assumed that two blades, due to structural differences, are de-tuned. Numerical calculation are divided on two parts, firstly the rotating system is exited by a torque given by regular harmonic function, than in the second part the torque is produced by chaotic Duffing oscillator. The synchronisation phenomenon between the beams is analysed both either for regular or chaotic motions. Partial differential equations of motion are solved numerically and resonance curves, time series and Poincaré maps are presented for selected excitation torques.

Driving-induced multistability in coupled chaotic oscillators: Symmetries and riddled basins

Energy Technology Data Exchange (ETDEWEB)

Ujjwal, Sangeeta Rani; Ramaswamy, Ram [School of Physical Sciences, Jawaharlal Nehru University, New Delhi 110067 (India); Punetha, Nirmal; Prasad, Awadhesh [Department of Physics and Astrophysics, University of Delhi, Delhi 110007 (India); Agrawal, Manish [Department of Physics, Sri Aurobindo College, University of Delhi, New Delhi 110017 (India)

2016-06-15

We study the multistability that results when a chaotic response system that has an invariant symmetry is driven by another chaotic oscillator. We observe that there is a transition from a desynchronized state to a situation of multistability. In the case considered, there are three coexisting attractors, two of which are synchronized and one is desynchronized. For large coupling, the asynchronous attractor disappears, leaving the system bistable. We study the basins of attraction of the system in the regime of multistability. The three attractor basins are interwoven in a complex manner, with extensive riddling within a sizeable region of (but not the entire) phase space. A quantitative characterization of the riddling behavior is made via the so–called uncertainty exponent, as well as by evaluating the scaling behavior of tongue–like structures emanating from the synchronization manifold.

On the New Scenario of Annihilation of the Cross-Well Chaotic Attractor in a Nonlinear Oscillator

International Nuclear Information System (INIS)

Szemplinska, W.; Zubrzycki, A.; Tyrkiel, E.

1999-01-01

The twin-well potential Duffing oscillator is considered and the investigations are focused on a new scenario of destruction of the cross-well chaotic attractor. The new phenomenon belongs to the category of subduction bifurcation and consists in replacement of the cross-well chaotic attractor by a pair of unsymmetric 2T-periodic attractors. It is shown that the new scenario forms a transition zone in the system control parameter plane, the zone, which separates the two known scenarios of annihilation of the cross-well chaotic attractor: the boundary crisis, and the subduction in which the two single-well T-periodic attractors are born in a saddle-node bifurcation. (author)

Control of chaotic oscillators via a class of model free active controller: Suppresion and synchronization

Energy Technology Data Exchange (ETDEWEB)

Aguilar-Lopez, Ricardo [Division de Ciencias Basicas e Ingenieria, Universidad Autonoma Metropolitana, Av. San Pablo No. 180, Reynosa-Tamaulipas, 02200, Azcapotzalco, Mexico D.F. (Mexico)], E-mail: raguilar@correo.azc.uam.mx; Martinez-Guerra, Rafael [Departamento de Control Automatico, CINVESTAV-IPN, Apartado Postal 14-740, 07360 Mexico D.F. (Mexico)], E-mail: rguerra@ctrl.cinvestav.mx

2008-10-15

The goal of this work is related with the control of chaotic oscillators for chaos suppression and synchronization purposes. The proposed methodology is related with a class of robust active control (RAC) law, where the stabilizing part of the control structure is related with an integral high order sliding-mode and proportional form of the so-called control error. The proposed controller is applied to chaos suppression, synchronization and anti-synchronization tasks for nonlinear oscillators with different order and structure. Numerical experiments illustrate the satisfactory performance of the proposed methodology, when it is applied to Duffing and Chen oscillators.

Control of chaotic oscillators via a class of model free active controller: Suppresion and synchronization

International Nuclear Information System (INIS)

Aguilar-Lopez, Ricardo; Martinez-Guerra, Rafael

2008-01-01

The goal of this work is related with the control of chaotic oscillators for chaos suppression and synchronization purposes. The proposed methodology is related with a class of robust active control (RAC) law, where the stabilizing part of the control structure is related with an integral high order sliding-mode and proportional form of the so-called control error. The proposed controller is applied to chaos suppression, synchronization and anti-synchronization tasks for nonlinear oscillators with different order and structure. Numerical experiments illustrate the satisfactory performance of the proposed methodology, when it is applied to Duffing and Chen oscillators

A Data Gathering Scheme in Wireless Sensor Networks Based on Synchronization of Chaotic Spiking Oscillator Networks

International Nuclear Information System (INIS)

Nakano, Hidehiro; Utani, Akihide; Miyauchi, Arata; Yamamoto, Hisao

2011-01-01

This paper studies chaos-based data gathering scheme in multiple sink wireless sensor networks. In the proposed scheme, each wireless sensor node has a simple chaotic oscillator. The oscillators generate spike signals with chaotic interspike intervals, and are impulsively coupled by the signals via wireless communication. Each wireless sensor node transmits and receives sensor information only in the timing of the couplings. The proposed scheme can exhibit various chaos synchronous phenomena and their breakdown phenomena, and can effectively gather sensor information with the significantly small number of transmissions and receptions compared with the conventional scheme. Also, the proposed scheme can flexibly adapt various wireless sensor networks not only with a single sink node but also with multiple sink nodes. This paper introduces our previous works. Through simulation experiments, we show effectiveness of the proposed scheme and discuss its development potential.

Mixed synchronization in chaotic oscillators using scalar coupling

Energy Technology Data Exchange (ETDEWEB)

Bhowmick, Sourav K.; Hens, Chittaranjan [CSIR – Indian Institute of Chemical Biology, Jadavpur, Kolkata 700032 (India); Ghosh, Dibakar, E-mail: drghosh_math@yahoo.co.in [Department of Mathematics, University of Kalyani, West Bengal 741235 (India); Dana, Syamal K. [CSIR – Indian Institute of Chemical Biology, Jadavpur, Kolkata 700032 (India)

2012-07-23

We report experimental evidence of mixed synchronization in two unidirectionally coupled chaotic oscillators using a scalar coupling. In this synchronization regime, some of the state variables may be in complete synchronization while others may be in anti-synchronization state. We extended the theory by using an adaptive controller with an updating law based on Lyapunov function stability to include parameter fluctuation. Using the scheme, we implemented a cryptographic encoding for digital signal through parameter modulation. -- Highlights: ► We provided experimental evidence of the mixed synchronization scheme while other methods are mostly theoretical nature. ► We numerically studied adaptive mixed synchronization when the parameters are not completely known using scalar coupling. ► We proposed a secure communication system where three digital messages are transmitted using parameter modulation.

Quantum-chaotic cryptography

Science.gov (United States)

de Oliveira, G. L.; Ramos, R. V.

2018-03-01

In this work, it is presented an optical scheme for quantum key distribution employing two synchronized optoelectronic oscillators (OEO) working in the chaotic regime. The produced key depends on the chaotic dynamic, and the synchronization between Alice's and Bob's OEOs uses quantum states. An attack on the synchronization signals will disturb the synchronization of the chaotic systems increasing the error rate in the final key.

Analysis of bus width and delay on a fully digital signum nonlinearity chaotic oscillator

KAUST Repository

Mansingka, Abhinav S.; Radwan, Ahmed G.; Salama, Khaled N.; Zidan, Mohammed A.

2012-01-01

This paper introduces the first fully digital implementation of a 3rd order ODE-based chaotic oscillator with signum nonlinearity. A threshold bus width of 12-bits for reliable chaotic behavior is observed, below which the system output becomes periodic. Beyond this threshold, the maximum Lyapunov exponent (MLE) is shown to improve up to a peak value at 16-bits and subsequently decrease with increasing bus width. The MLE is also shown to gradually increase with number of introduced internal delay cycles until a peak value at 14 cycles, after which the system loses chaotic properties. Introduced external delay cycles are shown to rotate the attractors in 3-D phase space. Bus width and delay elements can be independently modulated to optimize the system to suit specifications. The experimental results of the system show low area and high performance on a Xilinx Virtex 4 FPGA with throughput of 13.35 Gbits/s for a 32-bit implementation.

Analysis of bus width and delay on a fully digital signum nonlinearity chaotic oscillator

KAUST Repository

Mansingka, Abhinav S.

2012-07-29

This paper introduces the first fully digital implementation of a 3rd order ODE-based chaotic oscillator with signum nonlinearity. A threshold bus width of 12-bits for reliable chaotic behavior is observed, below which the system output becomes periodic. Beyond this threshold, the maximum Lyapunov exponent (MLE) is shown to improve up to a peak value at 16-bits and subsequently decrease with increasing bus width. The MLE is also shown to gradually increase with number of introduced internal delay cycles until a peak value at 14 cycles, after which the system loses chaotic properties. Introduced external delay cycles are shown to rotate the attractors in 3-D phase space. Bus width and delay elements can be independently modulated to optimize the system to suit specifications. The experimental results of the system show low area and high performance on a Xilinx Virtex 4 FPGA with throughput of 13.35 Gbits/s for a 32-bit implementation.

Partial synchronization of different chaotic oscillators using robust PID feedback

Energy Technology Data Exchange (ETDEWEB)

Aguilar-Lopez, Ricardo [Departamento de Energia, Universidad Autonoma Metropolitana - Azcapotzalco, San Pablo 180, Reynosa-Tamaulipas, Azcapotzalco, 02200 Mexico, D.F. (Mexico)]. E-mail: raguilar@correo.azc.uam.mx; Martinez-Guerra, Rafael [Departamento de Control Automatico, CINVESTAV IPN, Apartado Postal 14-740, Mexico, D.F. C.P. 07360 (Mexico)]. E-mail: rguerra@ctrl.cinvestav.mx

2007-07-15

This work deals with the partial synchronization problem of two different chaotic oscillators considering model uncertainties in the slave system via control approach. The slave system is forced to follow the master signal via a linearizing controller based on model uncertainty reconstructor which leads to proportional-integral-derivative (PID) control structure. This reconstructor is related with a proportional-derivative (PD) reduced-order observer, it would be considered as a sub-slave system for the original slave of the synchronization procedure. The asymptotic performance of the synchronization methodology is proven via the dynamic of the synchronization error. Numerical experiment illustrates the closed-loop behavior of the proposed methodology.

Partial synchronization of different chaotic oscillators using robust PID feedback

International Nuclear Information System (INIS)

Aguilar-Lopez, Ricardo; Martinez-Guerra, Rafael

2007-01-01

This work deals with the partial synchronization problem of two different chaotic oscillators considering model uncertainties in the slave system via control approach. The slave system is forced to follow the master signal via a linearizing controller based on model uncertainty reconstructor which leads to proportional-integral-derivative (PID) control structure. This reconstructor is related with a proportional-derivative (PD) reduced-order observer, it would be considered as a sub-slave system for the original slave of the synchronization procedure. The asymptotic performance of the synchronization methodology is proven via the dynamic of the synchronization error. Numerical experiment illustrates the closed-loop behavior of the proposed methodology

Current oscillations in avalanche particle detectors with PNIPN-structure

International Nuclear Information System (INIS)

Lukin, K.A.

1995-08-01

The model of an avalanche high energy particle detector consisting of two pn-junctions, connected through an intrinsic semiconductor with a reverse biased voltage applied. This detector is able to generate the oscillatory response on the single particle passage through the structure. The possibility of oscillations leading to chaotic behaviour is pointed out

Quorum Sensing in Populations of Spatially Extended Chaotic Oscillators Coupled Indirectly via a Heterogeneous Environment

Science.gov (United States)

Li, Bing-Wei; Cao, Xiao-Zhi; Fu, Chenbo

2017-12-01

Many biological and chemical systems could be modeled by a population of oscillators coupled indirectly via a dynamical environment. Essentially, the environment by which the individual element communicates with each other is heterogeneous. Nevertheless, most of previous works considered the homogeneous case only. Here we investigated the dynamical behaviors in a population of spatially distributed chaotic oscillators immersed in a heterogeneous environment. Various dynamical synchronization states (such as oscillation death, phase synchronization, and complete synchronized oscillation) as well as their transitions were explored. In particular, we uncovered a non-traditional quorum sensing transition: increasing the population density leaded to a transition from oscillation death to synchronized oscillation at first, but further increasing the density resulted in degeneration from complete synchronization to phase synchronization or even from phase synchronization to desynchronization. The underlying mechanism of this finding was attributed to the dual roles played by the population density. What's more, by treating the environment as another component of the oscillator, the full system was then effectively equivalent to a locally coupled system. This fact allowed us to utilize the master stability functions approach to predict the occurrence of complete synchronization oscillation, which agreed with that from the direct numerical integration of the system. The potential candidates for the experimental realization of our model were also discussed.

New Chaotic Dynamical System with a Conic-Shaped Equilibrium Located on the Plane Structure

Directory of Open Access Journals (Sweden)

Jiri Petrzela

2017-09-01

Full Text Available This paper presents a new autonomous deterministic dynamical system with equilibrium degenerated into a plane-oriented hyperbolic geometrical structure. It is demonstrated via numerical analysis and laboratory experiments that the discovered system has both a structurally stable strange attractor and experimentally measurable chaotic behavior. It is shown that the evolution of complex dynamics can be associated with a single parameter of a mathematical model and, due to one-to-one correspondence, to a single circuit parameter. Two-dimensional high resolution plots of the largest Lyapunov exponent and basins of attraction expressed in terms of final state energy are calculated and put into the context of the discovered third-order mathematical model and real chaotic oscillator. Both voltage- and current-mode analog chaotic oscillators are presented and verified by visualization of the typical chaotic attractor in a different fashion.

Chaotic dynamics in nanoscale NbO2 Mott memristors for analogue computing

Science.gov (United States)

Kumar, Suhas; Strachan, John Paul; Williams, R. Stanley

2017-08-01

At present, machine learning systems use simplified neuron models that lack the rich nonlinear phenomena observed in biological systems, which display spatio-temporal cooperative dynamics. There is evidence that neurons operate in a regime called the edge of chaos that may be central to complexity, learning efficiency, adaptability and analogue (non-Boolean) computation in brains. Neural networks have exhibited enhanced computational complexity when operated at the edge of chaos, and networks of chaotic elements have been proposed for solving combinatorial or global optimization problems. Thus, a source of controllable chaotic behaviour that can be incorporated into a neural-inspired circuit may be an essential component of future computational systems. Such chaotic elements have been simulated using elaborate transistor circuits that simulate known equations of chaos, but an experimental realization of chaotic dynamics from a single scalable electronic device has been lacking. Here we describe niobium dioxide (NbO2) Mott memristors each less than 100 nanometres across that exhibit both a nonlinear-transport-driven current-controlled negative differential resistance and a Mott-transition-driven temperature-controlled negative differential resistance. Mott materials have a temperature-dependent metal-insulator transition that acts as an electronic switch, which introduces a history-dependent resistance into the device. We incorporate these memristors into a relaxation oscillator and observe a tunable range of periodic and chaotic self-oscillations. We show that the nonlinear current transport coupled with thermal fluctuations at the nanoscale generates chaotic oscillations. Such memristors could be useful in certain types of neural-inspired computation by introducing a pseudo-random signal that prevents global synchronization and could also assist in finding a global minimum during a constrained search. We specifically demonstrate that incorporating such

Intermittent chaotic chimeras for coupled rotators

DEFF Research Database (Denmark)

Olmi, Simona; Martens, Erik Andreas; Thutupalli, Shashi

2015-01-01

Two symmetrically coupled populations of N oscillators with inertia m display chaotic solutions with broken symmetry similar to experimental observations with mechanical pendulums. In particular, we report evidence of intermittent chaotic chimeras, where one population is synchronized and the other...

Does the classically chaotic Henon–Heiles oscillator exhibit ...

Indian Academy of Sciences (India)

–12]. In contrast to a classically chaotic system, where the exponential divergence of trajectories in phase-space is an unambiguous and confirmatory signature of chaos. [15–17], the decision about whether a quantum system is chaotic or not is ...

Mixed-mode chaotic circuit with Wien-bridge configuration: The results of experimental verification

International Nuclear Information System (INIS)

Kilic, Recai

2007-01-01

In this paper, we deal with the experimentally implementation of inductorless Wien bridge-based mixed-mode chaotic circuit (MMCC) which is capable to exhibit both linear and nonlinear oscillations. The results of experimental implementation agree with the results of theoretical and computer simulation presented in literature. Since the proposed implementation of MMCC circuit uses different design blocks such as Wien bridge-based autonomous circuit part, CFOA (current feedback operational amplifier)-based floating inductance simulator, CFOA-based Chua's diode and switching mechanism, it offers very versatile chaotic circuit model for studying autonomous and nonautonomous chaotic dynamics

Encryption in Chaotic Systems with Sinusoidal Excitations

Directory of Open Access Journals (Sweden)

G. Obregón-Pulido

2014-01-01

Full Text Available In this contribution an encryption method using a chaotic oscillator, excited by “n” sinusoidal signals, is presented. The chaotic oscillator is excited by a sum of “n” sinusoidal signals and a message. The objective is to encrypt such a message using the chaotic behavior and transmit it, and, as the chaotic system is perturbed by the sinusoidal signal, the transmission security could be increased due to the effect of such a perturbation. The procedure is based on the regulation theory and consider that the receiver knows the frequencies of the perturbing signal, with this considerations the algorithm estimates the excitation in such a way that the receiver can cancel out the perturbation and all the undesirable dynamics in order to produce only the message. In this way we consider that the security level is increased.

Regular and chaotic dynamics in time-dependent relativistic mean-field theory

International Nuclear Information System (INIS)

Vretenar, D.; Ring, P.; Lalazissis, G.A.; Poeschl, W.

1997-01-01

Isoscalar and isovector monopole oscillations that correspond to giant resonances in spherical nuclei are described in the framework of time-dependent relativistic mean-field theory. Time-dependent and self-consistent calculations that reproduce experimental data on monopole resonances in 208 Pb show that the motion of the collective coordinate is regular for isoscalar oscillations, and that it becomes chaotic when initial conditions correspond to the isovector mode. Regular collective dynamics coexists with chaotic oscillations on the microscopic level. Time histories, Fourier spectra, state-space plots, Poincare sections, autocorrelation functions, and Lyapunov exponents are used to characterize the nonlinear system and to identify chaotic oscillations. Analogous considerations apply to higher multipolarities. copyright 1997 The American Physical Society

Synchronization of hyperchaotic oscillators

DEFF Research Database (Denmark)

Tamasevicius, A.; Cenys, A.; Mykolaitis, G.

1997-01-01

Synchronization of chaotic oscillators is believed to have promising applications in secure communications. Hyperchaotic systems with multiple positive Lyapunov exponents (LEs) have an advantage over common chaotic systems with only one positive LE. Three different types of hyperchaotic electronic...... oscillators are investigated demonstrating synchronization by means of only one properly selected variable....

Design of optimised backstepping controller for the synchronisation of chaotic Colpitts oscillator using shark smell algorithm

Science.gov (United States)

Fouladi, Ehsan; Mojallali, Hamed

2018-01-01

In this paper, an adaptive backstepping controller has been tuned to synchronise two chaotic Colpitts oscillators in a master-slave configuration. The parameters of the controller are determined using shark smell optimisation (SSO) algorithm. Numerical results are presented and compared with those of particle swarm optimisation (PSO) algorithm. Simulation results show better performance in terms of accuracy and convergence for the proposed optimised method compared to PSO optimised controller or any non-optimised backstepping controller.

Generation and control of multi-scroll chaotic attractors in fractional order systems

International Nuclear Information System (INIS)

Ahmad, Wajdi M.

2005-01-01

The objective of this paper is twofold: on one hand we demonstrate the generation of multi-scroll attractors in fractional order chaotic systems. Then, we design state feedback controllers to eliminate chaos from the system trajectories. It is demonstrated that modifying the underlying nonlinearity of the fractional chaotic system results in the birth of multiple chaotic attractors, thus forming the so called multi-scroll attractors. The presence of chaotic behavior is evidenced by a positive largest Lyapunov exponent computed for the output time series. We investigate generation and control of multi-scroll attractors in two different models, both of which are fractional order and chaotic: an electronic oscillator, and a mechanical 'jerk' model. The current findings extend previously reported results on generation of n-scroll attractors from the domain of integer order to the domain of fractional order chaotic systems, and addresses the issue of controlling such chaotic behaviors. Our investigations are validated through numerical simulations

Mixing enhancement and transport reduction in chaotic advection

OpenAIRE

Benzekri , Tounsia; Chandre , Cristel; Leoncini , Xavier; Lima , Ricardo; Vittot , Michel

2005-01-01

We present a method for reducing chaotic transport in a model of chaotic advection due to time-periodic forcing of an oscillating vortex chain. We show that by a suitable modification of this forcing, the modified model combines two effects: enhancement of mixing within the rolls and suppression of chaotic transport along the channel.

Mixed-mode chaotic circuit with Wien-bridge configuration: The results of experimental verification

Energy Technology Data Exchange (ETDEWEB)

Kilic, Recai [Erciyes University, Department of Electronic Engineering, 38039 Kayseri (Turkey)]. E-mail: kilic@erciyes.edu.tr

2007-05-15

In this paper, we deal with the experimentally implementation of inductorless Wien bridge-based mixed-mode chaotic circuit (MMCC) which is capable to exhibit both linear and nonlinear oscillations. The results of experimental implementation agree with the results of theoretical and computer simulation presented in literature. Since the proposed implementation of MMCC circuit uses different design blocks such as Wien bridge-based autonomous circuit part, CFOA (current feedback operational amplifier)-based floating inductance simulator, CFOA-based Chua's diode and switching mechanism, it offers very versatile chaotic circuit model for studying autonomous and nonautonomous chaotic dynamics.

Quantifying chaotic dynamics from integrate-and-fire processes

Energy Technology Data Exchange (ETDEWEB)

Pavlov, A. N. [Department of Physics, Saratov State University, Astrakhanskaya Str. 83, 410012 Saratov (Russian Federation); Saratov State Technical University, Politehnicheskaya Str. 77, 410054 Saratov (Russian Federation); Pavlova, O. N. [Department of Physics, Saratov State University, Astrakhanskaya Str. 83, 410012 Saratov (Russian Federation); Mohammad, Y. K. [Department of Physics, Saratov State University, Astrakhanskaya Str. 83, 410012 Saratov (Russian Federation); Tikrit University Salahudin, Tikrit Qadisiyah, University Str. P.O. Box 42, Tikrit (Iraq); Kurths, J. [Potsdam Institute for Climate Impact Research, Telegraphenberg A 31, 14473 Potsdam (Germany); Institute of Physics, Humboldt University Berlin, 12489 Berlin (Germany)

2015-01-15

Characterizing chaotic dynamics from integrate-and-fire (IF) interspike intervals (ISIs) is relatively easy performed at high firing rates. When the firing rate is low, a correct estimation of Lyapunov exponents (LEs) describing dynamical features of complex oscillations reflected in the IF ISI sequences becomes more complicated. In this work we discuss peculiarities and limitations of quantifying chaotic dynamics from IF point processes. We consider main factors leading to underestimated LEs and demonstrate a way of improving numerical determining of LEs from IF ISI sequences. We show that estimations of the two largest LEs can be performed using around 400 mean periods of chaotic oscillations in the regime of phase-coherent chaos. Application to real data is discussed.

Synchronization of chaotic systems

International Nuclear Information System (INIS)

Pecora, Louis M.; Carroll, Thomas L.

2015-01-01

We review some of the history and early work in the area of synchronization in chaotic systems. We start with our own discovery of the phenomenon, but go on to establish the historical timeline of this topic back to the earliest known paper. The topic of synchronization of chaotic systems has always been intriguing, since chaotic systems are known to resist synchronization because of their positive Lyapunov exponents. The convergence of the two systems to identical trajectories is a surprise. We show how people originally thought about this process and how the concept of synchronization changed over the years to a more geometric view using synchronization manifolds. We also show that building synchronizing systems leads naturally to engineering more complex systems whose constituents are chaotic, but which can be tuned to output various chaotic signals. We finally end up at a topic that is still in very active exploration today and that is synchronization of dynamical systems in networks of oscillators

Analytically solvable chaotic oscillator based on a first-order filter

Energy Technology Data Exchange (ETDEWEB)

Corron, Ned J.; Cooper, Roy M.; Blakely, Jonathan N. [Charles M. Bowden Laboratory, Aviation and Missile Research, Development and Engineering Center, U.S. Army RDECOM, Redstone Arsenal, Alabama 35898 (United States)

2016-02-15

A chaotic hybrid dynamical system is introduced and its analytic solution is derived. The system is described as an unstable first order filter subject to occasional switching of a set point according to a feedback rule. The system qualitatively differs from other recently studied solvable chaotic hybrid systems in that the timing of the switching is regulated by an external clock. The chaotic analytic solution is an optimal waveform for communications in noise when a resistor-capacitor-integrate-and-dump filter is used as a receiver. As such, these results provide evidence in support of a recent conjecture that the optimal communication waveform for any stable infinite-impulse response filter is chaotic.

Restoration of oscillation in network of oscillators in presence of direct and indirect interactions

Energy Technology Data Exchange (ETDEWEB)

Majhi, Soumen; Bera, Bidesh K. [Physics and Applied Mathematics Unit, Indian Statistical Institute, Kolkata-700108 (India); Bhowmick, Sourav K. [Department of Electronics, Asutosh College, Kolkata-700026 (India); Ghosh, Dibakar, E-mail: diba.ghosh@gmail.com [Physics and Applied Mathematics Unit, Indian Statistical Institute, Kolkata-700108 (India)

2016-10-23

The suppression of oscillations in coupled systems may lead to several unwanted situations, which requires a suitable treatment to overcome the suppression. In this paper, we show that the environmental coupling in the presence of direct interaction, which can suppress oscillation even in a network of identical oscillators, can be modified by introducing a feedback factor in the coupling scheme in order to restore the oscillation. We inspect how the introduction of the feedback factor helps to resurrect oscillation from various kinds of death states. We numerically verify the resurrection of oscillations for two paradigmatic limit cycle systems, namely Landau–Stuart and Van der Pol oscillators and also in generic chaotic Lorenz oscillator. We also study the effect of parameter mismatch in the process of restoring oscillation for coupled oscillators. - Highlights: • Amplitude death is observed using direct and indirect coupling. • Revival of oscillation using feedback parameter is discussed. • Restoration of oscillation is observed in limit cycle and chaotic systems.

Insect flight on fluid interfaces: a chaotic interfacial oscillator

Science.gov (United States)

Mukundarajan, Haripriya; Prakash, Manu

2013-11-01

Flight is critical to the dominance of insect species on our planet, with about 98 percent of insect species having wings. How complex flight control systems developed in insects is unknown, and arboreal or aquatic origins have been hypothesized. We examine the biomechanics of aquatic origins of flight. We recently reported discovery of a novel mode of ``2D flight'' in Galerucella beetles, which skim along an air-water interface using flapping wing flight. This unique flight mode is characterized by a balance between capillary forces from the interface and biomechanical forces exerted by the flapping wings. Complex interactions on the fluid interface form capillary wave trains behind the insect, and produce vertical oscillations at the surface due to non-linear forces arising from deformation of the fluid meniscus. We present both experimental observations of 2D flight kinematics and a dynamic model explaining the observed phenomena. Careful examination of this interaction predicts the chaotic nature of interfacial flight and takeoff from the interface into airborne flight. The role of wingbeat frequency, stroke plane angle and body angle in determining transition between interfacial and fully airborne flight is highlighted, shedding light on the aquatic theory of flight evolution.

Chaotic examination

Science.gov (United States)

Bildirici, Melike; Sonustun, Fulya Ozaksoy; Sonustun, Bahri

2018-01-01

In the regards of chaos theory, new concepts such as complexity, determinism, quantum mechanics, relativity, multiple equilibrium, complexity, (continuously) instability, nonlinearity, heterogeneous agents, irregularity were widely questioned in economics. It is noticed that linear models are insufficient for analyzing unpredictable, irregular and noncyclical oscillations of economies, and for predicting bubbles, financial crisis, business cycles in financial markets. Therefore, economists gave great consequence to use appropriate tools for modelling non-linear dynamical structures and chaotic behaviors of the economies especially in macro and the financial economy. In this paper, we aim to model the chaotic structure of exchange rates (USD-TL and EUR-TL). To determine non-linear patterns of the selected time series, daily returns of the exchange rates were tested by BDS during the period from January 01, 2002 to May 11, 2017 which covers after the era of the 2001 financial crisis. After specifying the non-linear structure of the selected time series, it was aimed to examine the chaotic characteristic for the selected time period by Lyapunov Exponents. The findings verify the existence of the chaotic structure of the exchange rate returns in the analyzed time period.

Fully Digital Chaotic Oscillators Applied to Pseudo Random Number Generation

KAUST Repository

Mansingka, Abhinav S.

2012-05-01

This thesis presents a generalized approach for the fully digital design and implementation of chaos generators through the numerical solution of chaotic ordinary differential equations. In particular, implementations use the Euler approximation with a fixed-point twos complement number representation system for optimal hardware and performance. In general, digital design enables significant benefits in terms of power, area, throughput, reliability, repeatability and portability over analog implementations of chaos due to lower process, voltage and temperature sensitivities and easy compatibility with other digital systems such as microprocessors, digital signal processing units, communication systems and encryption systems. Furthermore, this thesis introduces the idea of implementing multidimensional chaotic systems rather than 1-D chaotic maps to enable wider throughputs and multiplier-free architectures that provide significant performance and area benefits. This work focuses efforts on the well-understood family of autonomous 3rd order "jerk" chaotic systems. The effect of implementation precision, internal delay cycles and external delay cycles on the chaotic response are assessed. Multiplexing of parameters is implemented to enable switching between chaotic and periodic modes of operation. Enhanced chaos generators that exploit long-term divergence in two identical systems of different precision are also explored. Digital design is shown to enable real-time controllability of 1D multiscroll systems and 4th order hyperchaotic systems, essentially creating non-autonomous chaos that has thus far been difficult to implement in the analog domain. Seven different systems are mathematically assessed for chaotic properties, implemented at the register transfer level in Verilog HDL and experimentally verified on a Xilinx Virtex 4 FPGA. The statistical properties of the output are rigorously studied using the NIST SP. 800-22 statistical testing suite. The output is

Chaotic Dynamics of a Josephson Junction with a Ratchet Potential and Current-Modulating Damping

Science.gov (United States)

Li, Fei; Li, Wenwu; Xu, Lan

2018-04-01

The chaotic dynamics of a Josephson junction with a ratchet potential and current-modulating damping are studied. Under the first-order approximation, we construct the general solution of the first-order equation whose boundedness condition contains the famous Melnikov chaotic criterion. Based on the general solution, the incomputability and unpredictability of the system's chaotic behavior are discussed. For the case beyond perturbation conditions, the evolution of stroboscopic Poincaré sections shows that the system undergoes a quasi-periodic transition to chaos with an increasing intensity of the rf-current. Through a suitable feedback controlling strategy, the chaos can be effectively suppressed and the intensity of the controller can vary in a large range. It is also found that the current between the two separated superconductors increases monotonously in some specific parameter spaces.

Role of the Absorbing Area in Chaotic Synchronization

DEFF Research Database (Denmark)

Maistrenko, Yu.L.; Maistrenko, V.L.; Popovich, A.

1998-01-01

When two identical chaotic oscillators interact, one or more intervals of coupling parameters generally exist in which the synchronized state is weakly stable, and its basin of attraction is riddled with holes that are repelled from it. The paper discusses the role of the absorbing area for the e......When two identical chaotic oscillators interact, one or more intervals of coupling parameters generally exist in which the synchronized state is weakly stable, and its basin of attraction is riddled with holes that are repelled from it. The paper discusses the role of the absorbing area...

Adaptive Synchronization of Memristor-based Chaotic Neural Systems

Directory of Open Access Journals (Sweden)

Xiaofang Hu

2014-11-01

Full Text Available Chaotic neural networks consisting of a great number of chaotic neurons are able to reproduce the rich dynamics observed in biological nervous systems. In recent years, the memristor has attracted much interest in the efficient implementation of artificial synapses and neurons. This work addresses adaptive synchronization of a class of memristor-based neural chaotic systems using a novel adaptive backstepping approach. A systematic design procedure is presented. Simulation results have demonstrated the effectiveness of the proposed adaptive synchronization method and its potential in practical application of memristive chaotic oscillators in secure communication.

Modelling chaotic Hamiltonian systems as a Markov Chain ...

African Journals Online (AJOL)

The behaviour of chaotic Hamiltonian system has been characterised qualitatively in recent times by its appearance on the Poincaré section and quantitatively by the Lyapunov exponent. Studying the dynamics of the two chaotic Hamiltonian systems: the Henon-Heiles system and non-linearly coupled oscillators as their ...

poincare surface analysis of two coupled quintic oscillators in a ...

African Journals Online (AJOL)

DJFLEX

We have investigated the chaotic dynamics of two coupled quintic oscillators in a single well potential as the energy of the oscillator increases, keeping the coupling strength constant. The degree of chaoticity does not increase monotonously with the energy as regular regions reappear within chaotic seas as the energy ...

Poincare surface analysis of two coupled quintic oscillators in a ...

African Journals Online (AJOL)

We have investigated the chaotic dynamics of two coupled quintic oscillators in a single well potential as the energy of the oscillator increases, keeping the coupling strength constant. The degree of chaoticity does not increase monotonously with the energy as regular regions reappear within chaotic seas as the energy ...

Electrochemical Noise Chaotic Analysis of NiCoAg Alloy in Hank Solution

Directory of Open Access Journals (Sweden)

D. Bahena

2011-01-01

Full Text Available The potential and current oscillations during corrosion of NiCoAg alloy in Hank solution were studied. Detailed nonlinear fractal analyses were used to characterize complex time series clearly showing that the irregularity in these time series corresponds to deterministic chaos rather than to random noise. The chaotic oscillations were characterized by power spectral densities, phase space, and Lyapunov exponents. Electrochemical impedance was also applied the fractal dimensions for the corroded surface was obtained, and a corrosion mechanism was proposed.

Chaotic wave trains in an oscillatory/excitable medium

International Nuclear Information System (INIS)

Rabinovitch, A.; Gutman, M.; Biton, Y.; Aviram, I.

2006-01-01

We study the chaotic dynamics of a heterogeneous reaction-diffusion medium composed of two uniform regions: one oscillatory, and the other excitable. It is shown that, by altering the diffusion coefficient, local chaotic oscillations can be induced at the interface between regions, which in turn, generate different chaotic sequences of pulses traveling in the excitable region. We analyze the properties of the local chaotic driver, as well as the diffusion-induced transitions. A procedure based on the abnormal frequency-locking phenomenon is proposed for controlling such sequences. Relevance of the obtained results to cardiac dynamics is briefly discussed

Breaking of ensembles of linear and nonlinear oscillators

International Nuclear Information System (INIS)

Buts, V.A.

2016-01-01

Some results concerning the study of the dynamics of ensembles of linear and nonlinear oscillators are stated. It is shown that, in general, a stable ensemble of linear oscillator has a limited number of oscillators. This number has been defined for some simple models. It is shown that the features of the dynamics of linear oscillators can be used for conversion of the low-frequency energy oscillations into high frequency oscillations. The dynamics of coupled nonlinear oscillators in most cases is chaotic. For such a case, it is shown that the statistical characteristics (moments) of chaotic motion can significantly reduce potential barriers that keep the particles in the capture region

Design of Threshold Controller Based Chaotic Circuits

DEFF Research Database (Denmark)

Mohamed, I. Raja; Murali, K.; Sinha, Sudeshna

2010-01-01

We propose a very simple implementation of a second-order nonautonomous chaotic oscillator, using a threshold controller as the only source of nonlinearity. We demonstrate the efficacy and simplicity of our design through numerical and experimental results. Further, we show that this approach...... of using a threshold controller as a nonlinear element, can be extended to obtain autonomous and multiscroll chaotic attractor circuits as well....

Localized chaoticity in two linearly coupled inverted double-well ...

African Journals Online (AJOL)

Two linearly coupled inverted double-well oscillators for a fixed energy and varying coupling strength were studied. The dynamics yielded a chaotic system in which the Poincare surface was characterised by two non-mixing regions, one of regular motion and the other region that became chaotic as the coupling increased.

OnWien Bridge Oscillators as Modified Multi-vibrators

DEFF Research Database (Denmark)

Lindberg, Erik

2014-01-01

A tutorial introduction to electrical oscilla- tors. Investigating Wien bridge oscillators as modified multi-vibrators. Introducing chaotic behavior into a Wien bridge oscillator by means of adding a simple nonlinear cir- cuit as a load of one of the amplifier input terminals......A tutorial introduction to electrical oscilla- tors. Investigating Wien bridge oscillators as modified multi-vibrators. Introducing chaotic behavior into a Wien bridge oscillator by means of adding a simple nonlinear cir- cuit as a load of one of the amplifier input terminals...

Amplification through chaotic synchronization in spatially extended beam-plasma systems

Science.gov (United States)

Moskalenko, Olga I.; Frolov, Nikita S.; Koronovskii, Alexey A.; Hramov, Alexander E.

2017-12-01

In this paper, we have studied the relationship between chaotic synchronization and microwave signal amplification in coupled beam-plasma systems. We have considered a 1D particle-in-cell numerical model of unidirectionally coupled beam-plasma oscillatory media being in the regime of electron pattern formation. We have shown the significant gain of microwave oscillation power in coupled beam-plasma media being in the different regimes of generation. The discovered effect has a close connection with the chaotic synchronization phenomenon, so we have observed that amplification appears after the onset of the complete time scale synchronization regime in the analyzed coupled spatially extended systems. We have also provided the numerical study of physical processes in the chain of beam-plasma systems leading to the chaotic synchronization and the amplification of microwave oscillations power, respectively.

Anticipating synchronization in a chain of chaotic oscillators with switching parameters

Energy Technology Data Exchange (ETDEWEB)

Pyragienė, T., E-mail: tatjana.pyragiene@ftmc.lt; Pyragas, K.

2015-12-18

A new coupling scheme for anticipating synchronization of chaotic systems is proposed. The scheme consists of a master system and two in series coupled slave systems with periodically switching parameters. The scheme does not require the presence of any time-delay terms either in a master or in slave systems and provides long-term anticipation. The value of anticipation time as well as the conditions of synchronization are derived in an analytical form. Analytical results are tested by numerical experiments with the chaotic Rössler and Lorenz systems as well as the Hindmarsh–Rose neuron in a regime of chaotic bursting. Also a robustness of the scheme with respect to parameter mismatch and noise is demonstrated. - Highlights: • A new coupling scheme for anticipating chaotic synchronization is proposed. • The scheme consists of three coupled systems with periodically switching parameters. • Long-term anticipation is achieved without using time-delay terms. • The method is verified for the Rössler, Lorenz and Hindmarsh–Rose neuron systems.

Anticipating synchronization in a chain of chaotic oscillators with switching parameters

International Nuclear Information System (INIS)

Pyragienė, T.; Pyragas, K.

2015-01-01

A new coupling scheme for anticipating synchronization of chaotic systems is proposed. The scheme consists of a master system and two in series coupled slave systems with periodically switching parameters. The scheme does not require the presence of any time-delay terms either in a master or in slave systems and provides long-term anticipation. The value of anticipation time as well as the conditions of synchronization are derived in an analytical form. Analytical results are tested by numerical experiments with the chaotic Rössler and Lorenz systems as well as the Hindmarsh–Rose neuron in a regime of chaotic bursting. Also a robustness of the scheme with respect to parameter mismatch and noise is demonstrated. - Highlights: • A new coupling scheme for anticipating chaotic synchronization is proposed. • The scheme consists of three coupled systems with periodically switching parameters. • Long-term anticipation is achieved without using time-delay terms. • The method is verified for the Rössler, Lorenz and Hindmarsh–Rose neuron systems.

Replicate periodic windows in the parameter space of driven oscillators

Energy Technology Data Exchange (ETDEWEB)

Medeiros, E.S., E-mail: esm@if.usp.br [Instituto de Fisica, Universidade de Sao Paulo, Sao Paulo (Brazil); Souza, S.L.T. de [Universidade Federal de Sao Joao del-Rei, Campus Alto Paraopeba, Minas Gerais (Brazil); Medrano-T, R.O. [Departamento de Ciencias Exatas e da Terra, Universidade Federal de Sao Paulo, Diadema, Sao Paulo (Brazil); Caldas, I.L. [Instituto de Fisica, Universidade de Sao Paulo, Sao Paulo (Brazil)

2011-11-15

Highlights: > We apply a weak harmonic perturbation to control chaos in two driven oscillators. > We find replicate periodic windows in the driven oscillator parameter space. > We find that the periodic window replication is associated with the chaos control. - Abstract: In the bi-dimensional parameter space of driven oscillators, shrimp-shaped periodic windows are immersed in chaotic regions. For two of these oscillators, namely, Duffing and Josephson junction, we show that a weak harmonic perturbation replicates these periodic windows giving rise to parameter regions correspondent to periodic orbits. The new windows are composed of parameters whose periodic orbits have the same periodicity and pattern of stable and unstable periodic orbits already existent for the unperturbed oscillator. Moreover, these unstable periodic orbits are embedded in chaotic attractors in phase space regions where the new stable orbits are identified. Thus, the observed periodic window replication is an effective oscillator control process, once chaotic orbits are replaced by regular ones.

The transition to chaotic phase synchronization

DEFF Research Database (Denmark)

Mosekilde, E.; Laugesen, J. L.; Zhusubaliyev, Zh. T.

2012-01-01

The transition to chaotic phase synchronization for a periodically driven spiral-type chaotic oscillator is known to involve a dense set of saddle-node bifurcations. By following the synchronization transition through the cascade of period-doubling bifurcations in a forced Ro¨ssler system...... to the torus doubling bifurcations that take place outside this domain. By examining a physiology-based model of the blood flow regulation to the individual functional unit (nephron) of the kidney we demonstrate how a similar bifurcation structure may arise in this system as a response to a periodically...

Partial synchronization and spontaneous spatial ordering in coupled chaotic systems

International Nuclear Information System (INIS)

Ying Zhang; Gang Hu; Cerdeira, Hilda A.; Shigang Chen; Braun, Thomas; Yugui Yao

2000-11-01

A model of many symmetrically and locally coupled chaotic oscillators is studied. Partial chaotic synchronizations associated with spontaneous spatial ordering are demonstrated. Very rich patterns of the system are revealed, based on partial synchronization analysis. The stabilities of different partially synchronous spatiotemporal structures and some novel dynamical behaviors of these states are discussed both numerically and analytically. (author)

Chaotic bursting in semiconductor lasers

Science.gov (United States)

Ruschel, Stefan; Yanchuk, Serhiy

2017-11-01

We investigate the dynamic mechanisms for low frequency fluctuations in semiconductor lasers subjected to delayed optical feedback, using the Lang-Kobayashi model. This system of delay differential equations displays pronounced envelope dynamics, ranging from erratic, so called low frequency fluctuations to regular pulse packages, if the time scales of fast oscillations and envelope dynamics are well separated. We investigate the parameter regions where low frequency fluctuations occur and compute their Lyapunov spectra. Using the geometric singular perturbation theory, we study this intermittent chaotic behavior and characterize these solutions as bursting slow-fast oscillations.

Implementing a memristive Van der Pol oscillator coupled to a linear oscillator: synchronization and application to secure communication

International Nuclear Information System (INIS)

Megam Ngouonkadi, E B; Fotsin, H B; Louodop Fotso, P

2014-01-01

This paper investigates the dynamics of a memristor-based Van der Pol oscillator coupled to a linear circuit (VDPCL). This chaotic oscillator is a modification of the classical Van der Pol coupled to a linear circuit, and is obtained by replacing the classical cubic nonlinearity by the memristive one. The memristive VDPCL oscillator, in addition to having a very special stability property, exhibits interesting spectral characteristics, which makes it suitable for chaos-based secure communication applications. The memristor is realized by using off-the-shelf components. The basic properties of the circuit are analyzed by means of bifurcation analysis. Chaotic attractors from numerical and experimental analysis are presented, followed by a comparison of results obtained from the modified VDPCL oscillator and those from the classical VDPCL oscillator. An application to synchronization and chaos secure communication is also presented. (paper)

Adaptive Synchronization of Chaotic Systems considering Performance Parameters of Operational Amplifiers

Directory of Open Access Journals (Sweden)

Sergio Ruíz-Hernández

2015-01-01

Full Text Available This paper addresses an adaptive control approach for synchronizing two chaotic oscillators with saturated nonlinear function series as nonlinear functions. Mathematical models to characterize the behavior of the transmitter and receiver circuit were derived, including in the latter the adaptive control and taking into account, for both chaotic oscillators, the most influential performance parameters associated with operational amplifiers. Asymptotic stability of the full synchronization system is studied by using Lyapunov direct method. Theoretical derivations and related results are experimentally validated through implementations from commercially available devices. Finally, the full synchronization system can easily be reproducible at a low cost.

Terahertz radiation induced chaotic electron transport in semiconductor superlattices with a tilted magnetic field

Energy Technology Data Exchange (ETDEWEB)

Wang, C., E-mail: cwang@mail.sim.ac.cn; Wang, F.; Cao, J. C., E-mail: jccao@mail.sim.ac.cn [Key Laboratory of Terahertz Solid-State Technology, Shanghai Institute of Microsystem and Information Technology, Chinese Academy of Sciences, 865 Changning Road, Shanghai 200050 (China)

2014-09-01

Chaotic electron transport in semiconductor superlattice induced by terahertz electric field that is superimposed on a dc electric field along the superlattice axis are studied using the semiclassical motion equations including the effect of dissipation. A magnetic field that is tilted relative to the superlattice axis is also applied to the system. Numerical simulation shows that electrons in superlattice miniband exhibit complicate nonlinear oscillating modes with the influence of terahertz radiation. Transitions between frequency-locking and chaos via pattern forming bifurcations are observed with the varying of terahertz amplitude. It is found that the chaotic regions gradually contract as the dissipation increases. We attribute the appearance of complicate nonlinear oscillation in superlattice to the interaction between terahertz radiation and internal cooperative oscillating mode relative to Bloch oscillation and cyclotron oscillation.

Terahertz radiation induced chaotic electron transport in semiconductor superlattices with a tilted magnetic field

International Nuclear Information System (INIS)

Wang, C.; Wang, F.; Cao, J. C.

2014-01-01

Chaotic electron transport in semiconductor superlattice induced by terahertz electric field that is superimposed on a dc electric field along the superlattice axis are studied using the semiclassical motion equations including the effect of dissipation. A magnetic field that is tilted relative to the superlattice axis is also applied to the system. Numerical simulation shows that electrons in superlattice miniband exhibit complicate nonlinear oscillating modes with the influence of terahertz radiation. Transitions between frequency-locking and chaos via pattern forming bifurcations are observed with the varying of terahertz amplitude. It is found that the chaotic regions gradually contract as the dissipation increases. We attribute the appearance of complicate nonlinear oscillation in superlattice to the interaction between terahertz radiation and internal cooperative oscillating mode relative to Bloch oscillation and cyclotron oscillation

Terahertz radiation induced chaotic electron transport in semiconductor superlattices with a tilted magnetic field.

Science.gov (United States)

Wang, C; Wang, F; Cao, J C

2014-09-01

Chaotic electron transport in semiconductor superlattice induced by terahertz electric field that is superimposed on a dc electric field along the superlattice axis are studied using the semiclassical motion equations including the effect of dissipation. A magnetic field that is tilted relative to the superlattice axis is also applied to the system. Numerical simulation shows that electrons in superlattice miniband exhibit complicate nonlinear oscillating modes with the influence of terahertz radiation. Transitions between frequency-locking and chaos via pattern forming bifurcations are observed with the varying of terahertz amplitude. It is found that the chaotic regions gradually contract as the dissipation increases. We attribute the appearance of complicate nonlinear oscillation in superlattice to the interaction between terahertz radiation and internal cooperative oscillating mode relative to Bloch oscillation and cyclotron oscillation.

Chaotic Darcy-Brinkman convection in a fluid saturated porous layer subjected to gravity modulation

Directory of Open Access Journals (Sweden)

Moli Zhao

2018-06-01

Full Text Available On the basis of Darcy-Brinkman model, the chaotic convection in a couple stress fluid saturated porous media under gravity modulation is investigated using the nonlinear stability analyses. The transition from steady convection to chaos is analysed with the effect of Darcy-Brinkman couple stress parameter and the gravity modulation. The results show that the chaotic behavior is connected with the critical value of Rayleigh number which is dependent upon the oscillation frequency and the Darcy-Brinkman couple stress parameter. If the oscillation frequency Ω is not zero, the Rayleigh number value R of the chaotic behavior increases with the increase of the Darcy-Brinkman couple stress parameter. The Darcy-Brinkman couple stress parameter and the gravity modulation decrease the rate of heat transfer. Keywords: Darcy-Brinkman model, Gravity modulation, Nonlinear stability, Chaotic convection

On nonlinear control design for autonomous chaotic systems of integer and fractional orders

International Nuclear Information System (INIS)

Ahmad, Wajdi M.; Harb, Ahmad M.

2003-01-01

In this paper, we address the problem of chaos control for autonomous nonlinear chaotic systems. We use the recursive 'backstepping' method of nonlinear control design to derive the nonlinear controllers. The controller effect is to stabilize the output chaotic trajectory by driving it to the nearest equilibrium point in the basin of attraction. We study two nonlinear chaotic systems: an electronic chaotic oscillator model, and a mechanical chaotic 'jerk' model. We demonstrate the robustness of the derived controllers against system order reduction arising from the use of fractional integrators in the system models. Our results are validated via numerical simulations

An aperiodic phenomenon of the unscented Kalman filter in filtering noisy chaotic signals

Institute of Scientific and Technical Information of China (English)

无

2007-01-01

A non-periodic oscillatory behavior of the unscented Kalman filter (UKF) when used to filter noisy contaminated chaotic signals is reported. We show both theoretically and experimentally that the gain of the UKF may not converge or diverge but oscillate aperiodically. More precisely, when a nonlinear system is periodic, the Kalman gain and error covariance of the UKF converge to zero. However, when the system being considered is chaotic, the Kalman gain either converges to a fixed point with a magnitude larger than zero or oscillates aperiodically.

Nonstationary oscillations in gyrotrons revisited

International Nuclear Information System (INIS)

Dumbrajs, O.; Kalis, H.

2015-01-01

Development of gyrotrons requires careful understanding of different regimes of gyrotron oscillations. It is known that in the planes of the generalized gyrotron variables: cyclotron resonance mismatch and dimensionless current or cyclotron resonance mismatch and dimensionless interaction length complicated alternating sequences of regions of stationary, periodic, automodulation, and chaotic oscillations exist. In the past, these regions were investigated on the supposition that the transit time of electrons through the interaction space is much shorter than the cavity decay time. This assumption is valid for short and/or high diffraction quality resonators. However, in the case of long and/or low diffraction quality resonators, which are often utilized, this assumption is no longer valid. In such a case, a different mathematical formalism has to be used for studying nonstationary oscillations. One example of such a formalism is described in the present paper

Complex economic dynamics: Chaotic saddle, crisis and intermittency

International Nuclear Information System (INIS)

Chian, Abraham C.-L.; Rempel, Erico L.; Rogers, Colin

2006-01-01

Complex economic dynamics is studied by a forced oscillator model of business cycles. The technique of numerical modeling is applied to characterize the fundamental properties of complex economic systems which exhibit multiscale and multistability behaviors, as well as coexistence of order and chaos. In particular, we focus on the dynamics and structure of unstable periodic orbits and chaotic saddles within a periodic window of the bifurcation diagram, at the onset of a saddle-node bifurcation and of an attractor merging crisis, and in the chaotic regions associated with type-I intermittency and crisis-induced intermittency, in non-linear economic cycles. Inside a periodic window, chaotic saddles are responsible for the transient motion preceding convergence to a periodic or a chaotic attractor. The links between chaotic saddles, crisis and intermittency in complex economic dynamics are discussed. We show that a chaotic attractor is composed of chaotic saddles and unstable periodic orbits located in the gap regions of chaotic saddles. Non-linear modeling of economic chaotic saddle, crisis and intermittency can improve our understanding of the dynamics of financial intermittency observed in stock market and foreign exchange market. Characterization of the complex dynamics of economic systems is a powerful tool for pattern recognition and forecasting of business and financial cycles, as well as for optimization of management strategy and decision technology

Current and Voltage Mode Multiphase Sinusoidal Oscillators Using CBTAs

Directory of Open Access Journals (Sweden)

M. Sagbas

2013-04-01

Full Text Available Current-mode (CM and voltage-mode (VM multiphase sinusoidal oscillator (MSO structures using current backward transconductance amplifier (CBTA are proposed. The proposed oscillators can generate n current or voltage signals (n being even or odd equally spaced in phase. n+1 CBTAs, n grounded capacitors and a grounded resistor are used for nth-state oscillator. The oscillation frequency can be independently controlled through transconductance (gm of the CBTAs which are adjustable via their bias currents. The effects caused by the non-ideality of the CBTA on the oscillation frequency and condition have been analyzed. The performance of the proposed circuits is demonstrated on third-stage and fifth-stage MSOs by using PSPICE simulations based on the 0.25 µm TSMC level-7 CMOS technology parameters.

Small-world networks of fuzzy chaotic oscillators

CERN Document Server

Bucolo, M; Fortuna, L

2003-01-01

Small-world topology has been used to build lattices of nonlinear fuzzy systems. Chaotic units, ruled by linguistic description and with specified Lyapunov exponent, have been realized and connected using linear diffusion coefficient. The dynamic features of the networks versus the number of systems connected have been investigated to underline phenomena like spatiotemporal chaos and complete regularization. The synchronization characteristics in case of sparse long-term connections and the performances comparison with regular and random network configurations are shown.

Hyperchaos in coupled Colpitts oscillators

DEFF Research Database (Denmark)

Cenys, Antanas; Tamasevicius, Arunas; Baziliauskas, Antanas

2003-01-01

The paper suggests a simple solution of building a hyperchaotic oscillator. Two chaotic Colpitts oscillators, either identical or non-identical ones are coupled by means of two linear resistors R-k. The hyperchaotic output signal v(t) is a linear combination, specifically the mean of the individual...

Electronically Tunable Current-Mode Quadrature Oscillator Using Single MCDTA

Directory of Open Access Journals (Sweden)

Y. Li

2010-12-01

Full Text Available This paper presents a modified current differencing transconductance amlpifier (MCDTA and the MCDTA based quadrature oscillator. The oscillator is current-mode and provides current output from high output impedance terminals. The circuit uses only one MCDTA and two grounded capacitors, and is easy to be integrated. Its oscillation frequency can be tuned electronically by tuning bias currents of MCDTA. Finally, frequency error is analyzed. The results of circuit simulations are in agreement with theory.

Chaotic Patterns in Aeroelastic Signals

Directory of Open Access Journals (Sweden)

F. D. Marques

2009-01-01

patterns. With the reconstructed state spaces, qualitative analyses may be done, and the attractors evolutions with parametric variation are presented. Overall results reveal complex system dynamics associated with highly separated flow effects together with nonlinear coupling between aeroelastic modes. Bifurcations to the nonlinear aeroelastic system are observed for two investigations, that is, considering oscillations-induced aeroelastic evolutions with varying freestream speed, and aeroelastic evolutions at constant freestream speed and varying oscillations. Finally, Lyapunov exponent calculation is proceeded in order to infer on chaotic behavior. Poincaré mappings also suggest bifurcations and chaos, reinforced by the attainment of maximum positive Lyapunov exponents.

Chaotic behavior in a hydrodynamic model of a fluidized bed reactor

International Nuclear Information System (INIS)

Schouten, J.C.; van den Bleek, C.M.

1991-01-01

Recent preliminary experimental studies using time-series analysis have demonstrated that the multi-phase flow in fluidized bed reactors can be characterized as chaotic. In the present paper, it is therefore argued that the chaotic time-dependence of fluidization is a characteristic feature which should be included in scaling rules for fluidized bed reactors. For example, the similarity groups applied in dimensionless fluidized bed scaling should be improved by extending them with functions of the relevant numbers from chaos theory, such as the correlation and embedding dimension or the maximum Lyapunov exponent. This requires that the dependence of these numbers on fluidization parameters must be theoretically and experimentally investigated. The concept of chaos in fluidization also requires that the classical, empirically developed, hydrodynamic models that are applied in fluidized bed scaling are amended to include time-dependence, non-linearity as well as a sufficient level of complexity before they can predict any chaotic behavior. An example is given of chaotic behavior generated in the classical counter-current flow model according to Van Deemter by writing the upwards solids velocity as a harmonic oscillating function of time. A low-dimensional strange attractor is found, embedded in two-dimensional phase space, of which the correlation dimension depends on the solids exchange coefficient

Synchronization of indirectly coupled Lorenz oscillators

Indian Academy of Sciences (India)

Synchronization of indirectly coupled Lorenz oscillators: An experimental study. Amit Sharma Manish Dev Shrimali. Synchronization, Coupled Systems and Networks Volume 77 Issue 5 November 2011 pp 881-889 ... The in-phase and anti-phase synchronization of indirectly coupled chaotic oscillators reported in Phys. Rev ...

A Simple Snap Oscillator with Coexisting Attractors, Its Time-Delayed Form, Physical Realization, and Communication Designs

Science.gov (United States)

Rajagopal, Karthikeyan; Jafari, Sajad; Akgul, Akif; Karthikeyan, Anitha; Çiçek, Serdar; Shekofteh, Yasser

2018-05-01

In this paper, we report a novel chaotic snap oscillator with one nonlinear function. Dynamic analysis of the system shows the existence of bistability. To study the time delay effects on the proposed snap oscillator, we introduce multiple time delay in the fourth state equation. Investigation of dynamical properties of the time-delayed system shows that the snap oscillator exhibits the same multistable properties as the nondelayed system. The new multistable hyperjerk chaotic system has been tested in chaos shift keying and symmetric choc shift keying modulated communication designs for engineering applications. It has been determined that the symmetric chaos shift keying modulated communication system implemented with the new chaotic system is more successful than the chaos shift keying modulation for secure communication. Also, circuit implementation of the chaotic snap oscillator with tangent function is carried out showing its feasibility.

FPGA implementation of fractional-order discrete memristor chaotic ...

Indian Academy of Sciences (India)

Anitha Karthikeyan

Corresponding author. E-mail: rkarthiekeyan@gmail.com. MS received 10 August 2017; revised 4 September 2017; accepted 5 September 2017; published online 30 December 2017. Abstract. A new fourth-order memristor chaotic oscillator is taken to investigate its fractional-order discrete synchronisation.

Multiscality in the Dynamics of Coupled Chaotic Systems

DEFF Research Database (Denmark)

Pavlov, A.N.; Sosnovtseva, Olga; Ziganshin, A.R.

2002-01-01

We investigate the scaling features of complex motions in systems of two coupled chaotic oscillators by means of the wavelet-transform modulus maxima method and the detrended fluctuation analysis. We show that the transition from asynchronous to synchronous dynamics typically reduces the degree...

Period-doubling bifurcation cascade observed in a ferromagnetic nanoparticle under the action of a spin-polarized current

Energy Technology Data Exchange (ETDEWEB)

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.

Chaotic exploration and learning of locomotion behaviors.

Science.gov (United States)

Shim, Yoonsik; Husbands, Phil

2012-08-01

We present a general and fully dynamic neural system, which exploits intrinsic chaotic dynamics, for the real-time goal-directed exploration and learning of the possible locomotion patterns of an articulated robot of an arbitrary morphology in an unknown environment. The controller is modeled as a network of neural oscillators that are initially coupled only through physical embodiment, and goal-directed exploration of coordinated motor patterns is achieved by chaotic search using adaptive bifurcation. The phase space of the indirectly coupled neural-body-environment system contains multiple transient or permanent self-organized dynamics, each of which is a candidate for a locomotion behavior. The adaptive bifurcation enables the system orbit to wander through various phase-coordinated states, using its intrinsic chaotic dynamics as a driving force, and stabilizes on to one of the states matching the given goal criteria. In order to improve the sustainability of useful transient patterns, sensory homeostasis has been introduced, which results in an increased diversity of motor outputs, thus achieving multiscale exploration. A rhythmic pattern discovered by this process is memorized and sustained by changing the wiring between initially disconnected oscillators using an adaptive synchronization method. Our results show that the novel neurorobotic system is able to create and learn multiple locomotion behaviors for a wide range of body configurations and physical environments and can readapt in realtime after sustaining damage.

Application of the Lyapunov exponent to detect noise-induced chaos in oscillating microbial cultures

International Nuclear Information System (INIS)

Patnaik, P.R.

2005-01-01

Oscillating microbial processes can, under certain conditions, gravitate into chaotic behavior induced by external noise. Detection and control of chaos are important for the survival of the microorganisms and to operate a process usefully. In this study the largest Lyapunov exponent is recommended as a convenient and reliable index of chaos in continuous oscillating cultures. For the growth of Saccharomyces cerevisiae as a model system, the exponents increase with the oxygen mass transfer coefficient and decrease as the dilution rate increases. By comparing with the corresponding time-domain oscillations determined earlier, it is inferred that weakly oscillating cultures are less likely to be driven to chaotic behavior. The main carbon source, glucose, is quite robust to chaotic destabilization, thus enhancing its suitability as a manipulated variable for bioreactor control

VHDL Descriptions for the FPGA Implementation of PWL-Function-Based Multi-Scroll Chaotic Oscillators.

Directory of Open Access Journals (Sweden)

Esteban Tlelo-Cuautle

Full Text Available Nowadays, chaos generators are an attractive field for research and the challenge is their realization for the development of engineering applications. From more than three decades ago, chaotic oscillators have been designed using discrete electronic devices, very few with integrated circuit technology, and in this work we propose the use of field-programmable gate arrays (FPGAs for fast prototyping. FPGA-based applications require that one be expert on programming with very-high-speed integrated circuits hardware description language (VHDL. In this manner, we detail the VHDL descriptions of chaos generators for fast prototyping from high-level programming using Python. The cases of study are three kinds of chaos generators based on piecewise-linear (PWL functions that can be systematically augmented to generate even and odd number of scrolls. We introduce new algorithms for the VHDL description of PWL functions like saturated functions series, negative slopes and sawtooth. The generated VHDL-code is portable, reusable and open source to be synthesized in an FPGA. Finally, we show experimental results for observing 2, 10 and 30-scroll attractors.

VHDL Descriptions for the FPGA Implementation of PWL-Function-Based Multi-Scroll Chaotic Oscillators.

Science.gov (United States)

Tlelo-Cuautle, Esteban; Quintas-Valles, Antonio de Jesus; de la Fraga, Luis Gerardo; Rangel-Magdaleno, Jose de Jesus

2016-01-01

Nowadays, chaos generators are an attractive field for research and the challenge is their realization for the development of engineering applications. From more than three decades ago, chaotic oscillators have been designed using discrete electronic devices, very few with integrated circuit technology, and in this work we propose the use of field-programmable gate arrays (FPGAs) for fast prototyping. FPGA-based applications require that one be expert on programming with very-high-speed integrated circuits hardware description language (VHDL). In this manner, we detail the VHDL descriptions of chaos generators for fast prototyping from high-level programming using Python. The cases of study are three kinds of chaos generators based on piecewise-linear (PWL) functions that can be systematically augmented to generate even and odd number of scrolls. We introduce new algorithms for the VHDL description of PWL functions like saturated functions series, negative slopes and sawtooth. The generated VHDL-code is portable, reusable and open source to be synthesized in an FPGA. Finally, we show experimental results for observing 2, 10 and 30-scroll attractors.

Experimental chaotic quantification in bistable vortex induced vibration systems

Science.gov (United States)

Huynh, B. H.; Tjahjowidodo, T.

2017-02-01

The study of energy harvesting by means of vortex induced vibration systems has been initiated a few years ago and it is considered to be potential as a low water current energy source. The energy harvester is realized by exposing an elastically supported blunt structure under water flow. However, it is realized that the system will only perform at a limited operating range (water flow) that is attributed to the resonance phenomenon that occurs only at a frequency that corresponds to the fluid flow. An introduction of nonlinear elements seems to be a prominent solution to overcome the problem. Among many nonlinear elements, a bistable spring is known to be able to improve the harvested power by a vortex induced vibrations (VIV) based energy converter at the low velocity water flows. However, it is also observed that chaotic vibrations will occur at different operating ranges that will erratically diminish the harvested power and cause a difficulty in controlling the system that is due to the unpredictability in motions of the VIV structure. In order to design a bistable VIV energy converter with improved harvested power and minimum negative effect of chaotic vibrations, the bifurcation map of the system for varying governing parameters is highly on demand. In this study, chaotic vibrations of a VIV energy converter enhanced by a bistable stiffness element are quantified in a wide range of the governing parameters, i.e. damping and bistable gap. Chaotic vibrations of the bistable VIV energy converter are simulated by utilization of a wake oscillator model and quantified based on the calculation of the Lyapunov exponent. Ultimately, a series of experiments of the system in a water tunnel, facilitated by a computer-based force-feedback testing platform, is carried out to validate the existence of chaotic responses. The main challenge in dealing with experimental data is in distinguishing chaotic response from noise-contaminated periodic responses as noise will smear

Predicting chaos in memristive oscillator via harmonic balance method.

Science.gov (United States)

Wang, Xin; Li, Chuandong; Huang, Tingwen; Duan, Shukai

2012-12-01

This paper studies the possible chaotic behaviors in a memristive oscillator with cubic nonlinearities via harmonic balance method which is also called the method of describing function. This method was proposed to detect chaos in classical Chua's circuit. We first transform the considered memristive oscillator system into Lur'e model and present the prediction of the existence of chaotic behaviors. To ensure the prediction result is correct, the distortion index is also measured. Numerical simulations are presented to show the effectiveness of theoretical results.

Nonlinear mode conversion with chaotic soliton generation at plasma resonance

International Nuclear Information System (INIS)

Pietsch, H.; Laedke, E.W.; Spatschek, K.H.

1993-01-01

The resonant absorption of electromagnetic waves near the critical density in inhomogeneous plasmas is studied. A driven nonlinear Schroedinger equation for the mode-converted oscillations is derived by multiple-scaling techniques. The model is simulated numerically. The generic transition from a stationary to a time-dependent solution is investigated. Depending on the parameters, a time-chaotic behavior is found. By a nonlinear analysis, based on the inverse scattering transform, solitons of a corresponding integrable equation are identified as the dominant coherent structures of the chaotic dynamics. Finally, a map is presented which predicts chaotic soliton generation and emission at the critical density. Its qualitative behavior, concerning the bifurcation points, is in excellent agreement with the numerical simulations

Potentiostatic current and galvanostatic potential oscillations during electrodeposition of cadmium.

Science.gov (United States)

López-Sauri, D A; Veleva, L; Pérez-Ángel, G

2015-09-14

Cathodic current and potential oscillations were observed during electrodeposition of cadmium from a cyanide electrolyte on a vertical platinum electrode, in potentiostatic and galvanostatic experiments. Electrochemical impedance spectroscopy experiments revealed a region of negative real impedance in a range of non-zero frequencies, in the second descending branch with a positive slope of the N-shape current-potential curve. This kind of dynamical behaviour is characteristic of the HN-NDR oscillators (oscillators with the N-Shape current-potential curve and hidden negative differential resistance). The oscillations could be mainly attributed to the changes in the real active cathodic area, due to the adsorption of hydrogen molecules and their detachment from the surface. The instabilities of the electrochemical processes were characterized by time series, Fast Fourier Transforms and 2-D phase portraits showing quasi-periodic oscillations.

Nonlinear effects on Turing patterns: Time oscillations and chaos

KAUST Repository

Aragó n, J. L.; Barrio, R. A.; Woolley, T. E.; Baker, R. E.; Maini, P. K.

2012-01-01

consequence, the patterns oscillate in time. When varying a single parameter, a series of bifurcations leads to period doubling, quasiperiodic, and chaotic oscillations without modifying the underlying Turing pattern. A Ruelle-Takens-Newhouse route to chaos

Synchronization of Tubular Pressure Oscillations in Interacting Nephrons

DEFF Research Database (Denmark)

Sosnovtseva, Olga; Postnov, D.E.; Mosekilde, Erik

2003-01-01

The pressure and flow regulation in the individual functional unit of the kidney (the nephron) tends to operate in an unstable regime. For normal rats, the regulation displays regular self-sustained oscillations, but for rats with high blood pressure the oscillations become chaotic. We explain...

Harmonic oscillations, chaos and synchronization in systems consisting of Van der Pol oscillator coupled to a linear oscillator

International Nuclear Information System (INIS)

Woafo, P.

1999-12-01

This paper deals with the dynamics of a model describing systems consisting of the classical Van der Pol oscillator coupled gyroscopically to a linear oscillator. Both the forced and autonomous cases are considered. Harmonic response is investigated along with its stability boundaries. Condition for quenching phenomena in the autonomous case is derived. Neimark bifurcation is observed and it is found that our model shows period doubling and period-m sudden transitions to chaos. Synchronization of two and more systems in their chaotic regime is presented. (author)

Intrinsic current oscillations in an asymmetric triple-barrier resonant tunnelling diode

International Nuclear Information System (INIS)

Wójcik, P; Spisak, B J; Wołoszyn, M; Adamowski, J

2010-01-01

The electronic transport characteristics of an asymmetric triple-barrier resonant tunnelling diode are calculated by the time-dependent Wigner–Poisson method. The intrinsic current oscillations are found in two separate bias voltage ranges. The first one is located below the resonant current peak, and the second lies in the negative differential resistance region. We provide the explanation of the current density oscillations in these two separate bias voltage ranges based on the analysis of the self-consistent potential profiles and changes of electron density. We have shown that two different formation mechanisms are responsible for the current density oscillations in these two bias voltage ranges. In the bias voltage range below the resonant current peak in the current–voltage characteristics, the current density oscillations are caused by the coupling between quasi-bound states in the left and right quantum wells. On the other hand, the current density oscillations in the negative differential resistance region result from the coupling between quasi-bound states in the left quantum well and the quantum well formed in the region of the left contact

Inhibition of chaotic escape from a potential well using small parametric modulations

International Nuclear Information System (INIS)

Chacon, R.; Balibrea, F.; Lopez, M.A.

1996-01-01

It is shown theoretically for the first time that, depending on its period, amplitude, and initial phase, a periodic parametric modulation can suppress a chaotic escape from a potential well. The instance of the Helmholtz oscillator is used to demonstrate, by means of Melnikov close-quote s method, that parametric modulations of the linear or quadratic potential terms inhibit chaotic escape when certain resonance conditions are met. copyright 1996 American Institute of Physics

Chimera states in a population of identical oscillators under planar ...

Indian Academy of Sciences (India)

finding, observed in both a collection of van der Pol oscillators and chaotic Rössler oscillators, fur- ther simplifies the existence criterion for chimeras, thereby broadens the range of their applicability to real-world situations. Keywords. Synchronization; chimera; Rössler system; van der Pol oscillator. PACS Nos 05.45.

Controlling a Chaotic System through Control Parameter Self-Modulation

International Nuclear Information System (INIS)

Pastor, I.

1994-01-01

A method for obtaining active control of a chaotic system based on the modulation of a control parameter by adding to it a small perturbation proportional to one output signal is proposed. From a theoretical point of view, chaos can be stabilized in the framework of this method because small modifications of the vector field controlling the dynamics are allowed, and thus some of the previously existing unstable periodic trajectories can be made stable. The method is much inspired on recent treatments of some related problems, and it is compared with them. One of its most attractive features is that it should be very easy to implement it on real experiments. The method is tested on a system of ordinary differential equations modelling the coupling of two self-oscillating electronic circuits (van der Pol oscillators). Some brief comments are made on the possibility that it could be applied to complex spatio-temporal systems where multiple chaotic structures can coexist for some values of the control parameters

A chaotic model for advertising diffusion problem with competition

Science.gov (United States)

Ip, W. H.; Yung, K. L.; Wang, Dingwei

2012-08-01

In this article, the author extends Dawid and Feichtinger's chaotic advertising diffusion model into the duopoly case. A computer simulation system is used to test this enhanced model. Based on the analysis of simulation results, it is found that the best advertising strategy in duopoly is to increase the advertising investment to reach the best Win-Win situation where the oscillation of market portion will not occur. In order to effectively arrive at the best situation, we define a synthetic index and two thresholds. An estimation method for the parameters of the index and thresholds is proposed in this research. We can reach the Win-Win situation by simply selecting the control parameters to make the synthetic index close to the threshold of min-oscillation state. The numerical example and computational results indicated that the proposed chaotic model is useful to describe and analyse advertising diffusion process in duopoly, it is an efficient tool for the selection and optimisation of advertising strategy.

Analysis, synchronisation and circuit design of a new highly nonlinear chaotic system

Science.gov (United States)

Mobayen, Saleh; Kingni, Sifeu Takougang; Pham, Viet-Thanh; Nazarimehr, Fahimeh; Jafari, Sajad

2018-02-01

This paper investigates a three-dimensional autonomous chaotic flow without linear terms. Dynamical behaviour of the proposed system is investigated through eigenvalue structures, phase portraits, bifurcation diagram, Lyapunov exponents and basin of attraction. For a suitable choice of the parameters, the proposed system can exhibit anti-monotonicity, periodic oscillations and double-scroll chaotic attractor. Basin of attraction of the proposed system shows that the chaotic attractor is self-excited. Furthermore, feasibility of double-scroll chaotic attractor in the real word is investigated by using the OrCAD-PSpice software via an electronic implementation of the proposed system. A good qualitative agreement is illustrated between the numerical simulations and the OrCAD-PSpice results. Finally, a finite-time control method based on dynamic sliding surface for the synchronisation of master and slave chaotic systems in the presence of external disturbances is performed. Using the suggested control technique, the superior master-slave synchronisation is attained. Illustrative simulation results on the studied chaotic system are presented to indicate the effectiveness of the suggested scheme.

Synchronization and chaos in spin-transfer-torque nano-oscillators coupled via a high-speed operational amplifier

International Nuclear Information System (INIS)

Sanid, C; Murugesh, S

2014-01-01

We propose a system of two coupled spin-torque nano-oscillators (STNOs), one driver and another response, and demonstrate using numerical studies the synchronization of the response system to the frequency of the driver system. To this end we use a high-speed operational amplifier in the form of a voltage follower, which essentially isolates the drive system from the response system. We find the occurrence of 1 : 1 as well as 2 : 1 synchronization in the system, wherein the oscillators show limit cycle dynamics. An increase in power output is noticed when the two oscillators are locked in 1 : 1 synchronization. Moreover in the crossover region between these two synchronization dynamics we show the existence of chaotic dynamics in the slave system. The coupled dynamics under periodic forcing, using a small ac input current in addition to that of the dc part, is also studied. The slave oscillator is seen to retain its qualitative identity in the parameter space in spite of being fed in, at times, a chaotic signal. Such electrically coupled STNOs will be highly useful in fabricating commercial spin-valve oscillators with high power output, when integrated with other spintronic devices. (paper)

A new type of chaotic synchronization with application to communication systems

International Nuclear Information System (INIS)

Kharel, Rupak; Busawon, Krishna

2011-01-01

In this paper, we propose a new methodology to synchronize a class of chaotic systems starting from different initial conditions under some given conditions. The method we propose is not based on the unidirectional synchronization method like the one proposed by Pecora-Caroll. The proposed method is unique in the sense that the chaotic oscillators to be synchronized have no direct connection between them; that is, there is no signal being sent from one to the other. Simulation result is presented to show the synchronization performance.

Crenelated fast oscillatory outputs of a two-delay electro-optic oscillator.

Science.gov (United States)

Weicker, Lionel; Erneux, Thomas; Jacquot, Maxime; Chembo, Yanne; Larger, Laurent

2012-02-01

An electro-optic oscillator subject to two distinct delayed feedbacks has been designed to develop pronounced broadband chaotic output. Its route to chaos starts with regular pulsating gigahertz oscillations that we investigate both experimentally and theoretically. Of particular physical interest are the transitions to various crenelated fast time-periodic oscillations, prior to the onset of chaotic regimes. The two-delay problem is described mathematically by two coupled delay-differential equations, which we analyze by using multiple-time-scale methods. We show that the interplay of a large delay and a relatively small delay is responsible for the onset of fast oscillations modulated by a slowly varying square-wave envelope. As the bifurcation parameter progressively increases, this envelope undergoes a sequence of bifurcations that corresponds to successive fixed points of a sine map.

Chattering-free fuzzy sliding-mode control strategy for uncertain chaotic systems

International Nuclear Information System (INIS)

Yau, H.-T.; Chen, C.-L.

2006-01-01

This paper proposes a chattering-free fuzzy sliding-mode control (FSMC) strategy for uncertain chaotic systems. A fuzzy logic control is used to replace the discontinuous sign function of the reaching law in traditional sliding-mode control (SMC), and hence a control input without chattering is obtained in the chaotic systems with uncertainties. Base on the Lyapunov stability theory, we address the design schemes of integration fuzzy sliding-mode control, where the reaching law is proposed by a set of linguistic rules and the control input is chattering free. The Genesio chaotic system is used to test the proposed control strategy and the simulation results show the FSMC not only can control the uncertain chaotic behaviors to a desired state without oscillator very fast, but also the switching function is smooth without chattering. This result implies that this strategy is feasible and effective for chaos control

Parameter-Independent Dynamical Behaviors in Memristor-Based Wien-Bridge Oscillator

Directory of Open Access Journals (Sweden)

Ning Wang

2017-01-01

Full Text Available This paper presents a novel memristor-based Wien-bridge oscillator and investigates its parameter-independent dynamical behaviors. The newly proposed memristive chaotic oscillator is constructed by linearly coupling a nonlinear active filter composed of memristor and capacitor to a Wien-bridge oscillator. For a set of circuit parameters, phase portraits of a double-scroll chaotic attractor are obtained by numerical simulations and then validated by hardware experiments. With a dimensionless system model and the determined system parameters, the initial condition-dependent dynamical behaviors are explored through bifurcation diagrams, Lyapunov exponents, and phase portraits, upon which the coexisting infinitely many attractors and transient chaos related to initial conditions are perfectly offered. These results are well verified by PSIM circuit simulations.

Simply Adjustable Sinusoidal Oscillator Based on Negative Three-Port Current Conveyors

Directory of Open Access Journals (Sweden)

R. Sotner

2010-09-01

Full Text Available The paper deals with sinusoidal oscillator employing two controlled second-generation negative-current conveyors and two capacitors. The proposed oscillator has a simple circuit configuration. Electronic (voltage adjusting of the oscillation frequency and condition of oscillation are possible. The presented circuit is verified in PSpice utilizing macro models of commercially available negative current conveyors. The circuit is also verified by experimental measurements. Important characteristics and drawbacks of the proposed circuit and influences of real active elements in the designed circuit are discussed in detail.

Transition to Coherence in Populations of Coupled Chaotic Oscillators: A Linear Response Approach

International Nuclear Information System (INIS)

Topaj, Dmitri; Kye, Won-Ho; Pikovsky, Arkady

2001-01-01

We consider the collective dynamics in an ensemble of globally coupled chaotic maps. The transition to the coherent state with a macroscopic mean field is analyzed in the framework of the linear response theory. The linear response function for the chaotic system is obtained using the perturbation approach to the Frobenius-Perron operator. The transition point is defined from this function by virtue of the self-excitation condition for the feedback loop. Analytical results for the coupled Bernoulli maps are confirmed by the numerics

Stabilizing periodic orbits of chaotic systems using fuzzy control of Poincare map

International Nuclear Information System (INIS)

Bonakdar, Mohammad; Samadi, Mostafa; Salarieh, Hassan; Alasty, Aria

2008-01-01

In this paper a fuzzy control algorithm is used to stabilize the fixed points of a chaotic system. No knowledge of the dynamic equations of the system is needed in this approach and the whole system is considered as a black box. Two main approaches have been investigated: fuzzy clustering and table look up methods. As illustrative examples these methods have been applied to Bonhoeffer van der Pol oscillator and the Henon chaotic system and the convergence toward fixed points is observed

Stabilizing periodic orbits of chaotic systems using fuzzy control of Poincare map

Energy Technology Data Exchange (ETDEWEB)

Bonakdar, Mohammad; Samadi, Mostafa [Center of Excellence in Design, Robotics and Automation (CEDRA), Department of Mechanical Engineering, Sharif University of Technology, Azadi Avenue, 1458889694 Tehran (Iran, Islamic Republic of); Salarieh, Hassan [Center of Excellence in Design, Robotics and Automation (CEDRA), Department of Mechanical Engineering, Sharif University of Technology, Azadi Avenue, 1458889694 Tehran (Iran, Islamic Republic of)], E-mail: salarieh@mech.sharif.edu; Alasty, Aria [Center of Excellence in Design, Robotics and Automation (CEDRA), Department of Mechanical Engineering, Sharif University of Technology, Azadi Avenue, 1458889694 Tehran (Iran, Islamic Republic of)

2008-05-15

In this paper a fuzzy control algorithm is used to stabilize the fixed points of a chaotic system. No knowledge of the dynamic equations of the system is needed in this approach and the whole system is considered as a black box. Two main approaches have been investigated: fuzzy clustering and table look up methods. As illustrative examples these methods have been applied to Bonhoeffer van der Pol oscillator and the Henon chaotic system and the convergence toward fixed points is observed.

Generation and Evolution of Chaos in Double-Well Duffing Oscillator under Parametrical Excitation

Directory of Open Access Journals (Sweden)

Ying Zhang

2016-01-01

Full Text Available The generation and evolution of chaotic motion in double-well Duffing oscillator under harmonic parametrical excitation are investigated. Firstly, the complex dynamical behaviors are studied by applying multibifurcation diagram and Poincaré sections. Secondly, by means of Melnikov’s approach, the threshold value of parameter μ for generation of chaotic behavior in Smale horseshoe sense is calculated. By the numerical simulation, it is obvious that as μ exceeds this threshold value, the behavior of Duffing oscillator is still steady-state periodic but the transient motion is chaotic; until the top Lyapunov exponent turns to positive, the motion of system turns to permanent chaos. Therefore, in order to gain an insight into the evolution of chaotic behavior after μ passing the threshold value, the transient motion, basin of attraction, and basin boundary are also investigated.

Characterization of chaotic electroconvection near flat electrodes under oscillatory voltages

Science.gov (United States)

Kim, Jeonglae; Davidson, Scott; Mani, Ali

2017-11-01

Onset of hydrodynamic instability and chaotic electroconvection in aqueous systems are studied by directly solving the two-dimensional coupled Poisson-Nernst-Planck and Navier-Stokes equations. An aqueous binary electrolyte is bounded by two planar electrodes where time-harmonic voltage is applied at a constant oscillation frequency. The governing equations are solved using a fully-conservative second-order-accurate finite volume discretization and a second-order implicit Euler time advancement. At a sufficiently high amplitude of applied voltage, the system exhibits chaotic behaviors involving strong hydrodynamic mixing and enhanced electroconvection. The system responses are characterized as a function of oscillation frequency, voltage magnitude, and the ratio of diffusivities of two ion species. Our results indicate that electroconvection is most enhanced for frequencies on the order of inverse system RC time scale. We will discuss the dependence of this optimal frequency on the asymmetry of the diffusion coefficients of ionic species. Supported by the Stanford's Precourt Institute.

Neutral current induced neutrino oscillations in a supernova

CERN Document Server

Kusenko, A; Kusenko, Alexander; Segre, Gino

1997-01-01

Neutral currents induced matter oscillations of electroweak-active (anti-)neutrinos to sterile neutrinos can explain the observed motion of pulsars. In contrast to a recently proposed explanation of the pulsar birth velocities based on the electron to tau (muon) neutrino oscillations [hep-ph/9606428], the heaviest neutrino (either active or sterile) would have to have mass of order several keV.

Wave Physics Oscillations - Solitons - Chaos

CERN Document Server

Nettel, Stephen

2009-01-01

This textbook is intended for those second year undergraduates in science and engineering who will later need an understanding of electromagnetic theory and quantum mechanics. The classical physics of oscillations and waves is developed at a more advanced level than has been customary for the second year, providing a basis for the quantum mechanics that follows. In this new edition the Green's function is explained, reinforcing the integration of quantum mechanics with classical physics. The text may also form the basis of an "introduction to theoretical physics" for physics majors. The concluding chapters give special attention to topics in current wave physics: nonlinear waves, solitons, and chaotic behavior.

Chaotic advection in the ocean

Energy Technology Data Exchange (ETDEWEB)

Koshel' , Konstantin V; Prants, Sergei V [V.I. Il' ichev Pacific Oceanological Institute, Far-Eastern Division of the Russian Academy of Sciences, Vladivostok (Russian Federation)

2006-11-30

The problem of chaotic advection of passive scalars in the ocean and its topological, dynamical, and fractal properties are considered from the standpoint of the theory of dynamical systems. Analytic and numerical results on Lagrangian transport and mixing in kinematic and dynamic chaotic advection models are described for meandering jet currents, topographical eddies in a barotropic ocean, and a two-layer baroclinic ocean. Laboratory experiments on hydrodynamic flows in rotating tanks as an imitation of geophysical chaotic advection are described. Perspectives of a dynamical system approach in physical oceanography are discussed. (reviews of topical problems)

Indirect Allee effect, bistability and chaotic oscillations in a predator-prey discrete model of logistic type

International Nuclear Information System (INIS)

Lopez-Ruiz, Ricardo; Fournier-Prunaret, Daniele

2005-01-01

A cubic discrete coupled logistic equation is proposed to model the predator-prey problem. The coupling depends on the population size of both species and on a positive constant λ, which could depend on the prey reproduction rate and on the predator hunting strategy. Different dynamical regimes are obtained when λ is modified. For small λ, the species become extinct. For a bigger λ, the preys survive but the predators extinguish. Only when the prey population reaches a critical value then predators can coexist with preys. For increasing λ, a bistable regime appears where the populations apart of being stabilized in fixed quantities can present periodic, quasiperiodic and chaotic oscillations. Finally, bistability is lost and the system settles down in a steady state, or, for the biggest permitted λ, in an invariant curve. We also present the basins for the different regimes. The use of the critical curves lets us determine the influence of the zones with different number of first rank preimages in the bifurcation mechanisms of those basins

Controlling a Chaotic System through Control Parameter Self-Modulation

International Nuclear Information System (INIS)

Pastor, I.

1994-01-01

A method for obtaining active control of a chaotic system based on the modulation of a control parameter by adding to it a small perturbation proportional to one output signal is proposed. From a theoretical point of view, chaos can be stabilized in the framework of this method because small modifications of the vector field controlling the dynamics are allowed, and thus some of the previously oxi sting unstable periodic trajectories can be made stable. The method is much inspired on recent treatments of some related problems, and i t is compared with them. One of its most attractive features is that is should be very easy to implement it on real experiments. The method is tested on a system of ordinary differential equations model ling the coupling of two se If - oscillating electronic circuits (van der Pol oscillators). Some brief comments are made on the no possibility that it could be applied to complex spatio-temporal systems where multiple chaotic structures can coexist for some values of the control parameters. (Author) 28 refs

Controlling a Chaotic System through Control Parameter Self-Modulation

Energy Technology Data Exchange (ETDEWEB)

Pastor, I

1994-07-01

A method for obtaining active control of a chaotic system based on the modulation of a control parameter by adding to it a small perturbation proportional to one output signal is proposed. From a theoretical point of view, chaos can be stabilized in the framework of this method because small modifications of the vector field controlling the dynamics are allowed, and thus some of the previously oxi sting unstable periodic trajectories can be made stable. The method is much inspired on recent treatments of some related problems, and i t is compared with them. One of its most attractive features is that is should be very easy to implement it on real experiments. The method is tested on a system of ordinary differential equations model ling the coupling of two se If - oscillating electronic circuits (van der Pol oscillators). Some brief comments are made on the no possibility that it could be applied to complex spatio-temporal systems where multiple chaotic structures can coexist for some values of the control parameters. (Author) 28 refs.

A vast amount of various invariant tori in the Nosé-Hoover oscillator.

Science.gov (United States)

Wang, Lei; Yang, Xiao-Song

2015-12-01

This letter restudies the Nosé-Hoover oscillator. Some new averagely conservative regions are found, each of which is filled with different sequences of nested tori with various knot types. Especially, the dynamical behaviors near the border of "chaotic region" and conservative regions are studied showing that there exist more complicated and thinner invariant tori around the boundaries of conservative regions bounded by tori. Our results suggest an infinite number of island chains in a "chaotic sea" for the Nosé-Hoover oscillator.

A vast amount of various invariant tori in the Nosé-Hoover oscillator

Science.gov (United States)

Wang, Lei; Yang, Xiao-Song

2015-12-01

This letter restudies the Nosé-Hoover oscillator. Some new averagely conservative regions are found, each of which is filled with different sequences of nested tori with various knot types. Especially, the dynamical behaviors near the border of "chaotic region" and conservative regions are studied showing that there exist more complicated and thinner invariant tori around the boundaries of conservative regions bounded by tori. Our results suggest an infinite number of island chains in a "chaotic sea" for the Nosé-Hoover oscillator.

Realization of Electronically Tunable Current- Mode Multiphase Sinusoidal Oscillators Using CFTAs

OpenAIRE

Prungsak Uttaphut

2012-01-01

An implementation of current-mode multiphase sinusoidal oscillators is presented. Using CFTA-based lossy integrators, odd and odd/even phase systems can be realized with following advantages. The condition of oscillation and frequency of oscillation can be orthogonally tuned. The high output impedances facilitate easy driving an external load without additional current buffers. The proposed MSOs provide odd or even phase signals that are equally spaced in phase and equal amplitude. The circui...

Chaotic expression dynamics implies pluripotency: when theory and experiment meet

Directory of Open Access Journals (Sweden)

Furusawa Chikara

2009-05-01

Full Text Available Abstract Background During normal development, cells undergo a unidirectional course of differentiation that progressively decreases the number of cell types they can potentially become. Pluripotent stem cells can differentiate into several types of cells, but terminally differentiated cells cannot differentiate any further. A fundamental problem in stem cell biology is the characterization of the difference in cellular states, e.g., gene expression profiles, between pluripotent stem cells and terminally differentiated cells. Presentation of the hypothesis To address the problem, we developed a dynamical systems model of cells with intracellular protein expression dynamics and interactions with each other. According to extensive simulations, cells with irregular (chaotic oscillations in gene expression dynamics have the potential to differentiate into other cell types. During development, such complex oscillations are lost successively, leading to a loss of pluripotency. These simulation results, together with recent single-cell-level measurements in stem cells, led us to the following hypothesis regarding pluripotency: Chaotic oscillation in the expression of some genes leads to cell pluripotency and affords cellular state heterogeneity, which is supported by itinerancy over quasi-stable states. Differentiation stabilizes these states, leading to a loss of pluripotency. Testing the hypothesis To test the hypothesis, it is crucial to measure the time course of gene expression levels at the single-cell level by fluorescence microscopy and fluorescence-activated cell sorting (FACS analysis. By analyzing the time series of single-cell-level expression data, one can distinguish whether the variation in protein expression level over time is due only to stochasticity in expression dynamics or originates from the chaotic dynamics inherent to cells, as our hypothesis predicts. By further analyzing the expression in differentiated cell types, one can

Oscillating field current drive for reversed field pinch discharges

International Nuclear Information System (INIS)

Schoenberg, K.F.; Gribble, R.F.; Baker, D.A.

1984-06-01

Oscillating Field Current Drive (OFCD), also known as F-THETA pumping, is a steady-state current-drive technique proposed for the Reversed Field Pinch (RFP). Unlike other current-drive techniques, which employ high-technology, invasive, and power intensive schemes using radio frequency or neutral particle injection, F-THETA pumping entails driving the toroidal and poloidal magnetic field circuits with low-frequency (audio) oscillating voltage sources. Current drive by this technique is a consequence of the strong nonlinear plasma coupling in the RFP. Because of its low frequency and efficient plasma coupling, F-THETA pumping shows excellent promise as a reactor-relevant current-drive technique. A conceptual and computational study of this concept, including its experimental and reactor relevance, is explored in this paper

Saturation and oscillation of current in semiconductors subjected to uniaxial deformation

International Nuclear Information System (INIS)

Zdebskii, A.P.; Olikh, Yu.A.; Savchuk, A.U.

1985-01-01

The influence of an external uniaxial deformation on the saturation and oscillations of current in photosensitive CdS monocrystals is investigated. The specimens were subjected to uniaxial pressure up to 6 x 10 7 N/m 2 , the pressure being either parallel or perpendicular to the c axis in CdS. With application of external pressure, the shape of current oscillations and their amplitude changed. In the case where the pressure was perpendicular to the direction of current I, the amplitude of oscillations and the saturation depth of the volt-ampere characteristic, VAC, were increased. With pressure being parallel to the current direction, the reverse phenomenon was observed, i.e. the efficiency of the acousto-electronic interaction was reduced

Two-dimensional collective electron magnetotransport, oscillations, and chaos in a semiconductor superlattice.

Science.gov (United States)

Bonilla, L L; Carretero, M; Segura, A

2017-12-01

When quantized, traces of classically chaotic single-particle systems include eigenvalue statistics and scars in eigenfuntions. Since 2001, many theoretical and experimental works have argued that classically chaotic single-electron dynamics influences and controls collective electron transport. For transport in semiconductor superlattices under tilted magnetic and electric fields, these theories rely on a reduction to a one-dimensional self-consistent drift model. A two-dimensional theory based on self-consistent Boltzmann transport does not support that single-electron chaos influences collective transport. This theory agrees with existing experimental evidence of current self-oscillations, predicts spontaneous collective chaos via a period doubling scenario, and could be tested unambiguously by measuring the electric potential inside the superlattice under a tilted magnetic field.

Two-dimensional collective electron magnetotransport, oscillations, and chaos in a semiconductor superlattice

Science.gov (United States)

Bonilla, L. L.; Carretero, M.; Segura, A.

2017-12-01

When quantized, traces of classically chaotic single-particle systems include eigenvalue statistics and scars in eigenfuntions. Since 2001, many theoretical and experimental works have argued that classically chaotic single-electron dynamics influences and controls collective electron transport. For transport in semiconductor superlattices under tilted magnetic and electric fields, these theories rely on a reduction to a one-dimensional self-consistent drift model. A two-dimensional theory based on self-consistent Boltzmann transport does not support that single-electron chaos influences collective transport. This theory agrees with existing experimental evidence of current self-oscillations, predicts spontaneous collective chaos via a period doubling scenario, and could be tested unambiguously by measuring the electric potential inside the superlattice under a tilted magnetic field.

Intermittent Chaos in the Bray-Liebhafsky Oscillator. Dependence of Dynamic States on the Iodate Concentration

Science.gov (United States)

Bubanja, I. N.; Ivanović-Šašić, A.; Čupić, Ž.; Anić, S.; Kolar-Anić, Lj.

2017-12-01

Chaotic dynamic states with intermittent oscillations were generated in a Bray-Liebhafsky (BL) oscillatory reaction in an isothermal open reactor i.e., in the continuously-fed well-stirred tank reactor (CSTR) when the inflow concentration of potassium iodate was the control parameter. They are found between periodic oscillations obtained when [KIO3]0 4.10 × 10-2 M. It was shown that the most chaotic states obtained experimentally somewhere in the middle of this region are in high correlation with results obtained by means of largest Lyapunov exponents and phenomenological analysis based on the quantitative characteristics of intermittent oscillations.

A vast amount of various invariant tori in the Nosé-Hoover oscillator

Energy Technology Data Exchange (ETDEWEB)

Wang, Lei [School of Mathematics and Statistics, Huazhong University of Science and Technology, Wuhan 430074 (China); Department of Mathematics and Physics, Hefei University, Hefei 230601 (China); Yang, Xiao-Song, E-mail: yangxs@hust.edu.cn [School of Mathematics and Statistics, Huazhong University of Science and Technology, Wuhan 430074 (China)

2015-12-15

This letter restudies the Nosé-Hoover oscillator. Some new averagely conservative regions are found, each of which is filled with different sequences of nested tori with various knot types. Especially, the dynamical behaviors near the border of “chaotic region” and conservative regions are studied showing that there exist more complicated and thinner invariant tori around the boundaries of conservative regions bounded by tori. Our results suggest an infinite number of island chains in a “chaotic sea” for the Nosé-Hoover oscillator.

Tool Wear Detection Based on Duffing-Holmes Oscillator

Directory of Open Access Journals (Sweden)

Wanqing Song

2008-01-01

Full Text Available The cutting sound in the audible range includes plenty of tool wear information. The sound is sampled by the acoustic emission (AE sensor as a short-time sequence, then worn wear can be detected by the Duffing-Holmes oscillator. A novel engineering method is proposed for determining the chaotic threshold of the Duffing-Holmes oscillator. First, a rough threshold value is calculated by local Lyapunov exponents with a step size 0.1. Second, the exact threshold value is calculated by the Duffing-Holmes system in terms of the law of the golden section. The advantage of the method is low computation cost. The feasibility for tool condition detection is demonstrated by the 27 kinds of cutting conditions with sharp tool and worn tool in turning experiments. The 54 group data sampled as noisy are embedded into the Duffing-Holmes oscillator, respectively. Finally, one chaotic threshold is determined conveniently which can distinguish between worn tool or sharp tool.

Nonlinear dynamics of a magnetically driven Duffing-type spring–magnet oscillator in the static magnetic field of a coil

International Nuclear Information System (INIS)

Donoso, Guillermo; Ladera, Celso L

2012-01-01

We study the nonlinear oscillations of a forced and weakly dissipative spring–magnet system moving in the magnetic fields of two fixed coaxial, hollow induction coils. As the first coil is excited with a dc current, both a linear and a cubic magnet-position dependent force appear on the magnet–spring system. The second coil, located below the first, excited with an ac current, provides the oscillating magnetic driving force on the system. From the magnet–coil interactions, we obtain, analytically, the nonlinear motion equation of the system, found to be a forced and damped cubic Duffing oscillator moving in a quartic potential. The relative strengths of the coefficients of the motion equation can be easily set by varying the coils’ dc and ac currents. We demonstrate, theoretically and experimentally, the nonlinear behaviour of this oscillator, including its oscillation modes and nonlinear resonances, the fold-over effect, the hysteresis and amplitude jumps, and its chaotic behaviour. It is an oscillating system suitable for teaching an advanced experiment in nonlinear dynamics both at senior undergraduate and graduate levels. (paper)

Control uncertain Genesio-Tesi chaotic system: Adaptive sliding mode approach

International Nuclear Information System (INIS)

Dadras, Sara; Momeni, Hamid Reza

2009-01-01

An adaptive sliding mode control (ASMC) technique is introduced in this paper for a chaotic dynamical system (Genesio-Tesi system). Using the sliding mode control technique, a sliding surface is determined and the control law is established. An adaptive sliding mode control law is derived to make the states of the Genesio-Tesi system asymptotically track and regulate the desired state. The designed control scheme can control the uncertain chaotic behaviors to a desired state without oscillating very fast and guarantee the property of asymptotical stability. An illustrative simulation result is given to demonstrate the effectiveness of the proposed adaptive sliding mode control design.

Analysis of the time structure of synchronization in multidimensional chaotic systems

Energy Technology Data Exchange (ETDEWEB)

Makarenko, A. V., E-mail: avm.science@mail.ru [Constructive Cybernetics Research Group (Russian Federation)

2015-05-15

A new approach is proposed to the integrated analysis of the time structure of synchronization of multidimensional chaotic systems. The method allows one to diagnose and quantitatively evaluate the intermittency characteristics during synchronization of chaotic oscillations in the T-synchronization mode. A system of two identical logistic mappings with unidirectional coupling that operate in the developed chaos regime is analyzed. It is shown that the widely used approach, in which only synchronization patterns are subjected to analysis while desynchronization areas are considered as a background signal and removed from analysis, should be regarded as methodologically incomplete.

Analysis of the time structure of synchronization in multidimensional chaotic systems

International Nuclear Information System (INIS)

Makarenko, A. V.

2015-01-01

A new approach is proposed to the integrated analysis of the time structure of synchronization of multidimensional chaotic systems. The method allows one to diagnose and quantitatively evaluate the intermittency characteristics during synchronization of chaotic oscillations in the T-synchronization mode. A system of two identical logistic mappings with unidirectional coupling that operate in the developed chaos regime is analyzed. It is shown that the widely used approach, in which only synchronization patterns are subjected to analysis while desynchronization areas are considered as a background signal and removed from analysis, should be regarded as methodologically incomplete

Resonant geomagnetic field oscillations and Birkeland currents in the morning sector

International Nuclear Information System (INIS)

Potemra, T.A.; Zanetti, L.J.; Bythrow, P.F.; Erlandson, R.E.; Lundin, R.; Marklund, G.T.; Block, L.P.; Lindqvist, P.A.

1988-01-01

Magnetic field, electric field, and particle measurements acquired by the Viking satellite and magnetic field measurements acquired by the Active Magnetosphere Particle Tracer Explorers (AMPTE) CCE satellite have been used to study the relationship between large-scale Birkeland currents and resonant oscillations in the Earth's magnetic field. Region 1, region 2, and northward B Z (NBZ) Birkeland currents were identified with the data acquired by the Viking magnetic field instrument. Magnetic field oscillations, present in each of the 10 consecutive Viking passes studied here, have periods between 1 min. and 6 min. and amplitudes from 5 nT to 60 nT. These oscillations extend from lower L shells where they correlate with the CCCE observations up to at least the interface between the region 1 and region 2 Birkeland current system. The Viking particle observations confirm that the region 1/region 2 interface maps closely to the interface between the low-latitude boundary layer (LLBL) and the central plasma sheet (CPS). Electric and magnetic field variations are closely correlated in the region 1 Birkeland current. In the region 2 system of Birkeland currents, the northward electric and eastward magnetic field components show the same resonance oscillations with the electric field variations leading the magnetic field by approximately 90 degree. There is evidence that the amplitudes of the oscillations observed by Viking are correlated with interplanetary magnetic field (IMF) cone angle. In one case, the energy-time dispersion signature of temporal magnetosheath plasma injection into the low-latitude boundary layer was associated with the resonant oscillations. These relationships and the presence of the resonant oscillations on field lines up to the region 1/region 2 (LLBL/CPS) interface lead us to conclude that there are several features in the solar wind and the direction of the IMF that can initiate magnetospheric pulsations

Chaotic jumps in the generalized first adiabatic invariant in current sheets

International Nuclear Information System (INIS)

Brittnacher, M.J.; Whipple, E.C.

1991-01-01

In attempting to develop a fluidlike model of plasma dynamics in a current sheet, kinetic effects due to chaotic non-adiabatic particle motion must be included in any realistic description. Using drift variables, derived by the Kruskal averaging procedure, to construct distribution functions may provide an approach in which to develop the fluid description. However, the drift motion is influenced by abrupt changes in the value of the generalized first adiabatic invariant J. In this letter, the authors indicate how the changes in J derived from separatrix crossing theory can be incorporated into the drift variable approach to generating distribution functions. In particular, the authors propose a method to determine distribution functions for an ensemble of particles following interactions with the tail current sheet by treating the interaction as a scattering problem characterized by changes in the invariant

Synchronization of identical chaotic systems through external chaotic driving

International Nuclear Information System (INIS)

Patidar, V.; Sud, K.K.

2005-11-01

In recent years, the study of synchronization of identical chaotic systems subjected to a common fluctuating random driving signal has drawn considerable interest. In this communication, we report that it is possible to achieve synchronization between two identical chaotic systems, which are not coupled directly but subjected to an external chaotic signal. The external chaotic signal may be obtained from any chaotic system identical or non-identical to both identical chaotic systems. Results of numerical simulations on well known Roessler and jerk dynamical systems have been presented. (author)

Magnetization oscillations and waves driven by pure spin currents

Energy Technology Data Exchange (ETDEWEB)

Demidov, V.E. [Institute for Applied Physics and Center for Nanotechnology, University of Muenster, Corrensstrasse 2-4, 48149 Muenster (Germany); Urazhdin, S. [Department of Physics, Emory University, Atlanta, GA 30322 (United States); Loubens, G. de [SPEC, CEA, CNRS, Université Paris-Saclay, CEA Saclay, 91191 Gif-sur-Yvette (France); Klein, O. [INAC-SPINTEC, CEA/CNRS and Univ. Grenoble Alpes, 38000 Grenoble (France); Cros, V.; Anane, A. [Unité Mixte de Physique CNRS, Thales, Univ. Paris Sud, Université Paris-Saclay, 91767 Palaiseau (France); Demokritov, S.O., E-mail: demokrit@uni-muenster.de [Institute for Applied Physics and Center for Nanotechnology, University of Muenster, Corrensstrasse 2-4, 48149 Muenster (Germany); Institute of Metal Physics, Ural Division of RAS, Yekaterinburg 620041 (Russian Federation)

2017-02-23

Recent advances in the studies of pure spin currents–flows of angular momentum (spin) not accompanied by the electric currents–have opened new horizons for the emerging technologies based on the electron’s spin degree of freedom, such as spintronics and magnonics. The main advantage of pure spin current, as compared to the spin-polarized electric current, is the possibility to exert spin transfer torque on the magnetization in thin magnetic films without the electrical current flow through the material. In addition to minimizing Joule heating and electromigration effects, this enables the implementation of spin torque devices based on the low-loss insulating magnetic materials, and offers an unprecedented geometric flexibility. Here we review the recent experimental achievements in investigations of magnetization oscillations excited by pure spin currents in different nanomagnetic systems based on metallic and insulating magnetic materials. We discuss the spectral properties of spin-current nano-oscillators, and relate them to the spatial characteristics of the excited dynamic magnetic modes determined by the spatially-resolved measurements. We also show that these systems support locking of the oscillations to external microwave signals, as well as their mutual synchronization, and can be used as efficient nanoscale sources of propagating spin waves.

Probing and exploiting the chaotic dynamics of a hydrodynamic photochemical oscillator to implement all the basic binary logic functions

Energy Technology Data Exchange (ETDEWEB)

Hayashi, Kenta [Department of Mechanical Engineering, Ritsumeikan University, 1-1-1 Nojihigashi, Kusatsu-shi, Shiga 525-8577 (Japan); Department of Chemistry, Biology, and Biotechnology, University of Perugia, 06123 Perugia (Italy); Gotoda, Hiroshi [Department of Mechanical Engineering, Tokyo University of Science, 6-3-1 Niijuku, Katsushika-ku, Tokyo 125-8585 (Japan); Gentili, Pier Luigi, E-mail: pierluigi.gentili@unipg.it [Department of Chemistry, Biology, and Biotechnology, University of Perugia, 06123 Perugia (Italy)

2016-05-15

The convective motions within a solution of a photochromic spiro-oxazine being irradiated by UV only on the bottom part of its volume, give rise to aperiodic spectrophotometric dynamics. In this paper, we study three nonlinear properties of the aperiodic time series: permutation entropy, short-term predictability and long-term unpredictability, and degree distribution of the visibility graph networks. After ascertaining the extracted chaotic features, we show how the aperiodic time series can be exploited to implement all the fundamental two-inputs binary logic functions (AND, OR, NAND, NOR, XOR, and XNOR) and some basic arithmetic operations (half-adder, full-adder, half-subtractor). This is possible due to the wide range of states a nonlinear system accesses in the course of its evolution. Therefore, the solution of the convective photochemical oscillator results in hardware for chaos-computing alternative to conventional complementary metal-oxide semiconductor-based integrated circuits.

Digital chaotic sequence generator based on coupled chaotic systems

International Nuclear Information System (INIS)

Shu-Bo, Liu; Jing, Sun; Jin-Shuo, Liu; Zheng-Quan, Xu

2009-01-01

Chaotic systems perform well as a new rich source of cryptography and pseudo-random coding. Unfortunately their digital dynamical properties would degrade due to the finite computing precision. Proposed in this paper is a modified digital chaotic sequence generator based on chaotic logistic systems with a coupling structure where one chaotic subsystem generates perturbation signals to disturb the control parameter of the other one. The numerical simulations show that the length of chaotic orbits, the output distribution of chaotic system, and the security of chaotic sequences have been greatly improved. Moreover the chaotic sequence period can be extended at least by one order of magnitude longer than that of the uncoupled logistic system and the difficulty in decrypting increases 2 128 *2 128 times indicating that the dynamical degradation of digital chaos is effectively improved. A field programmable gate array (FPGA) implementation of an algorithm is given and the corresponding experiment shows that the output speed of the generated chaotic sequences can reach 571.4 Mbps indicating that the designed generator can be applied to the real-time video image encryption. (general)

Attractors of relaxation discrete-time systems with chaotic dynamics on a fast time scale

International Nuclear Information System (INIS)

Maslennikov, Oleg V.; Nekorkin, Vladimir I.

2016-01-01

In this work, a new type of relaxation systems is considered. Their prominent feature is that they comprise two distinct epochs, one is slow regular motion and another is fast chaotic motion. Unlike traditionally studied slow-fast systems that have smooth manifolds of slow motions in the phase space and fast trajectories between them, in this new type one observes, apart the same geometric objects, areas of transient chaos. Alternating periods of slow regular motions and fast chaotic ones as well as transitions between them result in a specific chaotic attractor with chaos on a fast time scale. We formulate basic properties of such attractors in the framework of discrete-time systems and consider several examples. Finally, we provide an important application of such systems, the neuronal electrical activity in the form of chaotic spike-burst oscillations.

Qualitative identification of chaotic systems behaviours

International Nuclear Information System (INIS)

Vicha, T.; Dohnal, M.

2008-01-01

There are only three qualitative values positive, negative and zero. This means that there is a maximal number of qualitatively distinguishable scenarios, prescribed by the number of variables and the highest qualitative derivative taken into consideration. There are several chaos related tasks, which can be solved with great difficulties on the numerical level if multidimensional problems are studied. One of them is the identification of all qualitatively different behaviours. To make sure that all distinctive qualitative scenarios are identified a qualitative interpretation of a classical quantitative phase portrait is used. The highest derivatives are usually the second derivatives as it is not possible to safely identify higher derivatives if tasks related to ecology or economics are studied. Two classical models are discussed - Damped oscillation (non chaotic) and Lorenz model (chaotic). There are 191 scenarios of the Lorenz model if only the second derivatives are considered. If the third derivatives are taken into consideration then the number of scenarios is 2619. Complete qualitative results are given in details

Fully digital jerk-based chaotic oscillators for high throughput pseudo-random number generators up to 8.77Gbits/s

KAUST Repository

Mansingka, Abhinav S.

2014-06-18

This paper introduces fully digital implementations of four di erent systems in the 3rd order jerk-equation based chaotic family using the Euler approximation. The digitization approach enables controllable chaotic systems that reliably provide sinusoidal or chaotic output based on a selection input. New systems are introduced, derived using logical and arithmetic operations between two system implementations of different bus widths, with up to 100x higher maximum Lyapunov exponent than the original jerkequation based chaotic systems. The resulting chaotic output is shown to pass the NIST sp. 800-22 statistical test suite for pseudorandom number generators without post-processing by only eliminating the statistically defective bits. The systems are designed in Verilog HDL and experimentally verified on a Xilinx Virtex 4 FPGA for a maximum throughput of 15.59 Gbits/s for the native chaotic output and 8.77 Gbits/s for the resulting pseudo-random number generators.

Time-delay-induced amplitude death in chaotic map lattices and its avoiding control

International Nuclear Information System (INIS)

Konishi, Keiji; Kokame, Hideki

2007-01-01

The present Letter deals with amplitude death in chaotic map lattices coupled with a diffusive delay connection. It is shown that if a fixed point of the individual map satisfies an odd-number property, then amplitude death never occurs at the fixed point for any number of the maps, coupling strength, and delay time. From the viewpoint of engineering applications that utilize oscillatory behavior in coupled oscillators, death would be undesirable. This Letter proposes a feedback controller, which is added to each chaotic map, such that the fixed point of the individual map satisfies the odd-number property. Accordingly, it is guaranteed that death never occurs in the controlled chaotic-map-lattice. It is verified that the proposed controller works well in numerical simulations

Control of partial synchronization in chaotic oscillators

Indian Academy of Sciences (India)

2015-02-07

Feb 7, 2015 ... other real systems such as the brain network or the power grid, where multiple ..... 2D attractors of the driver oscillator (x2 vs. x3 plot) in the left and the response (y2 vs. y3 plot) in the right are given in the uppermost panels.

Chaotic synchronization of symbolic information in the discrete nonlinear Schroedinger equation

International Nuclear Information System (INIS)

Pando L, C.L.

2003-08-01

We have studied the discrete nonlinear Schrodinger equation (DNLSE) with on-site defects and periodic boundary conditions. When the array dynamics becomes chaotic, the otherwise quasiperiodic amplitude correlations between the oscillators are destroyed. However, we show that synchronization of symbolic information of suitable amplitude signals is possible in this hamiltonian system. (author)

Synchronization of complex chaotic systems in series expansion form

International Nuclear Information System (INIS)

Ge Zhengming; Yang Chenghsiung

2007-01-01

This paper studies the synchronization of complex chaotic systems in series expansion form by Lyapunov asymptotical stability theorem. A sufficient condition is given for the asymptotical stability of an error dynamics, and is applied to guiding the design of the secure communication. Finally, numerical results are studied for the Quantum-CNN oscillators synchronizing with unidirectional/bidirectional linear coupling to show the effectiveness of the proposed synchronization strategy

Chaotic behaviour of an electrical analogue to the mechanical double pendulum

Directory of Open Access Journals (Sweden)

M. P. Hanias

2008-02-01

Full Text Available In this paper the analogy between a mechanical double pendulum and an oscillating electrical system is presented. Instead of using analytic equations, we used the MultiSim circuit simulation environment in order to reproduce and interpret the response of the electrical oscillator. The electrical double pendulum presents a chaotic regime which is studied quantita-tively by means of state space reconstruction. For this purpose the optimal delay time is calculated and the minimum em-bedding dimension is found with the method of False Nearest Neighbors.

Titanium nitride coatings synthesized by IPD method with eliminated current oscillations

Directory of Open Access Journals (Sweden)

Chodun Rafał

2016-09-01

Full Text Available This paper presents the effects of elimination of current oscillations within the coaxial plasma accelerator during IPD deposition process on the morphology, phase structure and properties of synthesized TiN coatings. Current observations of waveforms have been made by use of an oscilloscope. As a test material for experiments, titanium nitride TiN coatings synthesized on silicon and high-speed steel substrates were used. The coatings morphology, phase composition and wear resistance properties were determined. The character of current waveforms in the plasma accelerator electric circuit plays a crucial role during the coatings synthesis process. Elimination of the current oscillations leads to obtaining an ultrafine grained structure of titanium nitride coatings and to disappearance of the tendency to structure columnarization. The coatings obtained during processes of a non-oscillating character are distinguished by better wear-resistance properties.

Robust state feedback controller design of STATCOM using chaotic optimization algorithm

Directory of Open Access Journals (Sweden)

Safari Amin

2010-01-01

Full Text Available In this paper, a new design technique for the design of robust state feedback controller for static synchronous compensator (STATCOM using Chaotic Optimization Algorithm (COA is presented. The design is formulated as an optimization problem which is solved by the COA. Since chaotic planning enjoys reliability, ergodicity and stochastic feature, the proposed technique presents chaos mapping using Lozi map chaotic sequences which increases its convergence rate. To ensure the robustness of the proposed damping controller, the design process takes into account a wide range of operating conditions and system configurations. The simulation results reveal that the proposed controller has an excellent capability in damping power system low frequency oscillations and enhances greatly the dynamic stability of the power systems. Moreover, the system performance analysis under different operating conditions shows that the phase based controller is superior compare to the magnitude based controller.

Different types of bursting calcium oscillations in non-excitable cells

International Nuclear Information System (INIS)

Perc, Matjaz; Marhl, Marko

2003-01-01

In the paper different types of bursting Ca 2+ oscillations are presented. We analyse bursting behaviour in four recent mathematical models for Ca 2+ oscillations in non-excitable cells. Separately, regular, quasi-periodic, and chaotic bursting Ca 2+ oscillations are classified into several subtypes. The classification is based on the dynamics of separated fast and slow subsystems, the so-called fast-slow burster analysis. For regular bursting Ca 2+ oscillations two types of bursting are specified: Point-Point and Point-Cycle bursting. In particular, the slow passage effect, important for the Hopf-Hopf and SubHopf-SubHopf bursting subtypes, is explained by local divergence calculated for the fast subsystem. Quasi-periodic bursting Ca 2+ oscillations can be found in only one of the four studied mathematical models and appear via a homoclinic bifurcation with a homoclinic torus structure. For chaotic bursting Ca 2+ oscillations, we found that bursting patterns resulting from the period doubling root to chaos considerably differ from those appearing via intermittency and have to be treated separately. The analysis and classification of different types of bursting Ca 2+ oscillations provides better insight into mechanisms of complex intra- and intercellular Ca 2+ signalling. This improves our understanding of several important biological phenomena in cellular signalling like complex frequency-amplitude signal encoding and synchronisation of intercellular signal transduction between coupled cells in tissue

Persistent chimera states in nonlocally coupled phase oscillators

OpenAIRE

Suda, Yusuke; Okuda, Koji

2015-01-01

Chimera states in the systems of nonlocally coupled phase oscillators are considered stable in the continuous limit of spatially distributed oscillators. However, it is reported that in the numerical simulations without taking such limit, chimera states are chaotic transient and finally collapse into the completely synchronous solution. In this Rapid Communication, we numerically study chimera states by using the coupling function different from the previous studies and obtain the result that...

Applications of chaotic neurodynamics in pattern recognition

Science.gov (United States)

Baird, Bill; Freeman, Walter J.; Eeckman, Frank H.; Yao, Yong

1991-08-01

Network algorithms and architectures for pattern recognition derived from neural models of the olfactory system are reviewed. These span a range from highly abstract to physiologically detailed, and employ the kind of dynamical complexity observed in olfactory cortex, ranging from oscillation to chaos. A simple architecture and algorithm for analytically guaranteed associative memory storage of analog patterns, continuous sequences, and chaotic attractors in the same network is described. A matrix inversion determines network weights, given prototype patterns to be stored. There are N units of capacity in an N node network with 3N2 weights. It costs one unit per static attractor, two per Fourier component of each sequence, and three to four per chaotic attractor. There are no spurious attractors, and for sequences there is a Liapunov function in a special coordinate system which governs the approach of transient states to stored trajectories. Unsupervised or supervised incremental learning algorithms for pattern classification, such as competitive learning or bootstrap Widrow-Hoff can easily be implemented. The architecture can be ''folded'' into a recurrent network with higher order weights that can be used as a model of cortex that stores oscillatory and chaotic attractors by a Hebb rule. Network performance is demonstrated by application to the problem of real-time handwritten digit recognition. An effective system with on-line learning has been written by Eeckman and Baird for the Macintosh. It utilizes static, oscillatory, and/or chaotic attractors of two kinds--Lorenze attractors, or attractors resulting from chaotically interacting oscillatory modes. The successful application to an industrial pattern recognition problem of a network architecture of considerable physiological and dynamical complexity, developed by Freeman and Yao, is described. The data sets of the problem come in three classes of difficulty, and performance of the biological network is

Chaotic universe model.

Science.gov (United States)

Aydiner, Ekrem

2018-01-15

In this study, we consider nonlinear interactions between components such as dark energy, dark matter, matter and radiation in the framework of the Friedman-Robertson-Walker space-time and propose a simple interaction model based on the time evolution of the densities of these components. By using this model we show that these interactions can be given by Lotka-Volterra type equations. We numerically solve these coupling equations and show that interaction dynamics between dark energy-dark matter-matter or dark energy-dark matter-matter-radiation has a strange attractor for 0 > w de  >-1, w dm  ≥ 0, w m  ≥ 0 and w r  ≥ 0 values. These strange attractors with the positive Lyapunov exponent clearly show that chaotic dynamics appears in the time evolution of the densities. These results provide that the time evolution of the universe is chaotic. The present model may have potential to solve some of the cosmological problems such as the singularity, cosmic coincidence, big crunch, big rip, horizon, oscillation, the emergence of the galaxies, matter distribution and large-scale organization of the universe. The model also connects between dynamics of the competing species in biological systems and dynamics of the time evolution of the universe and offers a new perspective and a new different scenario for the universe evolution.

Current oscillations, interacting Hall discs and boundary CFTs

International Nuclear Information System (INIS)

Balachandran, A.P.; Vaidya, S.; Bimonte, G.; Govindarajan, T.R.; Gupta, K.S.; John, V.

1998-12-01

In this paper, we discuss the behavior of conformal field theories interacting at a single point. The edge states of the quantum Hall effect (QHE) system gives rise to a particular representation of a chiral Kac-Moody current algebra. We show that in the case of QHE systems interacting at one point we obtain a 'twisted' representation of the current algebra. The condition for stationarity of currents is the same as the classical Kirchoff's law applied to the currents at the interaction point. We find that in the case of two discs touching at one point, since the currents are chiral, they are not stationary and one obtains current oscillations between the two discs. We determine the frequency of these oscillations in terms of an effective parameter characterizing the interactions. The chiral conformal field theories can be represented in terms of bosonic Lagrangians with a boundary interaction. We discuss how these one point interactions can be represented as boundary conditions on fields, and how the requirement of chirality leads to restrictions on the interactions described by these Lagrangians. By gauging these models we find that the theory is naturally coupled to a Chern-Simons gauge theory in 2+1 dimensions, and this coupling is completely determined by the requirement of anomaly cancellation. (author)

Experimentally determined chaotic phase synchronization in a neuronal system

OpenAIRE

Makarenko, Vladimir; Llinás, Rodolfo

1998-01-01

Mathematical analysis of the subthreshold oscillatory properties of inferior olivary neurons in vitro indicates that the oscillation is nonlinear and supports low dimensional chaotic dynamics. This property leads to the generation of complex functional states that can be attained rapidly via phase coherence that conform to the category of “generalized synchronization.” Functionally, this translates into neuronal ensemble properties that can support maximum functional permissiveness and that r...

Synchronization of chaotic systems involving fractional operators of Liouville-Caputo type with variable-order

Science.gov (United States)

Coronel-Escamilla, A.; Gómez-Aguilar, J. F.; Torres, L.; Escobar-Jiménez, R. F.; Valtierra-Rodríguez, M.

2017-12-01

In this paper, we propose a state-observer-based approach to synchronize variable-order fractional (VOF) chaotic systems. In particular, this work is focused on complete synchronization with a so-called unidirectional master-slave topology. The master is described by a dynamical system in state-space representation whereas the slave is described by a state observer. The slave is composed of a master copy and a correction term which in turn is constituted of an estimation error and an appropriate gain that assures the synchronization. The differential equations of the VOF chaotic system are described by the Liouville-Caputo and Atangana-Baleanu-Caputo derivatives. Numerical simulations involving the synchronization of Rössler oscillators, Chua's systems and multi-scrolls are studied. The simulations show that different chaotic behaviors can be obtained if different smooths functions defined in the interval (0 , 1 ] are used as the variable order of the fractional derivatives. Furthermore, simulations show that the VOF chaotic systems can be synchronized.

Quantization of a free particle interacting linearly with a harmonic oscillator

International Nuclear Information System (INIS)

Mainiero, Thomas; Porter, Mason A.

2007-01-01

We investigate the quantization of a free particle coupled linearly to a harmonic oscillator. This system, whose classical counterpart has clearly separated regular and chaotic regions, provides an ideal framework for studying the quantization of mixed systems. We identify key signatures of the classically chaotic and regular portions in the quantum system by constructing Husimi distributions and investigating avoided level crossings of eigenvalues as functions of the strength and range of the interaction between the system's two components. We show, in particular, that the Husimi structure becomes mixed and delocalized as the classical dynamics becomes more chaotic

Dynamical transitions in large systems of mean field-coupled Landau-Stuart oscillators: Extensive chaos and cluster states.

Science.gov (United States)

Ku, Wai Lim; Girvan, Michelle; Ott, Edward

2015-12-01

In this paper, we study dynamical systems in which a large number N of identical Landau-Stuart oscillators are globally coupled via a mean-field. Previously, it has been observed that this type of system can exhibit a variety of different dynamical behaviors. These behaviors include time periodic cluster states in which each oscillator is in one of a small number of groups for which all oscillators in each group have the same state which is different from group to group, as well as a behavior in which all oscillators have different states and the macroscopic dynamics of the mean field is chaotic. We argue that this second type of behavior is "extensive" in the sense that the chaotic attractor in the full phase space of the system has a fractal dimension that scales linearly with N and that the number of positive Lyapunov exponents of the attractor also scales linearly with N. An important focus of this paper is the transition between cluster states and extensive chaos as the system is subjected to slow adiabatic parameter change. We observe discontinuous transitions between the cluster states (which correspond to low dimensional dynamics) and the extensively chaotic states. Furthermore, examining the cluster state, as the system approaches the discontinuous transition to extensive chaos, we find that the oscillator population distribution between the clusters continually evolves so that the cluster state is always marginally stable. This behavior is used to reveal the mechanism of the discontinuous transition. We also apply the Kaplan-Yorke formula to study the fractal structure of the extensively chaotic attractors.

[Interdependence of plankton spatial distribution and plancton biomass temporal oscillations: mathematical simulation].

Science.gov (United States)

Medvedinskiĭ, A B; Tikhonova, I A; Li, B L; Malchow, H

2003-01-01

The dynamics of aquatic biological communities in a patchy environment is of great interest in respect to interrelations between phenomena at various spatial and time scales. To study the complex plankton dynamics in relation to variations of such a biologically essential parameter as the fish predation rate, we use a simple reaction-diffusion model of trophic interactions between phytoplankton, zooplankton, and fish. We suggest that plankton is distributed between two habitats one of which is fish-free due to hydrological inhomogeneity, while the other is fish-populated. We show that temporal variations in the fish predation rate do not violate the strong correspondence between the character of spatial distribution of plankton and changes of plankton biomass in time: regular temporal oscillations of plankton biomass correspond to large-scale plankton patches, while chaotic oscillations correspond to small-scale plankton patterns. As in the case of the constant fish predation rate, the chaotic plankton dynamics is characterized by coexistence of the chaotic attractor and limit cycle.

Competitive Modes for the Detection of Chaotic Parameter Regimes in the General Chaotic Bilinear System of Lorenz Type

Science.gov (United States)

Mallory, Kristina; van Gorder, Robert A.

We study chaotic behavior of solutions to the bilinear system of Lorenz type developed by Celikovsky and Vanecek [1994] through an application of competitive modes. This bilinear system of Lorenz type is one possible canonical form holding the Lorenz equation as a special case. Using a competitive modes analysis, which is a completely analytical method allowing one to identify parameter regimes for which chaos may occur, we are able to demonstrate a number of parameter regimes which admit a variety of distinct chaotic behaviors. Indeed, we are able to draw some interesting conclusions which relate the behavior of the mode frequencies arising from writing the state variables for the Celikovsky-Vanecek model as coupled oscillators, and the types of emergent chaotic behaviors observed. The competitive modes analysis is particularly useful if all but one of the model parameters are fixed, and the remaining free parameter is used to modify the chaos observed, in a manner analogous to a bifurcation parameter. Through a thorough application of the method, we are able to identify several parameter regimes which give new dynamics (such as specific forms of chaos) which were not observed or studied previously in the Celikovsky-Vanecek model. Therefore, the results demonstrate the advantage of the competitive modes approach for detecting new parameter regimes leading to chaos in third-order dynamical systems.

Targeting engineering synchronization in chaotic systems

Science.gov (United States)

Bhowmick, Sourav K.; Ghosh, Dibakar

2016-07-01

A method of targeting engineering synchronization states in two identical and mismatch chaotic systems is explained in detail. The method is proposed using linear feedback controller coupling for engineering synchronization such as mixed synchronization, linear and nonlinear generalized synchronization and targeting fixed point. The general form of coupling design to target any desire synchronization state under unidirectional coupling with the help of Lyapunov function stability theory is derived analytically. A scaling factor is introduced in the coupling definition to smooth control without any loss of synchrony. Numerical results are done on two mismatch Lorenz systems and two identical Sprott oscillators.

Transition from amplitude to oscillation death in a network of oscillators

International Nuclear Information System (INIS)

Nandan, Mauparna; Hens, C. R.; Dana, Syamal K.; Pal, Pinaki

2014-01-01

We report a transition from a homogeneous steady state (HSS) to inhomogeneous steady states (IHSSs) in a network of globally coupled identical oscillators. We perturb a synchronized population of oscillators in the network with a few local negative or repulsive mean field links. The whole population splits into two clusters for a certain number of repulsive mean field links and a range of coupling strength. For further increase of the strength of interaction, these clusters collapse into a HSS followed by a transition to IHSSs where all the oscillators populate either of the two stable steady states. We analytically determine the origin of HSS and its transition to IHSS in relation to the number of repulsive mean-field links and the strength of interaction using a reductionism approach to the model network. We verify the results with numerical examples of the paradigmatic Landau-Stuart limit cycle system and the chaotic Rössler oscillator as dynamical nodes. During the transition from HSS to IHSSs, the network follows the Turing type symmetry breaking pitchfork or transcritical bifurcation depending upon the system dynamics

Transition from amplitude to oscillation death in a network of oscillators

Energy Technology Data Exchange (ETDEWEB)

Nandan, Mauparna [Dr. B. C. Roy Engineering College, Durgapur 713206 (India); Department of Mathematics, National Institute of Technology, Durgapur 713209 (India); Hens, C. R.; Dana, Syamal K. [CSIR-Indian Institute of Chemical Biology, Jadavpur, Kolkata 700032 (India); Pal, Pinaki [Department of Mathematics, National Institute of Technology, Durgapur 713209 (India)

2014-12-01

We report a transition from a homogeneous steady state (HSS) to inhomogeneous steady states (IHSSs) in a network of globally coupled identical oscillators. We perturb a synchronized population of oscillators in the network with a few local negative or repulsive mean field links. The whole population splits into two clusters for a certain number of repulsive mean field links and a range of coupling strength. For further increase of the strength of interaction, these clusters collapse into a HSS followed by a transition to IHSSs where all the oscillators populate either of the two stable steady states. We analytically determine the origin of HSS and its transition to IHSS in relation to the number of repulsive mean-field links and the strength of interaction using a reductionism approach to the model network. We verify the results with numerical examples of the paradigmatic Landau-Stuart limit cycle system and the chaotic Rössler oscillator as dynamical nodes. During the transition from HSS to IHSSs, the network follows the Turing type symmetry breaking pitchfork or transcritical bifurcation depending upon the system dynamics.

Transition of chaotic motion to a limit cycle by intervention of economic policy: an empirical analysis in agriculture.

Science.gov (United States)

Sakai, Kenshi; Managi, Shunsuke; Vitanov, Nikolay K; Demura, Katsuhiko

2007-04-01

This paper investigates the transition of dynamics observed in an actual real agricultural economic dataset. Lyapunov spectrum analysis is conducted on the data to distinguish deterministic chaos and the limit cycle. Chaotic and periodic oscillation were identified before and after the second oil crisis, respectively. The statitonarity of the time series is investigated using recurrence plots. This shows that government intervention might reduce market instability by removing a chaotic market's long-term unpredictability.

Oscillation and chaos in physiological control systems.

Science.gov (United States)

Mackey, M C; Glass, L

1977-07-15

First-order nonlinear differential-delay equations describing physiological control systems are studied. The equations display a broad diversity of dynamical behavior including limit cycle oscillations, with a variety of wave forms, and apparently aperiodic or "chaotic" solutions. These results are discussed in relation to dynamical respiratory and hematopoietic diseases.

Connection adaption for control of networked mobile chaotic agents.

Science.gov (United States)

Zhou, Jie; Zou, Yong; Guan, Shuguang; Liu, Zonghua; Xiao, Gaoxi; Boccaletti, S

2017-11-22

In this paper, we propose a strategy for the control of mobile chaotic oscillators by adaptively rewiring connections between nearby agents with local information. In contrast to the dominant adaptive control schemes where coupling strength is adjusted continuously according to the states of the oscillators, our method does not request adaption of coupling strength. As the resulting interaction structure generated by this proposed strategy is strongly related to unidirectional chains, by investigating synchronization property of unidirectional chains, we reveal that there exists a certain coupling range in which the agents could be controlled regardless of the length of the chain. This feature enables the adaptive strategy to control the mobile oscillators regardless of their moving speed. Compared with existing adaptive control strategies for networked mobile agents, our proposed strategy is simpler for implementation where the resulting interaction networks are kept unweighted at all time.

Chaos of the Relativistic Forced van der Pol Oscillator

International Nuclear Information System (INIS)

Ashkenazya, Y.; Gorma, C; Horwitz, L. P.

1998-01-01

A manifestly relativistically covariant form of the van der Pol oscillator in 1 + 1 dimensions is studied. We show that the driven relativistic equations, for which z and t are coupled, relax very quickly to a pair of identical decoupled equations, due to a rapid vanishing of the angular momentum (the boost in 1 + 1 dimensions). A similar effect occurs in the damped driven covariant Duffing oscillator previously treated. This effect is an example of entrainment, or synchronization (phase locking) , of coupled chaotic systems. The Lyapunov exponents are calculated using the very efficient method of Habib and Ryne. We show a Poincare map that demonstrates this effect and maintains remarkable stability in spite of the inevitable accumulation of computer error in the chaotic region. For our choice of parameters, the positive Lyapunov exponent is about 0.242 almost independently of the integration method

On the short-term predictability of fully digital chaotic oscillators for pseudo-random number generation

KAUST Repository

Radwan, Ahmed Gomaa

2014-06-18

This paper presents a digital implementation of a 3rd order chaotic system using the Euler approximation. Short-term predictability is studied in relation to system precision, Euler step size and attractor size and optimal parameters for maximum performance are derived. Defective bits from the native chaotic output are neglected and the remaining pass the NIST SP. 800-22 tests without post-processing. The resulting optimized pseudorandom number generator has throughput up to 17.60 Gbits/s for a 64-bit design experimentally verified on a Xilinx Virtex 4 FPGA with logic utilization less than 1.85%.

On the short-term predictability of fully digital chaotic oscillators for pseudo-random number generation

KAUST Repository

Radwan, Ahmed Gomaa; Mansingka, Abhinav S.; Salama, Khaled N.; Zidan, Mohammed A.

2014-01-01

This paper presents a digital implementation of a 3rd order chaotic system using the Euler approximation. Short-term predictability is studied in relation to system precision, Euler step size and attractor size and optimal parameters for maximum performance are derived. Defective bits from the native chaotic output are neglected and the remaining pass the NIST SP. 800-22 tests without post-processing. The resulting optimized pseudorandom number generator has throughput up to 17.60 Gbits/s for a 64-bit design experimentally verified on a Xilinx Virtex 4 FPGA with logic utilization less than 1.85%.

Current observations with a decaying cosmological constant allow for chaotic cyclic cosmology

International Nuclear Information System (INIS)

Ellis, George F.R.; Platts, Emma; Weltman, Amanda; Sloan, David

2016-01-01

We use the phase plane analysis technique of Madsen and Ellis [1] to consider a universe with a true cosmological constant as well as a cosmological 'constant' that is decaying. Time symmetric dynamics for the inflationary era allows eternally bouncing models to occur. Allowing for scalar field dynamic evolution, we find that if dark energy decays in the future, chaotic cyclic universes exist provided the spatial curvature is positive. This is particularly interesting in light of current observations which do not yet rule out either closed universes or possible evolution of the cosmological constant. We present only a proof of principle, with no definite claim on the physical mechanism required for the present dark energy to decay

Chaotic orbits of a pendulum with variable length

Directory of Open Access Journals (Sweden)

Massimo Furi

2004-03-01

Full Text Available The main purpose of this investigation is to show that a pendulum, whose pivot oscillates vertically in a periodic fashion, has uncountably many chaotic orbits. The attribute chaotic is given according to the criterion we now describe. First, we associate to any orbit a finite or infinite sequence as follows. We write 1 or $-1$ every time the pendulum crosses the position of unstable equilibrium with positive (counterclockwise or negative (clockwise velocity, respectively. We write 0 whenever we find a pair of consecutive zero's of the velocity separated only by a crossing of the stable equilibrium, and with the understanding that different pairs cannot share a common time of zero velocity. Finally, the symbol $omega$, that is used only as the ending symbol of a finite sequence, indicates that the orbit tends asymptotically to the position of unstable equilibrium. Every infinite sequence of the three symbols ${1,-1,0}$ represents a real number of the interval $[0,1]$ written in base 3 when $-1$ is replaced with 2. An orbit is considered chaotic whenever the associated sequence of the three symbols ${1,2,0}$ is an irrational number of $[0,1]$. Our main goal is to show that there are uncountably many orbits of this type.

Distributed MIMO chaotic radar based on wavelength-division multiplexing technology.

Science.gov (United States)

Yao, Tingfeng; Zhu, Dan; Ben, De; Pan, Shilong

2015-04-15

A distributed multiple-input multiple-output chaotic radar based on wavelength-division multiplexing technology (WDM) is proposed and demonstrated. The wideband quasi-orthogonal chaotic signals generated by different optoelectronic oscillators (OEOs) are emitted by separated antennas to gain spatial diversity against the fluctuation of a target's radar cross section and enhance the detection capability. The received signals collected by the receive antennas and the reference signals from the OEOs are delivered to the central station for joint processing by exploiting WDM technology. The centralized signal processing avoids precise time synchronization of the distributed system and greatly simplifies the remote units, which improves the localization accuracy of the entire system. A proof-of-concept experiment for two-dimensional localization of a metal target is demonstrated. The maximum position error is less than 6.5 cm.

Higher-order chaotic oscillator using active bessel filter

DEFF Research Database (Denmark)

Lindberg, Erik; Mykolaitis, Gytis; Bumelien, Skaidra

2010-01-01

A higher-order oscillator, including a nonlinear unit and an 8th-order low-pass active Bessel filter is described. The Bessel unit plays the role of "three-in-one": a delay line, an amplifier and a filter. Results of hardware experiments and numerical simulation are presented. Depending...

Nonstationary behavior in a delayed feedback traveling wave tube folded waveguide oscillator

International Nuclear Information System (INIS)

Ryskin, N.M.; Titov, V.N.; Han, S.T.; So, J.K.; Jang, K.H.; Kang, Y.B.; Park, G.S.

2004-01-01

Folded waveguide traveling-wave tubes (FW TWT) are among the most promising candidates for powerful compact amplifiers and oscillators in millimeter and submillimeter wave bands. In this paper, the nonstationary behavior of a FW TWT oscillator with delayed feedback is investigated. Starting conditions of the oscillations are derived analytically. Results of numerical simulation of single-frequency, self-modulation (multifrequency) and chaotic generation regimes are presented. Mode competition phenomena, multistability and hysteresis are discussed

Nonlinear observer for synchronization of chaotic systems with application to secure data transmission

Science.gov (United States)

Aguilar-López, Ricardo; Martínez-Guerra, Rafael; Perez-Pinacho, Claudia A.

2014-06-01

The main issue of this work is related with the design of a class of nonlinear observer in order to synchronize chaotic dynamical systems in a master-slave scheme, considering different initial conditions. The oscillator of Chen is proposed as a benchmark model and a bounded-type observer is proposed to reach synchronicity between both two chaotic systems. The proposed observer contains a proportional and sigmoid form of a bounded function of the synchronization error in order to provide asymptotic synchronization with a satisfactory performance. Some numerical simulations were carrying out in order to show the operation of the proposed methodology, with possible applications to secure data communications issues.

Analogy between optically driven injection-locked laser diodes and driven damped linear oscillators

International Nuclear Information System (INIS)

Murakami, Atsushi; Shore, K. Alan

2006-01-01

An analytical study of optically driven laser diodes (LDs) has been undertaken to meet the requirement for a theoretical treatment for chaotic drive and synchronization occurring in the injection-locked LDs with strong injection. A small-signal analysis is performed for the sets of rate equations for the injection-locked LDs driven by a sinusoidal optical signal. In particular, as a model of chaotic driving signals from LD dynamics, an optical signal caused by direct modulation to the master LD is assumed, oscillating both in field amplitude and phase as is the case with chaotic driving signals. Consequently, we find conditions that allow reduction in the degrees of freedom of the driven LD. Under these conditions, the driven response is approximated to a simple form which is found to be equivalent to driven damped linear oscillators. The validity of the application of this theory to previous work on the synchronization of chaos and related phenomena occurring in the injection-locked LDs is demonstrated

Direction of coupling from phases of interacting oscillators: An information-theoretic approach

Science.gov (United States)

Paluš, Milan; Stefanovska, Aneta

2003-05-01

A directionality index based on conditional mutual information is proposed for application to the instantaneous phases of weakly coupled oscillators. Its abilities to distinguish unidirectional from bidirectional coupling, as well as to reveal and quantify asymmetry in bidirectional coupling, are demonstrated using numerical examples of quasiperiodic, chaotic, and noisy oscillators, as well as real human cardiorespiratory data.

Quantitative Measures of Chaotic Charged Particle Dynamics in the Magnetotail

Science.gov (United States)

Holland, D. L.; Martin, R. F., Jr.; Burris, C.

2017-12-01

It has long been noted that the motion of charged particles in magnetotail-like magnetic fields is chaotic, however, efforts to quantify the degree of chaos have had conflicting conclusions. In this paper we re-examine the question by focusing on quantitative measures of chaos. We first examine the percentage of orbits that enter the chaotic region of phase space and the average trapping time of those particles. We then examine the average exponential divergence rate (AEDR) of the chaotic particles between their first and last crossing of the mid-plane. We show that at resonant energies where the underlying phase space has a high degree of symmetry, only a small number of particle enter the chaotic region, but they are trapped for long periods of time and the time asymptotic value of the AEDR is very close to the average value of the AEDR. At the off-resonant energies where the phase space is highly asymmetric, the majority of the particle enter the chaotic region for fairly short periods of time and the time asymptotic value of the AEDR is much smaller than the average value. The root cause is that in the resonant case, the longest-lived orbits tend interact with the current many times and sample the entire chaotic region, whereas in the non-resonant case the longest-lived orbits only interact with the current sheet a small number of times but have very long mirrorings where the motion is nearly regular. Additionally we use an ad-hoc model where we model the current sheet as a Lorentz scattering system with each interaction with the current sheet being considered as a "collision". We find that the average kick per collision is greatest at off-resonant energies. Finally, we propose a chaos parameter as the product of the AEDR times the average chaotic particle trapping time times the percentage of orbits that are chaotic. We find that this takes on peak values at the resonant energies.

A chaotic system with an infinite number of equilibrium points located on a line and on a hyperbola and its fractional-order form

International Nuclear Information System (INIS)

Kingni, Sifeu Takougang; Pham, Viet-Thanh; Jafari, Sajad; Woafo, Paul

2017-01-01

A three-dimensional autonomous chaotic system with an infinite number of equilibrium points located on a line and a hyperbola is proposed in this paper. To analyze the dynamical behaviors of the proposed system, mathematical tools such as Routh-Hurwitz criteria, Lyapunov exponents and bifurcation diagram are exploited. For a suitable choice of the parameters, the proposed system can generate periodic oscillations and chaotic attractors of different shapes such as bistable and monostable chaotic attractors. In addition, an electronic circuit is designed and implemented to verify the feasibility of the proposed system. A good qualitative agreement is shown between the numerical simulations and the Orcard-PSpice results. Moreover, the fractional-order form of the proposed system is studied using analog and numerical simulations. It is found that chaos, periodic oscillations and periodic spiking exist in this proposed system with order less than three. Then an electronic circuit is designed for the commensurate fractional order α = 0.98, from which we can observe that a chaotic attractor exists in the fractional-order form of the proposed system. Finally, the problem of drive-response generalized projective synchronization of the fractional-order form of the chaotic proposed autonomous system is considered.

A New Simple Chaotic Circuit Based on Memristor

Science.gov (United States)

Wu, Renping; Wang, Chunhua

In this paper, a new memristor is proposed, and then an emulator built from off-the-shelf solid state components imitating the behavior of the proposed memristor is presented. Multisim simulation and breadboard experiment are done on the emulator, exhibiting a pinched hysteresis loop in the voltage-current plane when the emulator is driven by a periodic excitation voltage. In addition, a new simple chaotic circuit is designed by using the proposed memristor and other circuit elements. It is exciting that this circuit with only a linear negative resistor, a capacitor, an inductor and a memristor can generate a chaotic attractor. The dynamical behaviors of the proposed chaotic system are analyzed by Lyapunov exponents, phase portraits and bifurcation diagrams. Finally, an electronic circuit is designed to implement the chaotic system. For the sake of simple circuit topology, the proposed chaotic circuit can be easily manufactured at low cost.

Enhancement of multitasking performance and neural oscillations by transcranial alternating current stimulation

NARCIS (Netherlands)

Hsu, W.Y.; Zanto, T.P.; van Schouwenburg, M.R.; Gazzaley, A.

2017-01-01

Multitasking is associated with the generation of stimulus-locked theta (4–7 Hz) oscillations arising from prefrontal cortex (PFC). Transcranial alternating current stimulation (tACS) is a non-invasive brain stimulation technique that influences endogenous brain oscillations. Here, we investigate

Mesoscopic chaos mediated by Drude electron-hole plasma in silicon optomechanical oscillators

Science.gov (United States)

Wu, Jiagui; Huang, Shu-Wei; Huang, Yongjun; Zhou, Hao; Yang, Jinghui; Liu, Jia-Ming; Yu, Mingbin; Lo, Guoqiang; Kwong, Dim-Lee; Duan, Shukai; Wei Wong, Chee

2017-01-01

Chaos has revolutionized the field of nonlinear science and stimulated foundational studies from neural networks, extreme event statistics, to physics of electron transport. Recent studies in cavity optomechanics provide a new platform to uncover quintessential architectures of chaos generation and the underlying physics. Here, we report the generation of dynamical chaos in silicon-based monolithic optomechanical oscillators, enabled by the strong and coupled nonlinearities of two-photon absorption induced Drude electron–hole plasma. Deterministic chaotic oscillation is achieved, and statistical and entropic characterization quantifies the chaos complexity at 60 fJ intracavity energies. The correlation dimension D2 is determined at 1.67 for the chaotic attractor, along with a maximal Lyapunov exponent rate of about 2.94 times the fundamental optomechanical oscillation for fast adjacent trajectory divergence. Nonlinear dynamical maps demonstrate the subharmonics, bifurcations and stable regimes, along with distinct transitional routes into chaos. This provides a CMOS-compatible and scalable architecture for understanding complex dynamics on the mesoscopic scale. PMID:28598426

Observation of auto-oscillations and chaos in subsidiary absorption in yttrium iron garnet

International Nuclear Information System (INIS)

Srinivasan, G.; Chen, M.; Patton, C.E.

1988-01-01

Auto-oscillations of the dynamic magnetization and routes to chaos for the first-order transverse pump spin-wave instability have been studied in single-crystal yttrium-iron-garnet (YIG) films. The measurements reported here were made on a 20.8-μm-thick YIG film at 9.4 GHz with the static and microwave fields in the plane of the film. Auto-oscillations at 100--400 kHz were observed in the power absorbed by the film over a relatively narrow static field range of 1100--1460 Oe, compared to the first-order instability (FOI) range of 0--1630 Oe. The auto-oscillation frequency and threshold microwave field amplitude were both strongly field dependent. The threshold amplitudes were about a factor of 2 larger than the FOI threshold amplitudes. At even higher power levels and for an even narrower field range of 1300--1380 Oe, the auto-oscillations showed frequency changes indicative of chaotic behavior. Several different subharmonic bifurcation routes to chaos were observed for different fields within the chaotic region

Modulation of low-frequency oscillations in GaAs MESFETs' channel current by sidegating bias

Institute of Scientific and Technical Information of China (English)

DING Yong; LU Shengli; ZHAO Fuchuan

2005-01-01

Low-frequency oscillations in channel current are usually observed when measuring the GaAs MESFET's output characteristics. This paper studies the oscillations by testing the MESFET's output characteristics under different sidegate bias conditions. It is shown that the low-frequency oscillations of channel current are directly related to the sidegate bias. In other words, the sidegate bias can modulate the oscillations. Whether the sidegate bias varies positively or negatively, there will inevitably be a threshold voltage after which the low-frequency oscillations disappear. The observation is strongly dependent upon the peculiarities of channel-substrate (C-S) junction and impact ionization of traps-EL2 under high field. This conclusion is of particular pertinence to the design of low-noise GaAs IC's.

Proposal for a Domain Wall Nano-Oscillator driven by Non-uniform Spin Currents

Science.gov (United States)

Sharma, Sanchar; Muralidharan, Bhaskaran; Tulapurkar, Ashwin

2015-09-01

We propose a new mechanism and a related device concept for a robust, magnetic field tunable radio-frequency (rf) oscillator using the self oscillation of a magnetic domain wall subject to a uniform static magnetic field and a spatially non-uniform vertical dc spin current. The self oscillation of the domain wall is created as it translates periodically between two unstable positions, one being in the region where both the dc spin current and the magnetic field are present, and the other, being where only the magnetic field is present. The vertical dc spin current pushes it away from one unstable position while the magnetic field pushes it away from the other. We show that such oscillations are stable under noise and can exhibit a quality factor of over 1000. A domain wall under dynamic translation, not only being a source for rich physics, is also a promising candidate for advancements in nanoelectronics with the actively researched racetrack memory architecture, digital and analog switching paradigms as candidate examples. Devising a stable rf oscillator using a domain wall is hence another step towards the realization of an all domain wall logic scheme.

Applicability of Time-Averaged Holography for Micro-Electro-Mechanical System Performing Non-Linear Oscillations

Directory of Open Access Journals (Sweden)

Paulius Palevicius

2014-01-01

Full Text Available Optical investigation of movable microsystem components using time-averaged holography is investigated in this paper. It is shown that even a harmonic excitation of a non-linear microsystem may result in an unpredictable chaotic motion. Analytical results between parameters of the chaotic oscillations and the formation of time-averaged fringes provide a deeper insight into computational and experimental interpretation of time-averaged MEMS holograms.

Applicability of Time-Averaged Holography for Micro-Electro-Mechanical System Performing Non-Linear Oscillations

Science.gov (United States)

Palevicius, Paulius; Ragulskis, Minvydas; Palevicius, Arvydas; Ostasevicius, Vytautas

2014-01-01

Optical investigation of movable microsystem components using time-averaged holography is investigated in this paper. It is shown that even a harmonic excitation of a non-linear microsystem may result in an unpredictable chaotic motion. Analytical results between parameters of the chaotic oscillations and the formation of time-averaged fringes provide a deeper insight into computational and experimental interpretation of time-averaged MEMS holograms. PMID:24451467

Applicability of time-averaged holography for micro-electro-mechanical system performing non-linear oscillations.

Science.gov (United States)

Palevicius, Paulius; Ragulskis, Minvydas; Palevicius, Arvydas; Ostasevicius, Vytautas

2014-01-21

Optical investigation of movable microsystem components using time-averaged holography is investigated in this paper. It is shown that even a harmonic excitation of a non-linear microsystem may result in an unpredictable chaotic motion. Analytical results between parameters of the chaotic oscillations and the formation of time-averaged fringes provide a deeper insight into computational and experimental interpretation of time-averaged MEMS holograms.

A new chaotic cryptosystem

International Nuclear Information System (INIS)

Wei Jun; Liao Xiaofeng; Wong, Kwok-wo; Xiang Tao

2006-01-01

Based on the study of some previously proposed chaotic encryption algorithms, we found that it is dangerous to mix chaotic state or iteration number of the chaotic system with ciphertext. In this paper, a new chaotic cryptosystem is proposed. Instead of simply mixing the chaotic signal of the proposed chaotic cryptosystem with the ciphertext, a noise-like variable is utilized to govern the encryption and decryption processes. This adds statistical sense to the new cryptosystem. Numerical simulations show that the new cryptosystem is practical whenever efficiency, ciphertext length or security is concerned

Chaotic mechanics in systems with impacts and friction

CERN Document Server

Blazejczyk-Okolewska, Barbara; Kapitaniak, Tomasz; Wojewoda, Jerzy

1999-01-01

This book is devoted to the theory of chaotic oscillations in mechanical systems. Detailed descriptions of the basic types of nonlinearity - impacts and dry friction - are presented. The properties of such behavior are discussed, and the numerical and experimental results obtained by the authors are presented.The dynamic properties of systems described here can be useful in the proper design and use of mechanics where such behavior still creates problems.This book will be very useful for anyone with a fundamental knowledge of nonlinear mechanics who is beginning research in the field.

Generation of chaotic radiation in a driven traveling wave tube amplifier with time-delayed feedback

International Nuclear Information System (INIS)

Marchewka, Chad; Larsen, Paul; Bhattacharjee, Sudeep; Booske, John; Sengele, Sean; Ryskin, Nikita; Titov, Vladimir

2006-01-01

The application of chaos in communications and radar offers new and interesting possibilities. This article describes investigations on the generation of chaos in a traveling wave tube (TWT) amplifier and the experimental parameters responsible for sustaining stable chaos. Chaos is generated in a TWT amplifier when it is made to operate in a highly nonlinear regime by recirculating a fraction of the TWT output power back to the input in a delayed feedback configuration. A driver wave provides a constant external force to the system making it behave like a forced nonlinear oscillator. The effects of the feedback bandwidth, intensity, and phase are described. The study illuminates the different transitions to chaos and the effect of parameters such as the frequency and intensity of the driver wave. The detuning frequency, i.e., difference frequency between the driver wave and the natural oscillation of the system, has been identified as being an important physical parameter for controlling evolution to chaos. Among the observed routes to chaos, besides the more common period doubling, a new route called loss of frequency locking occurs when the driving frequency is adjacent to a natural oscillation mode. The feedback bandwidth controls the nonlinear dynamics of the system, particularly the number of natural oscillation modes. A computational model has been developed to simulate the experiments and reasonably good agreement is obtained between them. Experiments are described that demonstrate the feasibility of chaotic communications using two TWTs, where one is operated as a driven chaotic oscillator and the other as a time-delayed, open-loop amplifier

Generation of chaotic radiation in a driven traveling wave tube amplifier with time-delayed feedback

Science.gov (United States)

Marchewka, Chad; Larsen, Paul; Bhattacharjee, Sudeep; Booske, John; Sengele, Sean; Ryskin, Nikita; Titov, Vladimir

2006-01-01

The application of chaos in communications and radar offers new and interesting possibilities. This article describes investigations on the generation of chaos in a traveling wave tube (TWT) amplifier and the experimental parameters responsible for sustaining stable chaos. Chaos is generated in a TWT amplifier when it is made to operate in a highly nonlinear regime by recirculating a fraction of the TWT output power back to the input in a delayed feedback configuration. A driver wave provides a constant external force to the system making it behave like a forced nonlinear oscillator. The effects of the feedback bandwidth, intensity, and phase are described. The study illuminates the different transitions to chaos and the effect of parameters such as the frequency and intensity of the driver wave. The detuning frequency, i.e., difference frequency between the driver wave and the natural oscillation of the system, has been identified as being an important physical parameter for controlling evolution to chaos. Among the observed routes to chaos, besides the more common period doubling, a new route called loss of frequency locking occurs when the driving frequency is adjacent to a natural oscillation mode. The feedback bandwidth controls the nonlinear dynamics of the system, particularly the number of natural oscillation modes. A computational model has been developed to simulate the experiments and reasonably good agreement is obtained between them. Experiments are described that demonstrate the feasibility of chaotic communications using two TWTs, where one is operated as a driven chaotic oscillator and the other as a time-delayed, open-loop amplifier.

Pacemaker neuron and network oscillations depend on a neuromodulator-regulated linear current

Directory of Open Access Journals (Sweden)

Shunbing Zhao

2010-05-01

Full Text Available Linear leak currents have been implicated in the regulation of neuronal excitability, generation of neuronal and network oscillations, and network state transitions. Yet, few studies have directly tested the dependence of network oscillations on leak currents or explored the role of leak currents on network activity. In the oscillatory pyloric network of decapod crustaceans neuromodulatory inputs are necessary for pacemaker activity. A large subset of neuromodulators is known to activate a single voltage-gated inward current IMI, which has been shown to regulate the rhythmic activity of the network and its pacemaker neurons. Using the dynamic clamp technique, we show that the crucial component of IMI for the generation of oscillatory activity is only a close-to-linear portion of the current-voltage relationship. The nature of this conductance is such that the presence or the absence of neuromodulators effectively regulates the amount of leak current and the input resistance in the pacemaker neurons. When deprived of neuromodulatory inputs, pyloric oscillations are disrupted; yet, a linear reduction of the total conductance in a single neuron within the pacemaker group recovers not only the pacemaker activity in that neuron, but also leads to a recovery of oscillations in the entire pyloric network. The recovered activity produces proper frequency and phasing that is similar to that induced by neuromodulators. These results show that the passive properties of pacemaker neurons can significantly affect their capacity to generate and regulate the oscillatory activity of an entire network, and that this feature is exploited by neuromodulatory inputs.

Dynamic Parameter-Control Chaotic System.

Science.gov (United States)

Hua, Zhongyun; Zhou, Yicong

2016-12-01

This paper proposes a general framework of 1-D chaotic maps called the dynamic parameter-control chaotic system (DPCCS). It has a simple but effective structure that uses the outputs of a chaotic map (control map) to dynamically control the parameter of another chaotic map (seed map). Using any existing 1-D chaotic map as the control/seed map (or both), DPCCS is able to produce a huge number of new chaotic maps. Evaluations and comparisons show that chaotic maps generated by DPCCS are very sensitive to their initial states, and have wider chaotic ranges, better unpredictability and more complex chaotic behaviors than their seed maps. Using a chaotic map of DPCCS as an example, we provide a field-programmable gate array design of this chaotic map to show the simplicity of DPCCS in hardware implementation, and introduce a new pseudo-random number generator (PRNG) to investigate the applications of DPCCS. Analysis and testing results demonstrate the excellent randomness of the proposed PRNG.

Self-sustained spin-polarized current oscillations in multiquantum well structures

Energy Technology Data Exchange (ETDEWEB)

Escobedo, Ramon [Departamento de Matematica Aplicada y Ciencias de la Computacion, Universidad de Cantabria, 39005 Santander (Spain); Carretero, Manuel; Bonilla, Luis L [G. Millan Institute, Fluid Dynamics, Nanoscience and Industrial Mathematics, Universidad Carlos III de Madrid, 28911 Leganes (Spain); Platero, Gloria [Instituto de Ciencia de Materiales, CSIC, 28049 Cantoblanco (Spain)], E-mail: escobedo@unican.es, E-mail: manuel.carretero@uc3m.es, E-mail: bonilla@ing.uc3m.es, E-mail: gplatero@icmm.csic.es

2009-01-15

Nonlinear transport through diluted magnetic semiconductor nanostructures is investigated. We have considered a II-VI multiquantum well nanostructure whose wells are selectively doped with Mn. The response to a dc voltage bias may be either a stationary or an oscillatory current. We have studied the transition from stationary to time-dependent current as a function of the doping density and the number of quantum wells. Analysis and numerical solution of a nonlinear spin transport model shows that the current in a structure without magnetic impurities is stationary, whereas current oscillations may appear if at least one well contains magnetic impurities. For long structures having two wells with magnetic impurities, a detailed analysis of nucleation of charge dipole domains shows that self-sustained current oscillations are caused by repeated triggering of dipole domains at the magnetic wells and motion towards the collector. Depending on the location of the magnetic wells and the voltage, dipole domains may be triggered at both wells or at only one. In the latter case, the well closer to the collector may inhibit domain motion between the first and the second well inside the structure. Our study could allow design of oscillatory spin-polarized current injectors.

Long Range Dependence Prognostics for Bearing Vibration Intensity Chaotic Time Series

Directory of Open Access Journals (Sweden)

Qing Li

2016-01-01

Full Text Available According to the chaotic features and typical fractional order characteristics of the bearing vibration intensity time series, a forecasting approach based on long range dependence (LRD is proposed. In order to reveal the internal chaotic properties, vibration intensity time series are reconstructed based on chaos theory in phase-space, the delay time is computed with C-C method and the optimal embedding dimension and saturated correlation dimension are calculated via the Grassberger–Procaccia (G-P method, respectively, so that the chaotic characteristics of vibration intensity time series can be jointly determined by the largest Lyapunov exponent and phase plane trajectory of vibration intensity time series, meanwhile, the largest Lyapunov exponent is calculated by the Wolf method and phase plane trajectory is illustrated using Duffing-Holmes Oscillator (DHO. The Hurst exponent and long range dependence prediction method are proposed to verify the typical fractional order features and improve the prediction accuracy of bearing vibration intensity time series, respectively. Experience shows that the vibration intensity time series have chaotic properties and the LRD prediction method is better than the other prediction methods (largest Lyapunov, auto regressive moving average (ARMA and BP neural network (BPNN model in prediction accuracy and prediction performance, which provides a new approach for running tendency predictions for rotating machinery and provide some guidance value to the engineering practice.

Design of secure digital communication systems using chaotic modulation, cryptography and chaotic synchronization

International Nuclear Information System (INIS)

Chien, T.-I.; Liao, T.-L.

2005-01-01

This paper presents a secure digital communication system based on chaotic modulation, cryptography, and chaotic synchronization techniques. The proposed system consists of a Chaotic Modulator (CM), a Chaotic Secure Transmitter (CST), a Chaotic Secure Receiver (CSR) and a Chaotic Demodulator (CDM). The CM module incorporates a chaotic system and a novel Chaotic Differential Peaks Keying (CDPK) modulation scheme to generate analog patterns corresponding to the input digital bits. The CST and CSR modules are designed such that a single scalar signal is transmitted in the public channel. Furthermore, by giving certain structural conditions of a particular class of chaotic system, the CST and the nonlinear observer-based CSR with an appropriate observer gain are constructed to synchronize with each other. These two slave systems are driven simultaneously by the transmitted signal and are designed to synchronize and generate appropriate cryptography keys for encryption and decryption purposes. In the CDM module, a nonlinear observer is designed to estimate the chaotic modulating system in the CM. A demodulation mechanism is then applied to decode the transmitted input digital bits. The effectiveness of the proposed scheme is demonstrated through the numerical simulation of an illustrative communication system. Synchronization between the chaotic circuits of the transmitter and receiver modules is guaranteed through the Lyapunov stability theorem. Finally, the security features of the proposed system in the event of attack by an intruder in either the time domain or the frequency domain are discussed

New Quartz Crystal Oscillators Using the Current-Feedback Operational Amplifier

OpenAIRE

Muhammad Taher Abuelma'atti; Ahmad Al-Ghazwani

2000-01-01

New crystal oscillators using the current-feedback operational-amplifier (CFOA) are presented. Each circuit uses one CFOA, a crystal and, at most, five externally connected passive elements. Experimental results are included.

The chaotic environment

International Nuclear Information System (INIS)

Cook, A.

1990-09-01

An elementary account of the origin of chaotic behaviour in classical dynamics is given with examples from geophysics, and in conclusion some thoughts about what can be predicted of chaotic behaviour and what sorts of arguments can be used to guide human behaviour in chaotic conditions are presented. 4 refs

Conservative Chaos Generators with CCII+ Based on Mathematical Model of Nonlinear Oscillator

Directory of Open Access Journals (Sweden)

J. Slezak

2008-09-01

Full Text Available In this detailed paper, several novel oscillator's configurations which consist only of five positive second generation current conveyors (CCII+ are presented and experimentally verified. Each network is able to generate the conservative chaotic attractors with the certain degree of the structural stability. It represents a class of the autonomous deterministic dynamical systems with two-segment piecewise linear (PWL vector fields suitable also for the theoretical analysis. Route to chaos can be traced and observed by a simple change of the external dc voltage. Advantages and other possible improvements are briefly discussed in the text.

Circuit simulation and physical implementation for a memristor-based colpitts oscillator

Science.gov (United States)

Deng, Hongmin; Wang, Dongping

2017-03-01

This paper implements two kinds of memristor-based colpitts oscillators, namely, the circuit where the memristor is added into the feedback network of the oscillator in parallel and series, respectively. First, a MULTISIM simulation circuit for the memristive colpitts oscillator is built, where an emulator constructed by some off-the-shelf components is utilized to replace the memristor. Then the physical system is implemented in terms of the MULTISIM simulation circuit. Circuit simulation and experimental study show that this memristive colpitts oscillator can exhibit periodic, quasi-periodic, and chaotic behaviors with certain parameter's variances. Besides, in a sense, the circuit is robust with circuit parameters and device types.

Designing key-dependent chaotic S-box with larger key space

International Nuclear Information System (INIS)

Yin Ruming; Yuan Jian; Wang Jian; Shan Xiuming; Wang Xiqin

2009-01-01

The construction of cryptographically strong substitution boxes (S-boxes) is an important concern in designing secure cryptosystems. The key-dependent S-boxes designed using chaotic maps have received increasing attention in recent years. However, the key space of such S-boxes does not seem to be sufficiently large due to the limited parameter range of discretized chaotic maps. In this paper, we propose a new key-dependent S-box based on the iteration of continuous chaotic maps. We explore the continuous-valued state space of chaotic systems, and devise the discrete mapping between the input and the output of the S-box. A key-dependent S-box is constructed with the logistic map in this paper. We show that its key space could be much larger than the current key-dependent chaotic S-boxes.

Chaos Noise on Phase of Van Der Pol Oscillator

Directory of Open Access Journals (Sweden)

Xian He Huang

2010-12-01

Full Text Available Phase noise is the most important parameter in many oscillators. In this paper, based on nonlinear stochastic differential equation for phase noise analysis approach is proposed. And then discusses and compares the influence of two different sources of noise in the Van Der Pol oscillator adopted this method. One source of noise is a white noise process, which is a genuinely stochastic process; the other source of noise is actually a deterministic system, which exhibits chaotic behavior in some regions. The behavior of the oscillator under different conditions is investigated numerically. It is shown that the phase noise of the oscillator is affected more by noise arising from chaos than by noise arising from the genuine stochastic process at the same noise intensity.

A Possible Minimum Toy Model with Negative Differential Capacitance for Self-sustained Current Oscillation

International Nuclear Information System (INIS)

Xiong Gang; Sun Zhouzhou; Wang Xiangrong

2007-01-01

We generalize a simple model for superlattices to include the effect of differential capacitance. It is shown that the model always has a stable steady-state solution (SSS) if all differential capacitances are positive. On the other hand, when negative differential capacitance is included, the model can have no stable SSS and be in a self-sustained current oscillation behavior. Therefore, we find a possible minimum toy model with both negative differential resistance and negative differential capacitance which can include the phenomena of both self-sustained current oscillation and I-V oscillation of stable SSSs.

Control of chaotic vibration in automotive wiper systems

International Nuclear Information System (INIS)

Wang Zheng; Chau, K.T.

2009-01-01

Chaotic vibration has been identified in the automotive wiper system at certain wiping speeds. This irregular vibration not only decreases the wiping efficiency, but also degrades the driving comfort. The purpose of this paper is to propose a new approach to stabilize the chaotic vibration in the wiper system. The key is to employ the extended time-delay feedback control in such a way that the applied voltage of the wiper motor is online adjusted according to its armature current feedback. Based on a practical wiper system, it is verified that the proposed approach can successfully stabilize the chaotic vibration, and provide a wide range of wiping speeds

Parameters identification and adaptive full state hybrid projective synchronization of chaotic (hyper-chaotic) systems

International Nuclear Information System (INIS)

Hu Manfeng; Xu Zhenyuan; Zhang Rong; Hu Aihua

2007-01-01

Based on the active control idea and the invariance principle of differential equations, a general scheme of adaptive full state hybrid projective synchronization (FSHPS) and parameters identification of a class of chaotic (hyper-chaotic) systems with linearly dependent uncertain parameters is proposed in this Letter. With this effective scheme parameters identification and FSHPS of chaotic and hyper-chaotic systems can be realized simultaneously. Numerical simulations on the chaotic Chen system and the hyper-chaotic Chen system are presented to verify the effectiveness of the proposed scheme

Periodic or chaotic bursting dynamics via delayed pitchfork bifurcation in a slow-varying controlled system

Science.gov (United States)

Yu, Yue; Zhang, Zhengdi; Han, Xiujing

2018-03-01

In this work, we aim to demonstrate the novel routes to periodic and chaotic bursting, i.e., the different bursting dynamics via delayed pitchfork bifurcations around stable attractors, in the classical controlled Lü system. First, by computing the corresponding characteristic polynomial, we determine where some critical values about bifurcation behaviors appear in the Lü system. Moreover, the transition mechanism among different stable attractors has been introduced including homoclinic-type connections or chaotic attractors. Secondly, taking advantage of the above analytical results, we carry out a study of the mechanism for bursting dynamics in the Lü system with slowly periodic variation of certain control parameter. A distinct delayed supercritical pitchfork bifurcation behavior can be discussed when the control item passes through bifurcation points periodically. This delayed dynamical behavior may terminate at different parameter areas, which leads to different spiking modes around different stable attractors (equilibriums, limit cycles, or chaotic attractors). In particular, the chaotic attractor may appear by Shilnikov connections or chaos boundary crisis, which leads to the occurrence of impressive chaotic bursting oscillations. Our findings enrich the study of bursting dynamics and deepen the understanding of some similar sorts of delayed bursting phenomena. Finally, some numerical simulations are included to illustrate the validity of our study.

Control electron beam oscillation regimes in Pierce diode with overcritical current

International Nuclear Information System (INIS)

Rempen, I.S.; Khramov, A.E.

2001-01-01

The effect of the delayed feedback on the complex oscillation regimes in the electron flux with the overcritical current in the Pierce diode is studied. The possibility of controlling the oscillation regimes through changing the feedback parameters is shown. The finite-dimensional model, describing the behavior of the electron flux in the Pierce diode hydrodynamic model, is constructed. Its behavior under the effect of the delayed feedback is studied [ru

Wireless current sensing by near field induction from a spin transfer torque nano-oscillator

Energy Technology Data Exchange (ETDEWEB)

Ramaswamy, B. [Fischell Department of Bioengineering, University of Maryland, College Park, Maryland 20742 (United States); Algarin, J. M.; Waks, E., E-mail: edowaks@umd.edu [Institute for Research in Electronics and Applied Physics (IREAP), University of Maryland, College Park, Maryland 20742 (United States); Weinberg, I. N. [Weinberg Medical Physics LLC, Bethesda, Maryland 20817 (United States); Chen, Y.-J.; Krivorotov, I. N. [Department of Physics and Astronomy, University of California, Irvine, California 92697 (United States); Katine, J. A. [HGST Research Center, San Jose, California 95135 (United States); Shapiro, B. [Fischell Department of Bioengineering, University of Maryland, College Park, Maryland 20742 (United States); Institute for Systems Research (ISR), University of Maryland, College Park, Maryland 20742 (United States)

2016-06-13

We demonstrate that spin transfer torque nano-oscillators (STNO) can act as wireless sensors for local current. The STNO acts as a transducer that converts weak direct currents into microwave field oscillations that we detect using an inductive coil. We detect direct currents in the range of 300–700 μA and report them wirelessly to a receiving induction coil at distances exceeding 6.5 mm. This current sensor could find application in chemical and biological sensing and industrial inspection.

Cascade Chaotic System With Applications.

Science.gov (United States)

Zhou, Yicong; Hua, Zhongyun; Pun, Chi-Man; Chen, C L Philip

2015-09-01

Chaotic maps are widely used in different applications. Motivated by the cascade structure in electronic circuits, this paper introduces a general chaotic framework called the cascade chaotic system (CCS). Using two 1-D chaotic maps as seed maps, CCS is able to generate a huge number of new chaotic maps. Examples and evaluations show the CCS's robustness. Compared with corresponding seed maps, newly generated chaotic maps are more unpredictable and have better chaotic performance, more parameters, and complex chaotic properties. To investigate applications of CCS, we introduce a pseudo-random number generator (PRNG) and a data encryption system using a chaotic map generated by CCS. Simulation and analysis demonstrate that the proposed PRNG has high quality of randomness and that the data encryption system is able to protect different types of data with a high-security level.

Golden mean relevance for chaos inhibition in a system of two coupled modified van der Pol oscillators

International Nuclear Information System (INIS)

Stan, Cristina; Cristescu, C.P.; Agop, M.

2007-01-01

In this work, we present a novel evidence of the importance of the golden mean criticality of a system of oscillators in agreement with El Naschie's E-infinity theory. We focus on chaos inhibition in a system of two coupled modified van der Pol oscillators. Depending on the coupling between the two oscillators, the system shows chaotic behavior for different ranges of the coupling parameter. Chaos suppression, as a transition from irregular behavior to a periodical one, is induced by perturbing the system with a harmonic signal with amplitude considerably lower than the value which causes entrainment. The frequency of the perturbation is related to the main frequencies in the spectrum of the freely running system (without perturbation) by the golden mean. We demonstrate that this effect is also obtained for a perturbation with frequency such that the ratio of half the frequency of the first main component in the freely running chaotic spectrum over the frequency of the perturbation is very close (five digits coincidence) to the golden mean. This result is shown to hold for arbitrary values of the coupling parameter in the various ranges of chaotic dynamics of the free running system

Synchronization of tubular pressure oscillations in interacting nephrons

International Nuclear Information System (INIS)

Sosnovtseva, O.V.; Postnov, D.E.; Mosekilde, E.; Holstein-Rathlou, N.-H.

2003-01-01

The pressure and flow regulation in the individual functional unit of the kidney (the nephron) tends to operate in an unstable regime. For normal rats, the regulation displays regular self-sustained oscillations, but for rats with high blood pressure the oscillations become chaotic. We explain the mechanisms responsible for this behavior and discuss the involved bifurcations. Experimental data show that neighboring nephrons adjust their pressure and flow regulation in accordance with one another. For rats with normal blood pressure, in-phase as well as anti-phase synchronization can be observed. For spontaneously hypertensive rats, indications of chaotic phase synchronization are found. Accounting for a hermodynamics as well as for a vascular coupling between nephrons that share a common interlobular artery, we present a model of the interaction of the pressure and flow regulations between adjacent nephrons. It is shown that this model, with physiologically realistic parameter values, can reproduce the different types of experimentally observed synchronization, including multistability and partial phase synchronization with respect to the slow and fast dynamics

Synchronization of tubular pressure oscillations in interacting nephrons

Energy Technology Data Exchange (ETDEWEB)

Sosnovtseva, O.V. E-mail: olga@fysik.dtu.dk; Postnov, D.E.; Mosekilde, E.; Holstein-Rathlou, N.-H

2003-01-01

The pressure and flow regulation in the individual functional unit of the kidney (the nephron) tends to operate in an unstable regime. For normal rats, the regulation displays regular self-sustained oscillations, but for rats with high blood pressure the oscillations become chaotic. We explain the mechanisms responsible for this behavior and discuss the involved bifurcations. Experimental data show that neighboring nephrons adjust their pressure and flow regulation in accordance with one another. For rats with normal blood pressure, in-phase as well as anti-phase synchronization can be observed. For spontaneously hypertensive rats, indications of chaotic phase synchronization are found. Accounting for a hermodynamics as well as for a vascular coupling between nephrons that share a common interlobular artery, we present a model of the interaction of the pressure and flow regulations between adjacent nephrons. It is shown that this model, with physiologically realistic parameter values, can reproduce the different types of experimentally observed synchronization, including multistability and partial phase synchronization with respect to the slow and fast dynamics.

Parameter and state estimation of experimental chaotic systems using synchronization

Science.gov (United States)

Quinn, John C.; Bryant, Paul H.; Creveling, Daniel R.; Klein, Sallee R.; Abarbanel, Henry D. I.

2009-07-01

We examine the use of synchronization as a mechanism for extracting parameter and state information from experimental systems. We focus on important aspects of this problem that have received little attention previously and we explore them using experiments and simulations with the chaotic Colpitts oscillator as an example system. We explore the impact of model imperfection on the ability to extract valid information from an experimental system. We compare two optimization methods: an initial value method and a constrained method. Each of these involves coupling the model equations to the experimental data in order to regularize the chaotic motions on the synchronization manifold. We explore both time-dependent and time-independent coupling and discuss the use of periodic impulse coupling. We also examine both optimized and fixed (or manually adjusted) coupling. For the case of an optimized time-dependent coupling function u(t) we find a robust structure which includes sharp peaks and intervals where it is zero. This structure shows a strong correlation with the location in phase space and appears to depend on noise, imperfections of the model, and the Lyapunov direction vectors. For time-independent coupling we find the counterintuitive result that often the optimal rms error in fitting the model to the data initially increases with coupling strength. Comparison of this result with that obtained using simulated data may provide one measure of model imperfection. The constrained method with time-dependent coupling appears to have benefits in synchronizing long data sets with minimal impact, while the initial value method with time-independent coupling tends to be substantially faster, more flexible, and easier to use. We also describe a method of coupling which is useful for sparse experimental data sets. Our use of the Colpitts oscillator allows us to explore in detail the case of a system with one positive Lyapunov exponent. The methods we explored are easily

Chaos and routes to chaos in coupled Duffing oscillators with multiple degrees of freedom

International Nuclear Information System (INIS)

Musielak, D.E.; Musielak, Z.E.; Benner, J.W.

2005-01-01

New results are reported on the routes to chaos in increasingly complex Duffing oscillator systems, which are formed by coupling several oscillators, thereby increasing the number of degrees of freedom. Other forms of increasing system complexity through distributed excitation, different forcing function phasing, different excitation frequency ratios, and higher order coupling are also studied. Changes in the quantitative aspects of the chaotic regions and in the routes to chaos of complex Duffing systems are investigated by performing numerical simulations. It is shown that the number of chaotic regions in these systems is significantly reduced when compared to the original Duffing system, and that crisis replaces period doubling as the dominant route to chaos when the number of degrees of freedom is increased. A new discovered phenomenon is that chaos emerges in the symmetrically and asymmetrically coupled Duffing oscillators only after the quasi-periodic torus breaks down through a 3-periodic and 2-periodic window, respectively

Chaotic dynamic and control for micro-electro-mechanical systems of massive storage with harmonic base excitation

International Nuclear Information System (INIS)

Perez Polo, Manuel F.; Perez Molina, Manuel; Gil Chica, Javier

2009-01-01

This paper explores chaotic behaviour and control of micro-electro-mechanical systems (MEMS), which consist of thousands of small read/write probe tips that access gigabytes of data stored in a non-volatile magnetic surface. The model of the system is formed by two masses connected by a nonlinear spring and a viscous damping. The paper shows that, by means of an adequate feedback law, the masses can behave as two coupled Duffing's oscillators, which may reach chaotic behaviour when harmonic forces are applied. The chaotic motion is destroyed by applying the following control strategies: (i) static output feedback control law with constant forces and (ii) geometric nonlinear control. The aim is to drive the masses to a set point even with harmonic base excitation, by using chaotic dynamics and nonlinear control. The paper shows that it is possible to obtain a positioning time around a few ms with sub-nanometre accuracy, velocities, accelerations and forces, as it appears in the design of present MEMS devices. Numerical simulations are used to verify the mathematical discussions.

Chaotic dynamic and control for micro-electro-mechanical systems of massive storage with harmonic base excitation

Energy Technology Data Exchange (ETDEWEB)

Perez Polo, Manuel F. [Departamento de Fisica, Ingenieria de Sistemas y Teoria de la Senal, Universidad de Alicante, Escuela Politecnica Superior, Campus de San Vicente, 03071 Alicante (Spain)], E-mail: manolo@dfists.ua.es; Perez Molina, Manuel [Facultad de Ciencias Matematicas, Universidad Nacional de Educacion a Distancia. UNED, C/Boyero 12-1A, Alicante 03007 (Spain)], E-mail: ma_perez_m@hotmail.com; Gil Chica, Javier [Departamento de Fisica, Ingenieria de Sistemas y Teoria de la Senal, Universidad de Alicante, Escuela Politecnica Superior, Campus de San Vicente, 03071 Alicante (Spain)], E-mail: gil@dfists.ua.es

2009-02-15

This paper explores chaotic behaviour and control of micro-electro-mechanical systems (MEMS), which consist of thousands of small read/write probe tips that access gigabytes of data stored in a non-volatile magnetic surface. The model of the system is formed by two masses connected by a nonlinear spring and a viscous damping. The paper shows that, by means of an adequate feedback law, the masses can behave as two coupled Duffing's oscillators, which may reach chaotic behaviour when harmonic forces are applied. The chaotic motion is destroyed by applying the following control strategies: (i) static output feedback control law with constant forces and (ii) geometric nonlinear control. The aim is to drive the masses to a set point even with harmonic base excitation, by using chaotic dynamics and nonlinear control. The paper shows that it is possible to obtain a positioning time around a few ms with sub-nanometre accuracy, velocities, accelerations and forces, as it appears in the design of present MEMS devices. Numerical simulations are used to verify the mathematical discussions.

Feedback control of persistent-current oscillation based on the atomic-clock technique

Science.gov (United States)

Yu, Deshui; Dumke, Rainer

2018-05-01

We propose a scheme of stabilizing the persistent-current Rabi oscillation based on the flux qubit-resonator-atom hybrid structure. The low-Q L C resonator weakly interacts with the flux qubit and maps the persistent-current Rabi oscillation of the flux qubit onto the intraresonator electric field. This oscillating electric field is further coupled to a Rydberg-Rydberg transition of the 87Rb atoms. The Rabi-frequency fluctuation of the flux qubit is deduced from measuring the atomic population via the fluorescence detection and stabilized by feedback controlling the external flux bias. Our numerical simulation indicates that the feedback-control method can efficiently suppress the background fluctuations in the flux qubit, especially in the low-frequency limit. This technique may be extensively applicable to different types of superconducting circuits, paving a way to long-term-coherence superconducting quantum information processing.

Modeling and Analysis of a Fractional-Order Generalized Memristor-Based Chaotic System and Circuit Implementation

Science.gov (United States)

Yang, Ningning; Xu, Cheng; Wu, Chaojun; Jia, Rong; Liu, Chongxin

2017-12-01

Memristor is a nonlinear “missing circuit element”, that can easily achieve chaotic oscillation. Memristor-based chaotic systems have received more and more attention. Research shows that fractional-order systems are more close to real systems. As an important parameter, the order can increase the flexibility and degree of freedom of the system. In this paper, a fractional-order generalized memristor, which consists of a diode bridge and a parallel circuit with an equivalent unit circuit and a linear resistance, is proposed. Frequency and electrical characteristics of the fractional-order memristor are analyzed. A chain structure circuit is used to implement the fractional-order unit circuit. Then replacing the conventional Chua’s diode by the fractional-order generalized memristor, a fractional-order memristor-based chaotic circuit is proposed. A large amount of research work has been done to investigate the influence of the order on the dynamical behaviors of the fractional-order memristor-based chaotic circuit. Varying with the order, the system enters the chaotic state from the periodic state through the Hopf bifurcation and period-doubling bifurcation. The chaotic state of the system has two types of attractors: single-scroll and double-scroll attractor. The stability theory of fractional-order systems is used to determine the minimum order occurring Hopf bifurcation. And the influence of the initial value on the system is analyzed. Circuit simulations are designed to verify the results of theoretical analysis and numerical simulation.

Chaotic magnetic field line in toroidal plasmas

International Nuclear Information System (INIS)

Hatori, Tadatsugu; Abe, Yoshihiko; Urata, Kazuhiro; Irie, Haruyuki.

1989-05-01

This is an introductory review of chaotic magnetic field line in plasmas, together with some new results, with emphasis on the long-time tail and the fractional Brownian motion of the magnetic field line. The chaotic magnetic field line in toroidal plasmas is a typical chaotic phenomena in the Hamiltonian dynamical systems. The onset of stochasticity induced by a major magnetic perturbation is thought to cause a macroscopic rapid phenomena called the current disruption in the tokamak discharges. Numerical simulations on the basis of magnetohydrodynamics reveal in fact the disruptive phenomena. Some dynamical models which include the area-preserving mapping such as the standard mapping, and the two-wave Hamiltonian system can model the stochastic magnetic field. Theoretical results with use of the functional integral representation are given regarding the long-time tail on the basis of the radial twist mapping. It is shown that application of renormalization group technique to chaotic orbit in the two-wave Hamiltonian system proves decay of the velocity autocorrelation function with the power law. Some new numerical results are presented which supports these theoretical results. (author)

Chaotic characteristics of corona discharges in atmospheric air

International Nuclear Information System (INIS)

Tan Xiangyu; Zhang Qiaogen; Wang Xiuhuan; Sun Fu; Zha Wei; Jia Zhijie

2008-01-01

A point-plane electrode system in atmospheric air is established to investigate the mechanism of the corona discharge. By using this system, the current pulses of the corona discharges under the 50 Hz ac voltage are measured using partial discharge (PD) measurement instrument and constitute the point-plane voltage-current (V-I) characteristic equation together with the voltage. Then, this paper constructs the nonlinear circuit model and differential equations of the system in an attempt to give the underlying dynamic mechanism based on the nonlinear V-I characteristics of the point-plane corona discharges. The results show that the chaotic phenomenon is found in the corona circuit by the experimental study and nonlinear dynamic analysis. The basic dynamic characteristics, including the Lyapunov exponent, the existence of the strange attractors, and the equilibrium points, are also found and analyzed in the development process of the corona circuit. Moreover, the time series of the corona current pulses obtained in the experiment is used to demonstrate the chaotic characteristics of the corona current based on the nonlinear dynamic circuit theory and the experimental basis. It is pointed out that the corona phenomenon is not a purely stochastic phenomenon but a short term deterministic chaotic activity

Circuit simulation and physical implementation for a memristor-based colpitts oscillator

Directory of Open Access Journals (Sweden)

Hongmin Deng

2017-03-01

Full Text Available This paper implements two kinds of memristor-based colpitts oscillators, namely, the circuit where the memristor is added into the feedback network of the oscillator in parallel and series, respectively. First, a MULTISIM simulation circuit for the memristive colpitts oscillator is built, where an emulator constructed by some off-the-shelf components is utilized to replace the memristor. Then the physical system is implemented in terms of the MULTISIM simulation circuit. Circuit simulation and experimental study show that this memristive colpitts oscillator can exhibit periodic, quasi-periodic, and chaotic behaviors with certain parameter’s variances. Besides, in a sense, the circuit is robust with circuit parameters and device types.

Chaotic invasive weed optimization algorithm with application to parameter estimation of chaotic systems

International Nuclear Information System (INIS)

Ahmadi, Mohamadreza; Mojallali, Hamed

2012-01-01

Highlights: ► A new meta-heuristic optimization algorithm. ► Integration of invasive weed optimization and chaotic search methods. ► A novel parameter identification scheme for chaotic systems. - Abstract: This paper introduces a novel hybrid optimization algorithm by taking advantage of the stochastic properties of chaotic search and the invasive weed optimization (IWO) method. In order to deal with the weaknesses associated with the conventional method, the proposed chaotic invasive weed optimization (CIWO) algorithm is presented which incorporates the capabilities of chaotic search methods. The functionality of the proposed optimization algorithm is investigated through several benchmark multi-dimensional functions. Furthermore, an identification technique for chaotic systems based on the CIWO algorithm is outlined and validated by several examples. The results established upon the proposed scheme are also supplemented which demonstrate superior performance with respect to other conventional methods.

Global pulse synchronization of chaotic oscillators through fast-switching: theory and experiments

International Nuclear Information System (INIS)

Porfiri, Maurizio; Fiorilli, Francesca

2009-01-01

We study pulse synchronization of chaotic systems in master-slave configuration. The slave system is unidirectionally coupled to the master system through an intermittent linear error feedback coupling, whose gain matrix periodically switches among a finite set of constant matrices. Using Lyapunov-stability theory, fast-switching techniques, and the concept of matrix measure, we derive sufficient conditions for global synchronization. The derived conditions are specialized to the case of Chua's circuits. An inductorless realization of coupled Chua's circuits is developed to illustrate the effectiveness of the proposed approach.

Hysteresis compensation of the Prandtl-Ishlinskii model for piezoelectric actuators using modified particle swarm optimization with chaotic map.

Science.gov (United States)

Long, Zhili; Wang, Rui; Fang, Jiwen; Dai, Xufei; Li, Zuohua

2017-07-01

Piezoelectric actuators invariably exhibit hysteresis nonlinearities that tend to become significant under the open-loop condition and could cause oscillations and errors in nanometer-positioning tasks. Chaotic map modified particle swarm optimization (MPSO) is proposed and implemented to identify the Prandtl-Ishlinskii model for piezoelectric actuators. Hysteresis compensation is attained through application of an inverse Prandtl-Ishlinskii model, in which the parameters are formulated based on the original model with chaotic map MPSO. To strengthen the diversity and improve the searching ergodicity of the swarm, an initial method of adaptive inertia weight based on a chaotic map is proposed. To compare and prove that the swarm's convergence occurs before stochastic initialization and to attain an optimal particle swarm optimization algorithm, the parameters of a proportional-integral-derivative controller are searched using self-tuning, and the simulated results are used to verify the search effectiveness of chaotic map MPSO. The results show that chaotic map MPSO is superior to its competitors for identifying the Prandtl-Ishlinskii model and that the inverse Prandtl-Ishlinskii model can provide hysteresis compensation under different conditions in a simple and effective manner.

Reconfigurable chaotic logic gates based on novel chaotic circuit

International Nuclear Information System (INIS)

Behnia, S.; Pazhotan, Z.; Ezzati, N.; Akhshani, A.

2014-01-01

Highlights: • A novel method for implementing logic gates based on chaotic maps is introduced. • The logic gates can be implemented without any changes in the threshold voltage. • The chaos-based logic gates may serve as basic components of future computing devices. - Abstract: The logical operations are one of the key issues in today’s computer architecture. Nowadays, there is a great interest in developing alternative ways to get the logic operations by chaos computing. In this paper, a novel implementation method of reconfigurable logic gates based on one-parameter families of chaotic maps is introduced. The special behavior of these chaotic maps can be utilized to provide same threshold voltage for all logic gates. However, there is a wide interval for choosing a control parameter for all reconfigurable logic gates. Furthermore, an experimental implementation of this nonlinear system is presented to demonstrate the robustness of computing capability of chaotic circuits

Simulated wind-generated inertial oscillations compared to current measurements in the northern North Sea

Science.gov (United States)

Bruserud, Kjersti; Haver, Sverre; Myrhaug, Dag

2018-04-01

Measured current speed data show that episodes of wind-generated inertial oscillations dominate the current conditions in parts of the northern North Sea. In order to acquire current data of sufficient duration for robust estimation of joint metocean design conditions, such as wind, waves, and currents, a simple model for episodes of wind-generated inertial oscillations is adapted for the northern North Sea. The model is validated with and compared against measured current data at one location in the northern North Sea and found to reproduce the measured maximum current speed in each episode with considerable accuracy. The comparison is further improved when a small general background current is added to the simulated maximum current speeds. Extreme values of measured and simulated current speed are estimated and found to compare well. To assess the robustness of the model and the sensitivity of current conditions from location to location, the validated model is applied at three other locations in the northern North Sea. In general, the simulated maximum current speeds are smaller than the measured, suggesting that wind-generated inertial oscillations are not as prominent at these locations and that other current conditions may be governing. Further analysis of the simulated current speed and joint distribution of wind, waves, and currents for design of offshore structures will be presented in a separate paper.

Temperature oscillations in methanol partial oxidation reactor for the production of hydrogen

Energy Technology Data Exchange (ETDEWEB)

Kim, Jinsu; Byeon, Jeonguk; Seo, Il Gyu; Lee, Hyun Chan; Kim, Dong Hyun; Lee, Jietae [Kyungpook National University, Daegu (Korea, Republic of)

2013-04-15

Methanol partial oxidation (POX) is a well-known reforming reaction for the production of hydrogen from methanol. Since POX is relatively fast and highly exothermic, this reforming method will be efficient for the fast start-up and load-following operation. However, POX generates hot spots around catalyst and even oscillations in the reactor temperature. These should be relieved for longer operations of the reactor without catalyst degradations. For this, temperature oscillations in a POX reactor are investigated experimentally. Various patterns of temperature oscillations according to feed flow rates of reactants and reactor temperatures are obtained. The bifurcation phenomena from regular oscillations to chaotic oscillations are found as the methanol flow rate increases. These experimental results can be used for theoretical analyses of oscillations and for designing safe reforming reactors.

Temperature oscillations in methanol partial oxidation reactor for the production of hydrogen

International Nuclear Information System (INIS)

Kim, Jinsu; Byeon, Jeonguk; Seo, Il Gyu; Lee, Hyun Chan; Kim, Dong Hyun; Lee, Jietae

2013-01-01

Methanol partial oxidation (POX) is a well-known reforming reaction for the production of hydrogen from methanol. Since POX is relatively fast and highly exothermic, this reforming method will be efficient for the fast start-up and load-following operation. However, POX generates hot spots around catalyst and even oscillations in the reactor temperature. These should be relieved for longer operations of the reactor without catalyst degradations. For this, temperature oscillations in a POX reactor are investigated experimentally. Various patterns of temperature oscillations according to feed flow rates of reactants and reactor temperatures are obtained. The bifurcation phenomena from regular oscillations to chaotic oscillations are found as the methanol flow rate increases. These experimental results can be used for theoretical analyses of oscillations and for designing safe reforming reactors

Chaotic Flows Correlation effects and coherent structures

CERN Document Server

Bakunin, Oleg G

2011-01-01

The book introduces readers to and summarizes the current ideas and theories about the basic mechanisms for transport in chaotic flows. Typically no single paradigmatic approach exists as this topic is relevant for fields as diverse as plasma physics, geophysical flows and various branches of engineering. Accordingly, the dispersion of matter in chaotic or turbulent flows is analyzed from different perspectives. Partly based on lecture courses given by the author, this book addresses both graduate students and researchers in search of a high-level but approachable and broad introduction to the topic.

Critical current oscillations in S/F heterostructures in the presence of s-d scattering

International Nuclear Information System (INIS)

Vedyayev, A.V.; Ryzhanova, N.V.; Pugach, N.G.

2006-01-01

Josephson current is investigated in the superconductor/ferromagnet/superconductor junction. It was shown that the current exhibited damping oscillations as a function of the ferromagnetic layer thickness. Previous theories based on Usadel or Eilenberger equations have predicted that the damping length and oscillation period divided by 2π were the same for weak ferromagnetic spacer. This contradicts past experiments. A new calculation of the Josephson current is proposed. The Gorkov equations are solved taking into account s-d scattering in ferromagnet. It is shown that the oscillation period depends only on the exchange magnetic field in the spacer, whereas the damping length is connected to the ferromagnetic mean free path. The concordance with the former experiment allows one to conclude that s-d scattering as a pair-breaking mechanism plays a significant role in the proximity effect in S/F heterostructures

Role of multistability in the transition to chaotic phase synchronization

DEFF Research Database (Denmark)

Postnov, D.E.; Vadivasova, T.E.; Sosnovtseva, Olga

1999-01-01

In this paper we describe the transition to phase synchronization for systems of coupled nonlinear oscillators that individually follow the Feigenbaum route to chaos. A nested structure of phase synchronized regions of different attractor families is observed. With this structure, the transition...... to nonsynchronous behavior is determined by the loss of stability for the most stable synchronous mode. It is shown that the appearance of hyperchaos and the transition from lag synchronization to phase synchronization are related to the merging of chaotic attractors from different families. Numerical examples...

Chaotic inflation and baryogenesis by right-handed sneutrinos

International Nuclear Information System (INIS)

Murayama, H.; Suzuki, H.; Yanagida, T.; Yokoyama, J.i.

1993-01-01

We present a model of chaotic inflation driven by the superpartner of the right-handed neutrino (N R ). This model gives the correct magnitude of the density perturbation observed by the Cosmic Background Explorer satellite with a right-handed neutrino mass congruent 10 13 GeV, which is also preferred by the Mikheyev-Smirnov-Wolfenstein solution to the solar neutrino problem. The reheating process is the dacay of the coherently oscillating N R . This decay process also generates lepton asymmetry via CP violation, which will be converted to baryon asymmetry thanks to the electroweak anomaly. This model can incorporate the τ-neutrino mass congruent 10 eV

Stages of chaotic synchronization.

Science.gov (United States)

Tang, D. Y.; Dykstra, R.; Hamilton, M. W.; Heckenberg, N. R.

1998-09-01

In an experimental investigation of the response of a chaotic system to a chaotic driving force, we have observed synchronization of chaos of the response system in the forms of generalized synchronization, phase synchronization, and lag synchronization to the driving signal. In this paper we compare the features of these forms of synchronized chaos and study their relations and physical origins. We found that different forms of chaotic synchronization could be interpreted as different stages of nonlinear interaction between the coupled chaotic systems. (c) 1998 American Institute of Physics.

A new control strategy of SMES for mitigating subsynchronous oscillations

Energy Technology Data Exchange (ETDEWEB)

Farahani, Mohsen, E-mail: m.farahani@basu.ac.ir [Bu-Ali Sina University, Department of Electrical Engineering, Hamedan-Iran (Iran, Islamic Republic of)

2012-12-14

This paper proposes a new strategy to mitigate the subsynchronous oscillations in power systems compensated by series capacitors via control of active power of superconducting magnetic energy storage (SMES) unit. The strategy is based on the generator acceleration signal. So, the SMES absorbs or generates the energy imbalance caused by different disturbances in the power system and suppresses the subsynchronous oscillations. The chaotic optimization algorithm (COA) is used to achieve the optimal parameter of the proposed controller. To validate the capability of the SMES in damping oscillations, some simulations with different disturbances are performed on the first model of IEEE second benchmark model. All the simulation results show that the subsynchronous resonance as well as low frequency oscillation (LFO) is satisfactorily mitigated by the SMES controlled by the proposed strategy.

A new control strategy of SMES for mitigating subsynchronous oscillations

International Nuclear Information System (INIS)

Farahani, Mohsen

2012-01-01

This paper proposes a new strategy to mitigate the subsynchronous oscillations in power systems compensated by series capacitors via control of active power of superconducting magnetic energy storage (SMES) unit. The strategy is based on the generator acceleration signal. So, the SMES absorbs or generates the energy imbalance caused by different disturbances in the power system and suppresses the subsynchronous oscillations. The chaotic optimization algorithm (COA) is used to achieve the optimal parameter of the proposed controller. To validate the capability of the SMES in damping oscillations, some simulations with different disturbances are performed on the first model of IEEE second benchmark model. All the simulation results show that the subsynchronous resonance as well as low frequency oscillation (LFO) is satisfactorily mitigated by the SMES controlled by the proposed strategy.

Synchronization and symmetry-breaking bifurcations in constructive networks of coupled chaotic oscillators

International Nuclear Information System (INIS)

Jiang Yu; Lozada-Cassou, M.; Vinet, A.

2003-01-01

The spatiotemporal dynamics of networks based on a ring of coupled oscillators with regular shortcuts beyond the nearest-neighbor couplings is studied by using master stability equations and numerical simulations. The generic criterion for dynamic synchronization has been extended to arbitrary network topologies with zero row-sum. The symmetry-breaking oscillation patterns that resulted from the Hopf bifurcation from synchronous states are analyzed by the symmetry group theory

Chaotic, fractional, and complex dynamics new insights and perspectives

CERN Document Server

Macau, Elbert; Sanjuan, Miguel

2018-01-01

The book presents nonlinear, chaotic and fractional dynamics, complex systems and networks, together with cutting-edge research on related topics. The fifteen chapters – written by leading scientists working in the areas of nonlinear, chaotic and fractional dynamics, as well as complex systems and networks – offer an extensive overview of cutting-edge research on a range of topics, including fundamental and applied research. These include but are not limited to aspects of synchronization in complex dynamical systems, universality features in systems with specific fractional dynamics, and chaotic scattering. As such, the book provides an excellent and timely snapshot of the current state of research, blending the insights and experiences of many prominent researchers.

Quantum infinite square well with an oscillating wall

International Nuclear Information System (INIS)

Glasser, M.L.; Mateo, J.; Negro, J.; Nieto, L.M.

2009-01-01

A linear matrix equation is considered for determining the time dependent wave function for a particle in a one-dimensional infinite square well having one moving wall. By a truncation approximation, whose validity is checked in the exactly solvable case of a linearly contracting wall, we examine the cases of a simple harmonically oscillating wall and a non-harmonically oscillating wall for which the defining parameters can be varied. For the latter case, we examine in closer detail the dependence on the frequency changes, and we find three regimes: an adiabatic behabiour for low frequencies, a periodic one for high frequencies, and a chaotic behaviour for an intermediate range of frequencies.

Oscillation of Critical Current by Gate Voltage in Cooper Pair Transistor

International Nuclear Information System (INIS)

Kim, N.; Cheong, Y.; Song, W.

2010-01-01

We measured the critical current of a Cooper pair transistor consisting of two Josephson junctions and a gate electrode. The Cooper pair transistors were fabricated by using electron-beam lithography and double-angle evaporation technique. The Gate voltage dependence of critical current was measured by observing voltage jumps at various gate voltages while sweeping bias current. The observed oscillation was 2e-periodic, which shows the Cooper pair transistor had low level of quasiparticle poisoning.

Chaotic Boltzmann machines

Science.gov (United States)

Suzuki, Hideyuki; Imura, Jun-ichi; Horio, Yoshihiko; Aihara, Kazuyuki

2013-01-01

The chaotic Boltzmann machine proposed in this paper is a chaotic pseudo-billiard system that works as a Boltzmann machine. Chaotic Boltzmann machines are shown numerically to have computing abilities comparable to conventional (stochastic) Boltzmann machines. Since no randomness is required, efficient hardware implementation is expected. Moreover, the ferromagnetic phase transition of the Ising model is shown to be characterised by the largest Lyapunov exponent of the proposed system. In general, a method to relate probabilistic models to nonlinear dynamics by derandomising Gibbs sampling is presented. PMID:23558425

Noise-induced chaos in a quadratically nonlinear oscillator

International Nuclear Information System (INIS)

Gan Chunbiao

2006-01-01

The present paper focuses on the noise-induced chaos in a quadratically nonlinear oscillator. Simple zero points of the stochastic Melnikov integral theoretically mean the necessary rising of noise-induced chaotic response in the system based on the stochastic Melnikov method. To quantify the noise-induced chaos, the boundary of the system's safe basin is firstly studied and it is shown to be incursively fractal when chaos arises. Three cases are considered in simulating the safe basin of the system, i.e., the system is excited only by the harmonic excitation, by both the harmonic and the Gaussian white noise excitations, and only by the Gaussian white noise excitation. Secondly, the leading Lyapunov exponent by Rosenstein's algorithm is shown to quantify the chaotic nature of the sample time series of the system. The results show that the boundary of the safe basin can also be fractal even if the system is excited only by the external Gaussian white noise. Most importantly, the almost-harmonic, the noise-induced chaotic and the thoroughly random responses can be found in the system

A Novel Fault Line Selection Method Based on Improved Oscillator System of Power Distribution Network

Directory of Open Access Journals (Sweden)

Xiaowei Wang

2014-01-01

Full Text Available A novel method of fault line selection based on IOS is presented. Firstly, the IOS is established by using math model, which adopted TZSC signal to replace built-in signal of duffing chaotic oscillator by selecting appropriate parameters. Then, each line’s TZSC decomposed by db10 wavelet packet to get CFB with the maximum energy principle, and CFB was solved by IOS. Finally, maximum chaotic distance and average chaotic distance on the phase trajectory are used to judge fault line. Simulation results show that the proposed method can accurately judge fault line and healthy line in strong noisy background. Besides, the nondetection zones of proposed method are elaborated.

Cathode voltage and discharge current oscillations in HiPIMS

Czech Academy of Sciences Publication Activity Database

Klein, P.; Hnilica, J.; Hubička, Zdeněk; Čada, Martin; Šlapanská, M.; Zemánek, M.; Vašina, P.

2017-01-01

Roč. 26, č. 5 (2017), s. 1-12, č. článku 055015. ISSN 0963-0252 R&D Projects: GA ČR(CZ) GA15-00863S Institutional support: RVO:68378271 Keywords : HiPIMS * voltage and current oscillations * spokes Subject RIV: BL - Plasma and Gas Discharge Physics OBOR OECD: Fluids and plasma physics (including surface physics) Impact factor: 3.302, year: 2016

Quadrupole oscillations as paradigm of the chaotic motion in nuclei

International Nuclear Information System (INIS)

Berezovoj, V.P.; Bolotin, Yu.L.; Gonchar, V.Yu.; Granovsky, M.Ya.

2003-01-01

A complete description of classical dynamics, generated by the Hamiltonian of quadrupole nuclear oscillations, is presented. Those peculiarities of quantum dynamics, which can be interpreted as quantum manifestations of classical stochasticity are identified. Semiclassical approximation to an energy spectrum is developed through quantization of the Birkhoff-Gustavson normal form. We show that the type of classical motion is correlated with the structure of the stationary wave functions. Correlations were found both in the coordinate space (the lattice of nodal curves and the distribution of the probability density) and in the Hilbert space associated with the integrable part of the Hamiltonian. Quadrupole oscillations of nuclei were used to investigate the shell structure destruction induced by the increase of nonintegrable perturbation, which models residual nucleon-nucleon interaction. The process of wave packet tunneling through potential barrier is considered for the case of finite motion. We demonstrate that the stringent correlation between the level quasi-crossing and the wave function delocalization, which leads to the resonant tunneling, takes place [ru

Magnetization switching and microwave oscillations in nanomagnets driven by spin-polarized currents

International Nuclear Information System (INIS)

Bertotti, G.; Magni, A.; Serpico, C.; d'Aquino, M.; Mayergoyz, I. D.; Bonin, R.

2005-01-01

Full text: Considerable interest has been generated in recent years by the discovery that a current of spin-polarized electrons can apply appreciable torques to a nanoscale ferromagnet. This mechanism was theoretically predicted and subsequently confirmed by a number of experiments which have shown that spin transfer can indeed induce switching or microwave oscillations of the magnetization. Significant efforts have been devoted to the explanation of these results, in view of the new physics involved and of the possible applications to new types of current-controlled memory cells or microwave sources and resonators . However, the precise nature of magnetization dynamics when spin-polarized currents and external magnetic fields are simultaneously present has not yet been fully understood. The spin-transfer-driven nanomagnet is a nonlinear open system that is forced far from equilibrium by the injection of the current. Thus, the appropriate framework for the study of the problem is nonlinear dynamical system theory and bifurcation theory. In this talk, it is shown that within this framework the complexity and subtlety of spin-torque effects are fully revealed and quantified, once it is recognized that both intrinsic damping and spin transfer can be treated as perturbations of the free precessional dynamics typical of ferromagnetic resonance. Complete stability diagrams are derived for the case where spin torques and external magnetic fields are simultaneously present. Quantitative predictions are made for the critical currents and fields inducing magnetization switching; for the amplitude and frequency of magnetization self-oscillations; for the conditions leading to hysteretic transitions between self-oscillations and stationary states

General hybrid projective complete dislocated synchronization with non-derivative and derivative coupling based on parameter identification in several chaotic and hyperchaotic systems

International Nuclear Information System (INIS)

Sun Jun-Wei; Shen Yi; Zhang Guo-Dong; Wang Yan-Feng; Cui Guang-Zhao

2013-01-01

According to the Lyapunov stability theorem, a new general hybrid projective complete dislocated synchronization scheme with non-derivative and derivative coupling based on parameter identification is proposed under the framework of drive-response systems. Every state variable of the response system equals the summation of the hybrid drive systems in the previous hybrid synchronization. However, every state variable of the drive system equals the summation of the hybrid response systems while evolving with time in our method. Complete synchronization, hybrid dislocated synchronization, projective synchronization, non-derivative and derivative coupling, and parameter identification are included as its special item. The Lorenz chaotic system, Rössler chaotic system, memristor chaotic oscillator system, and hyperchaotic Lü system are discussed to show the effectiveness of the proposed methods. (general)

Non-reversible evolution of quantum chaotic system. Kinetic description

International Nuclear Information System (INIS)

Chotorlishvili, L.; Skrinnikov, V.

2008-01-01

It is well known that the appearance of non-reversibility in classical chaotic systems is connected with a local instability of phase trajectories relatively to a small change of initial conditions and parameters of the system. Classical chaotic systems reveal an exponential sensitivity to these changes. This leads to an exponential growth of initial error with time, and as the result after the statistical averaging over this error, the dynamics of the system becomes non-reversible. In spite of this, the question about the origin of non-reversibility in quantum case remains actual. The point is that the classical notion of instability of phase trajectories loses its sense during quantum consideration. The current work is dedicated to the clarification of the origin of non-reversibility in quantum chaotic systems. For this purpose we study a non-stationary dynamics of the chaotic quantum system. By analogy with classical chaos, we consider an influence of a small unavoidable error of the parameter of the system on the non-reversibility of the dynamics. It is shown in the Letter that due to the peculiarity of chaotic quantum systems, the statistical averaging over the small unavoidable error leads to the non-reversible transition from the pure state into the mixed one. The second part of the Letter is dedicated to the kinematic description of the chaotic quantum-mechanical system. Using the formalism of superoperators, a muster kinematic equation for chaotic quantum system was obtained from Liouville equation under a strict mathematical consideration

Disordered chaotic strings

DEFF Research Database (Denmark)

Schäfer, Mirko; Greiner, Martin

2011-01-01

to chaotic strings. Inhomogeneous coupling weights as well as small-world perturbations of the ring-network structure are discussed. It is found that certain combinations of coupling and network disorder preserve the empirical relationship between chaotic strings and the weak and strong sector...

Synchronisation in coupled quantum Hamiltonian superconducting oscillator via a control potential

International Nuclear Information System (INIS)

Al-Khawaja, Sameer

2009-01-01

This paper presents chaos synchronisation in a SQUID device mutually coupled to a resonant LC classical circuit. Via the Hamiltonian of the coupled quantum-classical system and by means of a 'control potential' in the form of a double-well, measure synchronisation has been found to exist. A transition from quasi-periodic to chaotically synchronised orbits in the phase space has been observed, as the strength of coupling is increased between both oscillators. The system reaches a non-synchronised state if the choice of the control potential were to render both oscillators non-identical.

Transition to chaos in the damped and forced non-lnear oscillator

International Nuclear Information System (INIS)

Montenegro Joo, J.; Universidad Nacional Mayor de San Marcos, Lima

2009-01-01

A Virtual Lab to study the Transition to Chaos in second order non-linear differential equations has been developed and successfully applied to the search for chaotic behavior in the damped and forced non-linear oscillator. This simulation and visualization software evaluates the equation under investigation at up to one million time-steps, generating in real-time and on the screen, plots like amplitude of oscillation, phase diagram, amplitude oscillation peaks and an animation of an oscillator governed by the problem equation. In this way the investigator not only gets important behavior graphs but he or she also gets a physical visualization of the system under investigation. Visualizing an animation of the system under study is an enormous help because it is not always easy to interpret behavior graphs. (author).

Chaotic behavior of a Watt-type predator-prey system with impulsive control strategy

International Nuclear Information System (INIS)

Wang, Xiaoqin; Wang Weiming; Lin Xiaolin

2008-01-01

In this paper, by using theories and methods of ecology and ODE, a predator-prey system with Watt-type functional response and impulsive perturbations on the predator is established. It proves that there exists a locally asymptotically stable prey-eradication periodic solution when the impulse period is less than some critical value, otherwise, the system can be permanent. Further, by using the method of computer simulation, the influences of the impulsive perturbations on the inherent oscillation are investigated, which shows the more complex dynamics of the system we considered, such as quasi-periodic oscillation, narrow periodic window, wide periodic window, chaotic bands, period doubling bifurcation, symmetry-breaking pitchfork bifurcation, period-halving bifurcation and crisis, etc. It will be useful for studying the dynamical complexity of ecosystems

Chaotic Dynamics Mediates Brain State Transitions, Driven by Changes in Extracellular Ion Concentrations

DEFF Research Database (Denmark)

Rasmussen, Rune; H. Jensen, Mogens; L. Heltberg, Mathias

2017-01-01

Previous studies have suggested that changes in extracellular ion concentrations initiate the transition from an activity state that characterizes sleep in cortical neurons to states that characterize wakeful- ness. However, because neuronal activity and extra- cellular ion concentrations...... are interdependent, isolating their unique roles during sleep-wake transitions is not possible in vivo. Here, we extend the Averaged-Neuron model and demonstrate that, although changes in extracellular ion concentrations occur concurrently, decreasing the conductance of calcium-dependent potassium channels initiates...... the transition from sleep to wakefulness. We find that sleep is governed by stable, self-sustained oscillations in neuronal firing patterns, whereas the quiet awake state and active awake state are both governed by irregular oscillations and chaotic dynamics; transitions between these separable awake states...

Direct numerical simulation of electrokinetic instability and transition to chaotic motion

Science.gov (United States)

Demekhin, E. A.; Nikitin, N. V.; Shelistov, V. S.

2013-12-01

experimentally observed absence of regular (near-sinusoidal) oscillations for the overlimiting regimes. There is a qualitative agreement of the experimental and the theoretical values of the threshold of instability, the dominant size of the observed coherent structures, and the experimental and theoretical volt-current characteristics.

Direct numerical simulation of electrokinetic instability and transition to chaotic motion

International Nuclear Information System (INIS)

Demekhin, E. A.; Nikitin, N. V.; Shelistov, V. S.

2013-01-01

experimentally observed absence of regular (near-sinusoidal) oscillations for the overlimiting regimes. There is a qualitative agreement of the experimental and the theoretical values of the threshold of instability, the dominant size of the observed coherent structures, and the experimental and theoretical volt–current characteristics

Direct numerical simulation of electrokinetic instability and transition to chaotic motion

Energy Technology Data Exchange (ETDEWEB)

Demekhin, E. A., E-mail: edemekhi@gmail.com [Laboratory of Micro- and Nanofluidics, Moscow State University, Moscow 119192 (Russian Federation); Department of Computation Mathematics and Computer Science, Kuban State University, Krasnodar 350040 (Russian Federation); Institute of Mechanics, Moscow State University, Moscow 117192 (Russian Federation); Nikitin, N. V. [Institute of Mechanics, Moscow State University, Moscow 117192 (Russian Federation); Shelistov, V. S. [Institute of Mechanics, Moscow State University, Moscow 117192 (Russian Federation); Scientific Research Department, Kuban State University, Krasnodar 350040 (Russian Federation)

2013-12-15

experimentally observed absence of regular (near-sinusoidal) oscillations for the overlimiting regimes. There is a qualitative agreement of the experimental and the theoretical values of the threshold of instability, the dominant size of the observed coherent structures, and the experimental and theoretical volt–current characteristics.

Chaotic spectroscopy

International Nuclear Information System (INIS)

Doron, E.; Smilanski, U.

1991-11-01

We discuss the spectra of quantized chaotic billiards from the point of view of scattering theory. We show that the spectral and resonance density functions both fluctuate about a common mean. A semiclassical treatment explains this in terms of classical scattering trajectories and periodic orbits of the poincare scattering map. This formalism is used to interpret recent experiments where the spectra of chaotic cavities where measured by microwave scattering. (author)

Can the use of pulsed direct current induce oscillation in the applied pressure during spark plasma sintering?

International Nuclear Information System (INIS)

Salamon, David; Eriksson, Mirva; Nygren, Mats; Shen Zhijian

2012-01-01

The spark plasma sintering (SPS) process is known for its rapid densification of metals and ceramics. The mechanism behind this rapid densification has been discussed during the last few decades and is yet uncertain. During our SPS experiments we noticed oscillations in the applied pressure, related to a change in electric current. In this study, we investigated the effect of pulsed electrical current on the applied mechanical pressure and related changes in temperature. We eliminated the effect of sample shrinkage in the SPS setup and used a transparent quartz die allowing direct observation of the sample. We found that the use of pulsed direct electric current in our apparatus induces pressure oscillations with the amplitude depending on the current density. While sintering Ti samples we observed temperature oscillations resulting from pressure oscillations, which we attribute to magnetic forces generated within the SPS apparatus. The described current–pressure–temperature relations might increase understanding of the SPS process.

CHAOTIC CAPTURE OF NEPTUNE TROJANS

International Nuclear Information System (INIS)

Nesvorny, David; Vokrouhlicky, David

2009-01-01

Neptune Trojans (NTs) are swarms of outer solar system objects that lead/trail planet Neptune during its revolutions around the Sun. Observations indicate that NTs form a thick cloud of objects with a population perhaps ∼10 times more numerous than that of Jupiter Trojans and orbital inclinations reaching ∼25 deg. The high inclinations of NTs are indicative of capture instead of in situ formation. Here we study a model in which NTs were captured by Neptune during planetary migration when secondary resonances associated with the mean-motion commensurabilities between Uranus and Neptune swept over Neptune's Lagrangian points. This process, known as chaotic capture, is similar to that previously proposed to explain the origin of Jupiter's Trojans. We show that chaotic capture of planetesimals from an ∼35 Earth-mass planetesimal disk can produce a population of NTs that is at least comparable in number to that inferred from current observations. The large orbital inclinations of NTs are a natural outcome of chaotic capture. To obtain the ∼4:1 ratio between high- and low-inclination populations suggested by observations, planetary migration into a dynamically excited planetesimal disk may be required. The required stirring could have been induced by Pluto-sized and larger objects that have formed in the disk.

Bifurcation study of phase oscillator systems with attractive and repulsive interaction

Science.gov (United States)

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.

Noise-enhanced chaos in a weakly coupled GaAs/(Al,Ga)As superlattice

Science.gov (United States)

Yin, Zhizhen; Song, Helun; Zhang, Yaohui; Ruiz-García, Miguel; Carretero, Manuel; Bonilla, Luis L.; Biermann, Klaus; Grahn, Holger T.

2017-01-01

Noise-enhanced chaos in a doped, weakly coupled GaAs /Al0.45Ga0.55As superlattice has been observed at room temperature in experiments as well as in the results of the simulation of nonlinear transport based on a discrete tunneling model. When external noise is added, both the measured and simulated current-versus-time traces contain irregularly spaced spikes for particular applied voltages, which separate a regime of periodic current oscillations from a region of no current oscillations at all. In the voltage region without current oscillations, the electric-field profile consist of a low-field domain near the emitter contact separated by a domain wall consisting of a charge accumulation layer from a high-field regime closer to the collector contact. With increasing noise amplitude, spontaneous chaotic current oscillations appear over a wider bias voltage range. For these bias voltages, the domain boundary between the two electric-field domains becomes unstable and very small current or voltage fluctuations can trigger the domain boundary to move toward the collector and induce chaotic current spikes. The experimentally observed features are qualitatively very well reproduced by the simulations. Increased noise can consequently enhance chaotic current oscillations in semiconductor superlattices.

Implementation of an integrated op-amp based chaotic neuron model and observation of its chaotic dynamics

International Nuclear Information System (INIS)

Jung, Jinwoo; Lee, Jewon; Song, Hanjung

2011-01-01

This paper presents a fully integrated circuit implementation of an operational amplifier (op-amp) based chaotic neuron model with a bipolar output function, experimental measurements, and analyses of its chaotic behavior. The proposed chaotic neuron model integrated circuit consists of several op-amps, sample and hold circuits, a nonlinear function block for chaotic signal generation, a clock generator, a nonlinear output function, etc. Based on the HSPICE (circuit program) simulation results, approximated empirical equations for analyses were formulated. Then, the chaotic dynamical responses such as bifurcation diagrams, time series, and Lyapunov exponent were calculated using these empirical equations. In addition, we performed simulations about two chaotic neuron systems with four synapses to confirm neural network connections and got normal behavior of the chaotic neuron such as internal state bifurcation diagram according to the synaptic weight variation. The proposed circuit was fabricated using a 0.8-μm single poly complementary metal-oxide semiconductor technology. Measurements of the fabricated single chaotic neuron with ±2.5 V power supplies and a 10 kHz sampling clock frequency were carried out and compared with the simulated results.

The Lyapunov-Krasovskii theorem and a sufficient criterion for local stability of isochronal synchronization in networks of delay-coupled oscillators

Science.gov (United States)

Grzybowski, J. M. V.; Macau, E. E. N.; Yoneyama, T.

2017-05-01

This paper presents a self-contained framework for the stability assessment of isochronal synchronization in networks of chaotic and limit-cycle oscillators. The results were based on the Lyapunov-Krasovskii theorem and they establish a sufficient condition for local synchronization stability of as a function of the system and network parameters. With this in mind, a network of mutually delay-coupled oscillators subject to direct self-coupling is considered and then the resulting error equations are block-diagonalized for the purpose of studying their stability. These error equations are evaluated by means of analytical stability results derived from the Lyapunov-Krasovskii theorem. The proposed approach is shown to be a feasible option for the investigation of local stability of isochronal synchronization for a variety of oscillators coupled through linear functions of the state variables under a given undirected graph structure. This ultimately permits the systematic identification of stability regions within the high-dimensionality of the network parameter space. Examples of applications of the results to a number of networks of delay-coupled chaotic and limit-cycle oscillators are provided, such as Lorenz, Rössler, Cubic Chua's circuit, Van der Pol oscillator and the Hindmarsh-Rose neuron.

The variation of the density functions on chaotic spheres in chaotic space-like Minkowski space time

International Nuclear Information System (INIS)

El-Ahmady, A.E.

2007-01-01

In this article we introduce types of chaotic spheres in chaotic space-like Minkowski space time M n+1 . The variations of the density functions under the folding of these chaotic spheres are defined. The foldings restriction imposed on the density function are also discussed. The relations between the folding of geometry and pure chaotic manifolds are deduced. Some theorems concerning these relations are presented

Advances and applications in chaotic systems

CERN Document Server

Volos, Christos

2016-01-01

This book reports on the latest advances and applications of chaotic systems. It consists of 25 contributed chapters by experts who are specialized in the various topics addressed in this book. The chapters cover a broad range of topics of chaotic systems such as chaos, hyperchaos, jerk systems, hyperjerk systems, conservative and dissipative systems, circulant chaotic systems, multi-scroll chaotic systems, finance chaotic system, highly chaotic systems, chaos control, chaos synchronization, circuit realization and applications of chaos theory in secure communications, mobile robot, memristors, cellular neural networks, etc. Special importance was given to chapters offering practical solutions, modeling and novel control methods for the recent research problems in chaos theory. This book will serve as a reference book for graduate students and researchers with a basic knowledge of chaos theory and control systems. The resulting design procedures on the chaotic systems are emphasized using MATLAB software.

Using Chaotic System in Encryption

Science.gov (United States)

Findik, Oğuz; Kahramanli, Şirzat

In this paper chaotic systems and RSA encryption algorithm are combined in order to develop an encryption algorithm which accomplishes the modern standards. E.Lorenz's weather forecast' equations which are used to simulate non-linear systems are utilized to create chaotic map. This equation can be used to generate random numbers. In order to achieve up-to-date standards and use online and offline status, a new encryption technique that combines chaotic systems and RSA encryption algorithm has been developed. The combination of RSA algorithm and chaotic systems makes encryption system.

Study of current oscillations and hard x-ray emissions in pre-cursor phase of major disruptions in Damavand tokamak

International Nuclear Information System (INIS)

Amrollahi, R.

2002-01-01

We notice that the hard x-ray activity before disruption consists of a series of spikes, uniformly distributed in time domain forming an orderly periodic series of oscillations at a frequency of 6.0 kHz. Disruption starts with an initial fast rise followed by decay. Current decay occurs in two regimes: the first corresponds to slow decay, in which the current is oscillating and reducing down to ∼70% its max value, and the second corresponds to fast decay, in which it totally vanishes abruptly in about 0.2 ms. In the first regime, the loop voltage also oscillates with considerable amplitude. The frequency of oscillations in the first regime is measured to be also about 6.0 kHz. As well, they follow the oscillation phase of hard x-rays. Thus the micro-instabilities driven by runaway electrons, being responsible for the production of hard x-rays bursts and small current oscillations, play a significant role in the disruption. (author)

Elementary chaotic snap flows

International Nuclear Information System (INIS)

Munmuangsaen, Buncha; Srisuchinwong, Banlue

2011-01-01

Highlights: → Five new elementary chaotic snap flows and a generalization of an existing chaotic snap flow have been presented. → Three of all are conservative systems whilst three others are dissipative systems. → Four cases need only a single control parameter and a single nonlinearity. → A cubic case in a jerk representation requires only two terms and a single nonlinearity. - Abstract: Hyperjerk systems with 4th-order derivative of the form x .... =f(x ... ,x .. ,x . ,x) have been referred to as snap systems. Five new elementary chaotic snap flows and a generalization of an existing flow are presented through an extensive numerical search. Four of these flows demonstrate elegant simplicity of a single control parameter based on a single nonlinearity of a quadratic, a piecewise-linear or an exponential type. Two others demonstrate elegant simplicity of all unity-in-magnitude parameters based on either a single cubic nonlinearity or three cubic nonlinearities. The chaotic snap flow with a single cubic nonlinearity requires only two terms and can be transformed to its equivalent dynamical form of only five terms which have a single nonlinearity. An advantage is that such a chaotic flow offers only five terms even though the (four) dimension is high. Three of the chaotic snap flows are characterized as conservative systems whilst three others are dissipative systems. Basic dynamical properties are described.

Alternation of regular and chaotic dynamics in a simple two-degree-of-freedom system with nonlinear inertial coupling.

Science.gov (United States)

Sigalov, G; Gendelman, O V; AL-Shudeifat, M A; Manevitch, L I; Vakakis, A F; Bergman, L A

2012-03-01

We show that nonlinear inertial coupling between a linear oscillator and an eccentric rotator can lead to very interesting interchanges between regular and chaotic dynamical behavior. Indeed, we show that this model demonstrates rather unusual behavior from the viewpoint of nonlinear dynamics. Specifically, at a discrete set of values of the total energy, the Hamiltonian system exhibits non-conventional nonlinear normal modes, whose shape is determined by phase locking of rotatory and oscillatory motions of the rotator at integer ratios of characteristic frequencies. Considering the weakly damped system, resonance capture of the dynamics into the vicinity of these modes brings about regular motion of the system. For energy levels far from these discrete values, the motion of the system is chaotic. Thus, the succession of resonance captures and escapes by a discrete set of the normal modes causes a sequence of transitions between regular and chaotic behavior, provided that the damping is sufficiently small. We begin from the Hamiltonian system and present a series of Poincaré sections manifesting the complex structure of the phase space of the considered system with inertial nonlinear coupling. Then an approximate analytical description is presented for the non-conventional nonlinear normal modes. We confirm the analytical results by numerical simulation and demonstrate the alternate transitions between regular and chaotic dynamics mentioned above. The origin of the chaotic behavior is also discussed.

Simple Chaotic Oscillator: From Mathematical Model to Practical Experiment

Directory of Open Access Journals (Sweden)

S. Hanus

2006-04-01

Full Text Available This paper shows the circuitry implementation and practical verification of the autonomous nonlinear oscillator. Since it is described by a single third-order differential equation, its state variables can be considered as the position, velocity and acceleration and thus have direct connection to a real physical system. Moreover, for some specific configurations of internal system parameters, it can exhibit a period doubling bifurcation leading to chaos. Two different structures of the nonlinear element were verified by a comparison of numerically integrated trajectory with the oscilloscope screenshots .

Least Squares Shadowing Sensitivity Analysis of Chaotic Flow Around a Two-Dimensional Airfoil

Science.gov (United States)

Blonigan, Patrick J.; Wang, Qiqi; Nielsen, Eric J.; Diskin, Boris

2016-01-01

Gradient-based sensitivity analysis has proven to be an enabling technology for many applications, including design of aerospace vehicles. However, conventional sensitivity analysis methods break down when applied to long-time averages of chaotic systems. This breakdown is a serious limitation because many aerospace applications involve physical phenomena that exhibit chaotic dynamics, most notably high-resolution large-eddy and direct numerical simulations of turbulent aerodynamic flows. A recently proposed methodology, Least Squares Shadowing (LSS), avoids this breakdown and advances the state of the art in sensitivity analysis for chaotic flows. The first application of LSS to a chaotic flow simulated with a large-scale computational fluid dynamics solver is presented. The LSS sensitivity computed for this chaotic flow is verified and shown to be accurate, but the computational cost of the current LSS implementation is high.

Fault Diagnosis of Broken Rotor Bars in Squirrel-Cage Induction Motor of Hoister Based on Duffing Oscillator and Multifractal Dimension

Directory of Open Access Journals (Sweden)

Zhike Zhao

2014-07-01

Full Text Available This paper is to propose a novel fault diagnosis method for broken rotor bars in squirrel-cage induction motor of hoister, which is based on duffing oscillator and multifractal dimension. Firstly, based on the analysis of the structure and performance of modified duffing oscillator, the end of transitional slope from chaotic area to large-scale cycle area is selected as the optimal critical threshold of duffing oscillator by bifurcation diagrams and Lyapunov exponent. Secondly, the phase transformation duffing oscillator from chaos to intermittent chaos is sensitive to the signals, whose frequency difference is quite weak from the reference signal. The spectrums of the largest Lyapunov exponents and bifurcation diagrams of the duffing oscillator are utilized to analyze the variance in different parameters of frequency. Finally, this paper is to analyze the characteristics of both single fractal (box-counting dimension and multifractal and make a comparison between them. Multifractal detrended fluctuation analysis is applied to detect extra frequency component of current signal. Experimental results reveal that the method is effective for early detection of broken rotor bars in squirrel-cage induction motor of hoister.

Field and power dependence of auto-oscillations in yttrium-iron-garnet films

International Nuclear Information System (INIS)

McMichael, R.D.; Wigen, P.E.

1988-01-01

The nonlinear response of the magnetic spin system in yttrium-iron-garnet (YIG) thin films to high-power ferromagnetic resonance (FMR) at perpendicular resonance was studied and the results are presented. A diagram of the regions of auto-oscillation of the system as a function of field and power is presented which shows the modes that appear in low-power FMR becoming unstable to auto-oscillations with increased power. The auto-oscillations exhibit periodic, quasiperiodic, period doubling, and chaotic behavior with typical frequencies in the MHz range. The domains of oscillatory behavior due to individual resonance modes are seen to merge and shift to lower fields as power is increased. Possible mechanisms for the behavior are proposed

From determinism and probability to chaos: chaotic evolution towards philosophy and methodology of chaotic optimization.

Science.gov (United States)

Pei, Yan

2015-01-01

We present and discuss philosophy and methodology of chaotic evolution that is theoretically supported by chaos theory. We introduce four chaotic systems, that is, logistic map, tent map, Gaussian map, and Hénon map, in a well-designed chaotic evolution algorithm framework to implement several chaotic evolution (CE) algorithms. By comparing our previous proposed CE algorithm with logistic map and two canonical differential evolution (DE) algorithms, we analyse and discuss optimization performance of CE algorithm. An investigation on the relationship between optimization capability of CE algorithm and distribution characteristic of chaotic system is conducted and analysed. From evaluation result, we find that distribution of chaotic system is an essential factor to influence optimization performance of CE algorithm. We propose a new interactive EC (IEC) algorithm, interactive chaotic evolution (ICE) that replaces fitness function with a real human in CE algorithm framework. There is a paired comparison-based mechanism behind CE search scheme in nature. A simulation experimental evaluation is conducted with a pseudo-IEC user to evaluate our proposed ICE algorithm. The evaluation result indicates that ICE algorithm can obtain a significant better performance than or the same performance as interactive DE. Some open topics on CE, ICE, fusion of these optimization techniques, algorithmic notation, and others are presented and discussed.

From Determinism and Probability to Chaos: Chaotic Evolution towards Philosophy and Methodology of Chaotic Optimization

Science.gov (United States)

2015-01-01

We present and discuss philosophy and methodology of chaotic evolution that is theoretically supported by chaos theory. We introduce four chaotic systems, that is, logistic map, tent map, Gaussian map, and Hénon map, in a well-designed chaotic evolution algorithm framework to implement several chaotic evolution (CE) algorithms. By comparing our previous proposed CE algorithm with logistic map and two canonical differential evolution (DE) algorithms, we analyse and discuss optimization performance of CE algorithm. An investigation on the relationship between optimization capability of CE algorithm and distribution characteristic of chaotic system is conducted and analysed. From evaluation result, we find that distribution of chaotic system is an essential factor to influence optimization performance of CE algorithm. We propose a new interactive EC (IEC) algorithm, interactive chaotic evolution (ICE) that replaces fitness function with a real human in CE algorithm framework. There is a paired comparison-based mechanism behind CE search scheme in nature. A simulation experimental evaluation is conducted with a pseudo-IEC user to evaluate our proposed ICE algorithm. The evaluation result indicates that ICE algorithm can obtain a significant better performance than or the same performance as interactive DE. Some open topics on CE, ICE, fusion of these optimization techniques, algorithmic notation, and others are presented and discussed. PMID:25879067

From Determinism and Probability to Chaos: Chaotic Evolution towards Philosophy and Methodology of Chaotic Optimization

Directory of Open Access Journals (Sweden)

Yan Pei

2015-01-01

Full Text Available We present and discuss philosophy and methodology of chaotic evolution that is theoretically supported by chaos theory. We introduce four chaotic systems, that is, logistic map, tent map, Gaussian map, and Hénon map, in a well-designed chaotic evolution algorithm framework to implement several chaotic evolution (CE algorithms. By comparing our previous proposed CE algorithm with logistic map and two canonical differential evolution (DE algorithms, we analyse and discuss optimization performance of CE algorithm. An investigation on the relationship between optimization capability of CE algorithm and distribution characteristic of chaotic system is conducted and analysed. From evaluation result, we find that distribution of chaotic system is an essential factor to influence optimization performance of CE algorithm. We propose a new interactive EC (IEC algorithm, interactive chaotic evolution (ICE that replaces fitness function with a real human in CE algorithm framework. There is a paired comparison-based mechanism behind CE search scheme in nature. A simulation experimental evaluation is conducted with a pseudo-IEC user to evaluate our proposed ICE algorithm. The evaluation result indicates that ICE algorithm can obtain a significant better performance than or the same performance as interactive DE. Some open topics on CE, ICE, fusion of these optimization techniques, algorithmic notation, and others are presented and discussed.

Period doubling cascades of limit cycles in cardiac action potential models as precursors to chaotic early Afterdepolarizations.

Science.gov (United States)

Kügler, Philipp; Bulelzai, M A K; Erhardt, André H

2017-04-04

Early afterdepolarizations (EADs) are pathological voltage oscillations during the repolarization phase of cardiac action potentials (APs). EADs are caused by drugs, oxidative stress or ion channel disease, and they are considered as potential precursors to cardiac arrhythmias in recent attempts to redefine the cardiac drug safety paradigm. The irregular behaviour of EADs observed in experiments has been previously attributed to chaotic EAD dynamics under periodic pacing, made possible by a homoclinic bifurcation in the fast subsystem of the deterministic AP system of differential equations. In this article we demonstrate that a homoclinic bifurcation in the fast subsystem of the action potential model is neither a necessary nor a sufficient condition for the genesis of chaotic EADs. We rather argue that a cascade of period doubling (PD) bifurcations of limit cycles in the full AP system paves the way to chaotic EAD dynamics across a variety of models including a) periodically paced and spontaneously active cardiomyocytes, b) periodically paced and non-active cardiomyocytes as well as c) unpaced and spontaneously active cardiomyocytes. Furthermore, our bifurcation analysis reveals that chaotic EAD dynamics may coexist in a stable manner with fully regular AP dynamics, where only the initial conditions decide which type of dynamics is displayed. EADs are a potential source of cardiac arrhythmias and hence are of relevance both from the viewpoint of drug cardiotoxicity testing and the treatment of cardiomyopathies. The model-independent association of chaotic EADs with period doubling cascades of limit cycles introduced in this article opens novel opportunities to study chaotic EADs by means of bifurcation control theory and inverse bifurcation analysis. Furthermore, our results may shed new light on the synchronization and propagation of chaotic EADs in homogeneous and heterogeneous multicellular and cardiac tissue preparations.

A simple chaotic delay differential equation

International Nuclear Information System (INIS)

Sprott, J.C.

2007-01-01

The simplest chaotic delay differential equation with a sinusoidal nonlinearity is described, including the route to chaos, Lyapunov exponent spectrum, and chaotic diffusion. It is prototypical of many other high-dimensional chaotic systems

Initial conditions for chaotic inflation

International Nuclear Information System (INIS)

Brandenberger, R.; Kung, J.; Feldman, H.

1991-01-01

In contrast to many other inflationary Universe models, chaotic inflation does not depend on fine tuning initial conditions. Within the context of linear perturbation theory, it is shown that chaotic inflation is stable towards both metric and matter perturbations. Neglecting gravitational perturbations, it is shown that chaotic inflation is an attractor in initial condition space. (orig.)

Amplitude oscillations in a non-equilibrium polariton condensate

Science.gov (United States)

Brierley, Richard; Littlewood, Peter; Eastham, Paul

2011-03-01

Like cold atomic gases, semiconductor nanostructures provide new opportunities for exploring non-equilibrium quantum dynamics. In semiconductor microcavities the strong coupling between trapped photons and excitons produces new quasiparticles, polaritons, which can undergo Bose-Einstein condensation. Quantum quenches can be realised by rapidly creating cold exciton populations with a laser [Eastham and Phillips, PRB 79 165303 (2009)]. The mean field theory of non-equilibrium polariton condensates predicts oscillations in the condensate amplitude due to the excitation of a Higgs mode. These oscillations are the analogs of those predicted in quenched cold atomic gases and may occur in the polariton system after performing a quench or by direct excitation of the amplitude mode. We have studied the stability of these oscillations beyond mean field theory. We show that homogeneous amplitude oscillations are unstable to decay into lower energy phase modes at finite wavevectors, suggesting the onset of chaotic behaviour. The resulting hierarchy of decay processes can be understood by analogy to optical parametric oscillators in microcavities. Polariton systems thus provide an interesting opportunity to study the dynamics of Higgs-like modes in a solid state system.

Applications of Chaotic Dynamics in Robotics

Directory of Open Access Journals (Sweden)

Xizhe Zang

2016-03-01

Full Text Available This article presents a summary of applications of chaos and fractals in robotics. Firstly, basic concepts of deterministic chaos and fractals are discussed. Then, fundamental tools of chaos theory used for identifying and quantifying chaotic dynamics will be shared. Principal applications of chaos and fractal structures in robotics research, such as chaotic mobile robots, chaotic behaviour exhibited by mobile robots interacting with the environment, chaotic optimization algorithms, chaotic dynamics in bipedal locomotion and fractal mechanisms in modular robots will be presented. A brief survey is reported and an analysis of the reviewed publications is also presented.

Closed-loop suppression of chaos in nonlinear driven oscillators

Science.gov (United States)

Aguirre, L. A.; Billings, S. A.

1995-05-01

This paper discusses the suppression of chaos in nonlinear driven oscillators via the addition of a periodic perturbation. Given a system originally undergoing chaotic motions, it is desired that such a system be driven to some periodic orbit. This can be achieved by the addition of a weak periodic signal to the oscillator input. This is usually accomplished in open loop, but this procedure presents some difficulties which are discussed in the paper. To ensure that this is attained despite uncertainties and possible disturbances on the system, a procedure is suggested to perform control in closed loop. In addition, it is illustrated how a model, estimated from input/output data, can be used in the design. Numerical examples which use the Duffing-Ueda and modified van der Pol oscillators are included to illustrate some of the properties of the new approach.

Mixed-mode oscillations and chaos in a prey-predator system with dormancy of predators.

Science.gov (United States)

Kuwamura, Masataka; Chiba, Hayato

2009-12-01

It is shown that the dormancy of predators induces mixed-mode oscillations and chaos in the population dynamics of a prey-predator system under certain conditions. The mixed-mode oscillations and chaos are shown to bifurcate from a coexisting equilibrium by means of the theory of fast-slow systems. These results may help to find experimental conditions under which one can demonstrate chaotic population dynamics in a simple phytoplankton-zooplankton (-resting eggs) community in a microcosm with a short duration.

Color image encryption based on Coupled Nonlinear Chaotic Map

International Nuclear Information System (INIS)

Mazloom, Sahar; Eftekhari-Moghadam, Amir Masud

2009-01-01

Image encryption is somehow different from text encryption due to some inherent features of image such as bulk data capacity and high correlation among pixels, which are generally difficult to handle by conventional methods. The desirable cryptographic properties of the chaotic maps such as sensitivity to initial conditions and random-like behavior have attracted the attention of cryptographers to develop new encryption algorithms. Therefore, recent researches of image encryption algorithms have been increasingly based on chaotic systems, though the drawbacks of small key space and weak security in one-dimensional chaotic cryptosystems are obvious. This paper proposes a Coupled Nonlinear Chaotic Map, called CNCM, and a novel chaos-based image encryption algorithm to encrypt color images by using CNCM. The chaotic cryptography technique which used in this paper is a symmetric key cryptography with a stream cipher structure. In order to increase the security of the proposed algorithm, 240 bit-long secret key is used to generate the initial conditions and parameters of the chaotic map by making some algebraic transformations to the key. These transformations as well as the nonlinearity and coupling structure of the CNCM have enhanced the cryptosystem security. For getting higher security and higher complexity, the current paper employs the image size and color components to cryptosystem, thereby significantly increasing the resistance to known/chosen-plaintext attacks. The results of several experimental, statistical analysis and key sensitivity tests show that the proposed image encryption scheme provides an efficient and secure way for real-time image encryption and transmission.

An electronically tunable current-mode quadrature oscillator using PCAs

OpenAIRE

Herencsár, Norbert; Lahiri, Abhirup; Vrba, Kamil; Koton, Jaroslav

2012-01-01

The paper presents a new realization of active RC sinusoidal oscillator with electronically tunable condition and frequency of oscillation. As compared to the class of three resistors, two capacitors (3R-2C) based canonic oscillators, the proposed circuit here uses only two resistors and two capacitors as the passive components and still provides non-interactive tuning laws for the condition of oscillation (CO) and the frequency of oscillation (FO). The proposed circuit employs new bipolar pr...

Estimating model parameters in nonautonomous chaotic systems using synchronization

International Nuclear Information System (INIS)

Yang, Xiaoli; Xu, Wei; Sun, Zhongkui

2007-01-01

In this Letter, a technique is addressed for estimating unknown model parameters of multivariate, in particular, nonautonomous chaotic systems from time series of state variables. This technique uses an adaptive strategy for tracking unknown parameters in addition to a linear feedback coupling for synchronizing systems, and then some general conditions, by means of the periodic version of the LaSalle invariance principle for differential equations, are analytically derived to ensure precise evaluation of unknown parameters and identical synchronization between the concerned experimental system and its corresponding receiver one. Exemplifies are presented by employing a parametrically excited 4D new oscillator and an additionally excited Ueda oscillator. The results of computer simulations reveal that the technique not only can quickly track the desired parameter values but also can rapidly respond to changes in operating parameters. In addition, the technique can be favorably robust against the effect of noise when the experimental system is corrupted by bounded disturbance and the normalized absolute error of parameter estimation grows almost linearly with the cutoff value of noise strength in simulation

Chaotic evolution of prisoner's dilemma game with volunteering on interdependent networks

Science.gov (United States)

Luo, Chao; Zhang, Xiaolin; Zheng, YuanJie

2017-06-01

In this article, the evolution of prisoner's dilemma game with volunteering on interdependent networks is investigated. Different from the traditional two-strategy game, voluntary participation as an additional strategy is involved in repeated game, that can introduce more complex evolutionary dynamics. And, interdependent networks provide a more generalized network architecture to study the intricate variability of dynamics. We have showed that voluntary participation could effectively promote the density of co-operation, that is also greatly affected by interdependent strength between two coupled networks. We further discussed the influence of interdependent strength on the densities of different strategies and found that an intermediate interdependence would play a bigger role on the evolution of dynamics. Subsequently, the critical values of the defection temptation for phase transitions under different conditions have been studied. Moreover, the global oscillations induced by the circle of dominance of three strategies on interdependent networks have been quantitatively investigated. Counter-intuitively, the oscillations of strategy densities are not periodic or stochastic, but have rich dynamical behaviors. By means of various analysis tools, we have demonstrated the global oscillations of strategy densities possessed chaotic characteristics.

Enhancement of multitasking performance and neural oscillations by transcranial alternating current stimulation.

Science.gov (United States)

Hsu, Wan-Yu; Zanto, Theodore P; van Schouwenburg, Martine R; Gazzaley, Adam

2017-01-01

Multitasking is associated with the generation of stimulus-locked theta (4-7 Hz) oscillations arising from prefrontal cortex (PFC). Transcranial alternating current stimulation (tACS) is a non-invasive brain stimulation technique that influences endogenous brain oscillations. Here, we investigate whether applying alternating current stimulation within the theta frequency band would affect multitasking performance, and explore tACS effects on neurophysiological measures. Brief runs of bilateral PFC theta-tACS were applied while participants were engaged in a multitasking paradigm accompanied by electroencephalography (EEG) data collection. Unlike an active control group, a tACS stimulation group showed enhancement of multitasking performance after a 90-minute session (F1,35 = 6.63, p = 0.01, ηp2 = 0.16; effect size = 0.96), coupled with significant modulation of posterior beta (13-30 Hz) activities (F1,32 = 7.66, p = 0.009, ηp2 = 0.19; effect size = 0.96). Across participant regression analyses indicated that those participants with greater increases in frontal theta, alpha and beta oscillations exhibited greater multitasking performance improvements. These results indicate frontal theta-tACS generates benefits on multitasking performance accompanied by widespread neuronal oscillatory changes, and suggests that future tACS studies with extended treatments are worth exploring as promising tools for cognitive enhancement.

Enhancement of multitasking performance and neural oscillations by transcranial alternating current stimulation.

Directory of Open Access Journals (Sweden)

Wan-Yu Hsu

Full Text Available Multitasking is associated with the generation of stimulus-locked theta (4-7 Hz oscillations arising from prefrontal cortex (PFC. Transcranial alternating current stimulation (tACS is a non-invasive brain stimulation technique that influences endogenous brain oscillations. Here, we investigate whether applying alternating current stimulation within the theta frequency band would affect multitasking performance, and explore tACS effects on neurophysiological measures. Brief runs of bilateral PFC theta-tACS were applied while participants were engaged in a multitasking paradigm accompanied by electroencephalography (EEG data collection. Unlike an active control group, a tACS stimulation group showed enhancement of multitasking performance after a 90-minute session (F1,35 = 6.63, p = 0.01, ηp2 = 0.16; effect size = 0.96, coupled with significant modulation of posterior beta (13-30 Hz activities (F1,32 = 7.66, p = 0.009, ηp2 = 0.19; effect size = 0.96. Across participant regression analyses indicated that those participants with greater increases in frontal theta, alpha and beta oscillations exhibited greater multitasking performance improvements. These results indicate frontal theta-tACS generates benefits on multitasking performance accompanied by widespread neuronal oscillatory changes, and suggests that future tACS studies with extended treatments are worth exploring as promising tools for cognitive enhancement.

A new chaotic secure communication scheme

International Nuclear Information System (INIS)

Hua Changchun; Yang Bo; Ouyang Gaoxiang; Guan Xinping

2005-01-01

A new chaotic secure communication scheme is constructed. Unified chaotic system is used to encrypt the emitted signal. Different from the existing chaotic secure communication methods, the useful information is embodied in the parameter of chaotic systems in this Letter. The receiver is designed which can succeed in recovering the former signal. Finally computer simulations are done to verify the proposed methods, and the results show that the obtained theoretic results are feasible and efficient

Sustained oscillations, irregular firing and chaotic dynamics in hierarchical modular networks with mixtures of electrophysiological cell types

Directory of Open Access Journals (Sweden)

Petar eTomov

2014-09-01

Full Text Available The cerebral cortex exhibits neural activity even in the absence of externalstimuli. This self-sustained activity is characterized by irregular firing ofindividual neurons and population oscillations with a broad frequency range.Questions that arise in this context, are: What are the mechanismsresponsible for the existence of neuronal spiking activity in the cortexwithout external input? Do these mechanisms depend on the structural organization of the cortical connections? Do they depend onintrinsic characteristics of the cortical neurons? To approach the answers to these questions, we have used computer simulations of cortical network models. Our networks have hierarchical modular architecture and are composedof combinations of neuron models that reproduce the firing behavior of the five main cortical electrophysiological cell classes: regular spiking (RS, chattering (CH, intrinsically bursting (IB, low threshold spiking (LTS and fast spiking (FS. The population of excitatory neurons is built of RS cells(always present and either CH or IB cells. Inhibitoryneurons belong to the same class, either LTS or FS. Long-lived self-sustained activity states in our networksimulations display irregular single neuron firing and oscillatoryactivity similar to experimentally measured ones. The duration of self-sustained activity strongly depends on the initial conditions,suggesting a transient chaotic regime. Extensive analysis of the self-sustainedactivity states showed that their lifetime expectancy increases with the numberof network modules and is favored when the network is composed of excitatory neurons of the RS and CH classes combined with inhibitory neurons of the LTS class. These results indicate that the existence and properties of the self-sustained cortical activity states depend on both the topology of the network and the neuronal mixture that comprises the network.

Sync or anti-sync – dynamical pattern selection in coupled self-sustained oscillator systems

International Nuclear Information System (INIS)

Davidova, Larissa; Újvári, Szeréna; Néda, Zoltán

2014-01-01

The dynamics of similar, self-sustained oscillators coupled by a common platform exhibits fascinating collective behavior. Experiments performed with pendulum clocks and metronomes reported both the absence of synchronization, in-phase synchronization, antiphase synchronization, beat-death phenomenon, or even chaotic dynamics. Here we present a numerical study on two identical self-sustained oscillators placed on a common movable platform. As order parameter for synchronization we use the Pearson correlation coefficient between the oscillators coordinates. As a function of the relevant physical parameters of this system we reproduce all the experimentally reported dynamics. We provide conditions for obtaining stable and emergent in-phase or anti-phase synchronization.

Self-excited current oscillations in a resonant tunneling diode described by a model based on the Caldeira–Leggett Hamiltonian

International Nuclear Information System (INIS)

Sakurai, Atsunori; Tanimura, Yoshitaka

2014-01-01

The quantum dissipative dynamics of a tunneling process through double barrier structures is investigated on the basis of non-perturbative and non-Markovian treatment. We employ a Caldeira–Leggett Hamiltonian with an effective potential calculated self-consistently, accounting for the electron distribution. With this Hamiltonian, we use the reduced hierarchy equations of motion in the Wigner space representation to study non-Markovian and non-perturbative thermal effects at finite temperature in a rigorous manner. We study current variation in time and the current–voltage (I–V ) relation of the resonant tunneling diode for several widths of the contact region, which consists of doped GaAs. Hysteresis and both single and double plateau-like behavior are observed in the negative differential resistance (NDR) region. While all of the current oscillations decay in time in the NDR region in the case of a strong system–bath coupling, there exist self-excited high-frequency current oscillations in some parts of the plateau in the NDR region in the case of weak coupling. We find that the effective potential in the oscillating case possesses a basin-like form on the emitter side (emitter basin) and that the current oscillation results from tunneling between the emitter basin and the quantum well in the barriers. We find two distinct types of current oscillations, with large and small oscillation amplitudes, respectively. These two types of oscillation appear differently in the Wigner space, with one exhibiting tornado-like motion and the other exhibiting a two piston engine-like motion. (paper)

A novel image block cryptosystem based on a spatiotemporal chaotic system and a chaotic neural network

International Nuclear Information System (INIS)

Wang Xing-Yuan; Bao Xue-Mei

2013-01-01

In this paper, we propose a novel block cryptographic scheme based on a spatiotemporal chaotic system and a chaotic neural network (CNN). The employed CNN comprises a 4-neuron layer called a chaotic neuron layer (CNL), where the spatiotemporal chaotic system participates in generating its weight matrix and other parameters. The spatiotemporal chaotic system used in our scheme is the typical coupled map lattice (CML), which can be easily implemented in parallel by hardware. A 160-bit-long binary sequence is used to generate the initial conditions of the CML. The decryption process is symmetric relative to the encryption process. Theoretical analysis and experimental results prove that the block cryptosystem is secure and practical, and suitable for image encryption. (general)

Bifurcations and Crises in a Shape Memory Oscillator

Directory of Open Access Journals (Sweden)

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.

THE ASTEROID BELT AS A RELIC FROM A CHAOTIC EARLY SOLAR SYSTEM

Energy Technology Data Exchange (ETDEWEB)

Izidoro, André; Raymond, Sean N.; Pierens, Arnaud [Laboratoire d’astrophysique de Bordeaux, Université de Bordeaux, CNRS, B18N, allée Geoffroy Saint-Hilaire, F-33615 Pessac (France); Morbidelli, Alessandro [University of Nice-Sophia Antipolis, CNRS, Observatoire de la Côte d’Azur, Laboratoire Lagrange, BP 4229, F-06304 Nice Cedex 4 (France); Winter, Othon C. [UNESP, Univ. Estadual Paulista—Grupo de Dinâmica Orbital and Planetologia, Guaratinguetá, CEP 12.516-410, São Paulo (Brazil); Nesvorny' , David, E-mail: izidoro.costa@gmail.com [Department of Space Studies, Southwest Research Institute, 1050 Walnut St., Suite 300, Boulder, CO 80302 (United States)

2016-12-10

The orbital structure of the asteroid belt holds a record of the solar system’s dynamical history. The current belt only contains ∼10{sup −3} Earth masses yet the asteroids’ orbits are dynamically excited, with a large spread in eccentricity and inclination. In the context of models of terrestrial planet formation, the belt may have been excited by Jupiter’s orbital migration. The terrestrial planets can also be reproduced without invoking a migrating Jupiter; however, as it requires a severe mass deficit beyond Earth’s orbit, this model systematically under-excites the asteroid belt. Here we show that the orbits of the asteroids may have been excited to their current state if Jupiter’s and Saturn’s early orbits were chaotic. Stochastic variations in the gas giants’ orbits cause resonances to continually jump across the main belt and excite the asteroids’ orbits on a timescale of tens of millions of years. While hydrodynamical simulations show that the gas giants were likely in mean motion resonance at the end of the gaseous disk phase, small perturbations could have driven them into a chaotic but stable state. The gas giants’ current orbits were achieved later, during an instability in the outer solar system. Although it is well known that the present-day solar system exhibits chaotic behavior, our results suggest that the early solar system may also have been chaotic.

Stochastic chaos in a Duffing oscillator and its control

International Nuclear Information System (INIS)

Wu Cunli; Lei Youming; Fang Tong

2006-01-01

Stochastic chaos discussed here means a kind of chaotic responses in a Duffing oscillator with bounded random parameters under harmonic excitations. A system with random parameters is usually called a stochastic system. The modifier 'stochastic' here implies dependent on some random parameter. As the system itself is stochastic, so is the response, even under harmonic excitations alone. In this paper stochastic chaos and its control are verified by the top Lyapunov exponent of the system. A non-feedback control strategy is adopted here by adding an adjustable noisy phase to the harmonic excitation, so that the control can be realized by adjusting the noise level. It is found that by this control strategy stochastic chaos can be tamed down to the small neighborhood of a periodic trajectory or an equilibrium state. In the analysis the stochastic Duffing oscillator is first transformed into an equivalent deterministic nonlinear system by the Gegenbauer polynomial approximation, so that the problem of controlling stochastic chaos can be reduced into the problem of controlling deterministic chaos in the equivalent system. Then the top Lyapunov exponent of the equivalent system is obtained by Wolf's method to examine the chaotic behavior of the response. Numerical simulations show that the random phase control strategy is an effective way to control stochastic chaos

Introduction To Control Of Oscillations And Chaos

International Nuclear Information System (INIS)

Fradkov, A. L.; Pogromsky, A. Yu.

1998-01-01

This book gives an exposition of the exciting field of control of oscillatory and chaotic systems, which has numerous potential applications in mechanics, laser and chemical technologies, communications, biology and medicine, economics, ecology, etc. A novelty of the book is its systematic application of modern nonlinear and adaptive control theory to the new class of problems. The proposed control design methods are based on the concepts of Lyapunov functions, Poincare maps, speed-gradient and gradient algorithms. The conditions which ensure such control goals as an excitation or suppression of oscillations, synchronization and transformation from chaotic mode to the periodic one or vice versa, are established. The performance and robustness of control systems under disturbances and uncertainties are evaluated.The described methods and algorithms are illustrated by a number of examples, including classical models of oscillatory and chaotic systems: coupled pendula, brusselator, Lorenz, Van dar Pol, Duffing, Henon and Chua systems. Practical examples from different fields of science and technology such as communications, growth of thin films, synchronization of chaotic generators based on tunnel diodes, stabilization of swings in power systems, increasing predictability of business-cycles are also presented. The book includes many results on nonlinear and adaptive control published previously in Russian and therefore were not known to the West. Researchers, teachers and graduate students in the fields of electrical and mechanical engineering, physics, chemistry, biology, economics will find this book most useful. Applied mathematicians and control engineers from various fields of technology dealing with complex oscillatory systems will also benefit from it

Nonlinear dynamics and chaotization of oscillations of a virtual cathode in an annular electron beam in a uniform external magnetic field

International Nuclear Information System (INIS)

Kurkin, S. A.; Koronovski, A. A.; Hramov, A. E.

2009-01-01

Results are presented from a numerical study of the effect of an external magnetic field on the conditions and mechanisms for the formation of a virtual cathode in a relativistic electron beam. Characteristic features of the nonlinear dynamics of an electron beam with a virtual cathode are considered when the external magnetic field is varied. Various mechanisms are investigated by which the virtual cathode oscillations become chaotic and their spectrum becomes a multifrequency spectrum, thereby complicating the dynamics of the vircator system. A general mechanism for chaotization of the oscillations of a virtual cathode in a vircator system is revealed: the electron structures that form in an electron beam interact by means of a common space charge field to give rise to additional internal feedback. That the oscillations of a virtual cathode change from the chaotic to the periodic regime is due to the suppression of the mechanism for forming secondary electron structures.

Design and experiment of controlled bistable vortex induced vibration energy harvesting systems operating in chaotic regions

Science.gov (United States)

Huynh, B. H.; Tjahjowidodo, T.; Zhong, Z.-W.; Wang, Y.; Srikanth, N.

2018-01-01

Vortex induced vibration based energy harvesting systems have gained interests in these recent years due to its potential as a low water current energy source. However, the effectiveness of the system is limited only at a certain water current due to the resonance principle that governs the concept. In order to extend the working range, a bistable spring to support the structure is introduced on the system. The improvement on the performance is essentially dependent on the bistable gap as one of the main parameters of the nonlinear spring. A sufficiently large bistable gap will result in a significant performance improvement. Unfortunately, a large bistable gap might also increase a chance of chaotic responses, which in turn will result in diminutive harvested power. To mitigate the problem, an appropriate control structure is required to stabilize the chaotic vibrations of a VIV energy converter with the bistable supporting structure. Based on the nature of the double-well potential energy in a bistable spring, the ideal control structure will attempt to drive the responses to inter-well periodic vibrations in order to maximize the harvested power. In this paper, the OGY control algorithm is designed and implemented to the system. The control strategy is selected since it requires only a small perturbation in a structural parameter to execute the control effort, thus, minimum power is needed to drive the control input. Facilitated by a wake oscillator model, the bistable VIV system is modelled as a 4-dimensional autonomous continuous-time dynamical system. To implement the controller strategy, the system is discretized at a period estimated from the subspace hyperplane intersecting to the chaotic trajectory, whereas the fixed points that correspond to the desired periodic orbits are estimated by the recurrence method. Simultaneously, the Jacobian and sensitivity matrices are estimated by the least square regression method. Based on the defined fixed point and the

Correlation control theory of chaotic laser systems

International Nuclear Information System (INIS)

Li Fuli.

1986-04-01

A novel control theory of chaotic systems is studied. The correlation functions are calculated and used as feedback signals of the chaotic lasers. Computer experiments have shown that in this way the chaotic systems can be controlled to have time-independent output when the external control parameters are in chaotic domain. (author)

On One Means of Hard Excitation of Oscillations in Nonlinear Flutter Systems

Directory of Open Access Journals (Sweden)

S. D. Glyzin

2014-01-01

Full Text Available Considered are so-called finite-dimensional flutter systems, i.e. systems of ordinary differential equations, arising from Galerkin approximations of certain boundary value problems of aeroelasticity theory as well as from a number of radiophysics applications. We study small oscillations of these equations in case of 1 : 3 resonance. By combining analytical and numerical methods, it is concluded that the mentioned resonance can cause a hard excitation of oscillations. Namely, for flutter systems shown is the possibility of coexistence, along with the stable zero state, of stable invariant tori of arbitrary finite dimension as well as chaotic attractors.

Dynamic control of chaotic resonators

KAUST Repository

Di Falco, A.; Bruck, R.; Liu, C.; Muskens, O.; Fratalocchi, Andrea

2016-01-01

We report on the all-optical control of chaotic optical resonators based on silicon on insulator (SOI) platform. We show that simple non-chaotic cavities can be tuned to exhibit chaotic behavior via intense optical pump- ing, inducing a local change of refractive index. To this extent we have fabricated a number of devices and demonstrated experimentally and theoretically that chaos can be triggered on demand on an optical chip. © 2016 SPIE.

Dynamic control of chaotic resonators

KAUST Repository

Di Falco, A.

2016-02-16

We report on the all-optical control of chaotic optical resonators based on silicon on insulator (SOI) platform. We show that simple non-chaotic cavities can be tuned to exhibit chaotic behavior via intense optical pump- ing, inducing a local change of refractive index. To this extent we have fabricated a number of devices and demonstrated experimentally and theoretically that chaos can be triggered on demand on an optical chip. © 2016 SPIE.

Co-existing hidden attractors in a radio-physical oscillator system

DEFF Research Database (Denmark)

Kuznetsov, A. P.; Kuznetsov, S. P.; Mosekilde, Erik

2015-01-01

The term `hidden attractor' relates to a stable periodic, quasiperiodic or chaotic state whose basin of attraction does not overlap with the neighborhood of an unstable equilibrium point. Considering a three-dimensional oscillator system that does not allow for the existence of an equilibrium point...... frequency, describe the bifurcations through which hidden attractors of different type arise and disappear, and illustrate the form of the basins of attraction....

A fast chaotic encryption scheme based on piecewise nonlinear chaotic maps

International Nuclear Information System (INIS)

Behnia, S.; Akhshani, A.; Ahadpour, S.; Mahmodi, H.; Akhavan, A.

2007-01-01

In recent years, a growing number of discrete chaotic cryptographic algorithms have been proposed. However, most of them encounter some problems such as the lack of robustness and security. In this Letter, we introduce a new image encryption algorithm based on one-dimensional piecewise nonlinear chaotic maps. The system is a measurable dynamical system with an interesting property of being either ergodic or having stable period-one fixed point. They bifurcate from a stable single periodic state to chaotic one and vice versa without having usual period-doubling or period-n-tippling scenario. Also, we present the KS-entropy of this maps with respect to control parameter. This algorithm tries to improve the problem of failure of encryption such as small key space, encryption speed and level of security

Engineering applications of fpgas chaotic systems, artificial neural networks, random number generators, and secure communication systems

CERN Document Server

Tlelo-Cuautle, Esteban; de la Fraga, Luis Gerardo

2016-01-01

This book offers readers a clear guide to implementing engineering applications with FPGAs, from the mathematical description to the hardware synthesis, including discussion of VHDL programming and co-simulation issues. Coverage includes FPGA realizations such as: chaos generators that are described from their mathematical models; artificial neural networks (ANNs) to predict chaotic time series, for which a discussion of different ANN topologies is included, with different learning techniques and activation functions; random number generators (RNGs) that are realized using different chaos generators, and discussions of their maximum Lyapunov exponent values and entropies. Finally, optimized chaotic oscillators are synchronized and realized to implement a secure communication system that processes black and white and grey-scale images. In each application, readers will find VHDL programming guidelines and computer arithmetic issues, along with co-simulation examples with Active-HDL and Simulink. Readers will b...

Robust intelligent sliding model control using recurrent cerebellar model articulation controller for uncertain nonlinear chaotic systems

International Nuclear Information System (INIS)

Peng Yafu

2009-01-01

In this paper, a robust intelligent sliding model control (RISMC) scheme using an adaptive recurrent cerebellar model articulation controller (RCMAC) is developed for a class of uncertain nonlinear chaotic systems. This RISMC system offers a design approach to drive the state trajectory to track a desired trajectory, and it is comprised of an adaptive RCMAC and a robust controller. The adaptive RCMAC is used to mimic an ideal sliding mode control (SMC) due to unknown system dynamics, and a robust controller is designed to recover the residual approximation error for guaranteeing the stable characteristic. Moreover, the Taylor linearization technique is employed to derive the linearized model of the RCMAC. The all adaptation laws of the RISMC system are derived based on the Lyapunov stability analysis and projection algorithm, so that the stability of the system can be guaranteed. Finally, the proposed RISMC system is applied to control a Van der Pol oscillator, a Genesio chaotic system and a Chua's chaotic circuit. The effectiveness of the proposed control scheme is verified by some simulation results with unknown system dynamics and existence of external disturbance. In addition, the advantages of the proposed RISMC are indicated in comparison with a SMC system

Temporal intermittency and the lifetime of chimera states in ensembles of nonlocally coupled chaotic oscillators

Science.gov (United States)

Semenova, N. I.; Strelkova, G. I.; Anishchenko, V. S.; Zakharova, A.

2017-06-01

We describe numerical results for the dynamics of networks of nonlocally coupled chaotic maps. Switchings in time between amplitude and phase chimera states have been first established and studied. It has been shown that in autonomous ensembles, a nonstationary regime of switchings has a finite lifetime and represents a transient process towards a stationary regime of phase chimera. The lifetime of the nonstationary switching regime can be increased to infinity by applying short-term noise perturbations.

Anti-synchronization between different chaotic complex systems

International Nuclear Information System (INIS)

Liu Ping; Liu Shutang

2011-01-01

Many studies on the anti-synchronization of nonlinear real dynamic systems have been carried out, whereas the anti-synchronization of chaotic complex systems has not been studied extensively. In this work, the anti-synchronization between a new chaotic complex system and a complex Lorenz system and that between a new chaotic complex system and a complex Lue system were separately investigated by active control and nonlinear control methods, and explicit expressions were derived for the controllers that are used to achieve the anti-synchronization of chaotic complex systems. These expressions were tested numerically and excellent agreement was found. Concerning the new chaotic complex system, we discuss its dynamical properties including dissipation, chaotic behavior, fixed points, and their stability and invariance.

Visibility graphlet approach to chaotic time series

Energy Technology Data Exchange (ETDEWEB)

Mutua, Stephen [Business School, University of Shanghai for Science and Technology, Shanghai 200093 (China); Computer Science Department, Masinde Muliro University of Science and Technology, P.O. Box 190-50100, Kakamega (Kenya); Gu, Changgui, E-mail: gu-changgui@163.com, E-mail: hjyang@ustc.edu.cn; Yang, Huijie, E-mail: gu-changgui@163.com, E-mail: hjyang@ustc.edu.cn [Business School, University of Shanghai for Science and Technology, Shanghai 200093 (China)

2016-05-15

Many novel methods have been proposed for mapping time series into complex networks. Although some dynamical behaviors can be effectively captured by existing approaches, the preservation and tracking of the temporal behaviors of a chaotic system remains an open problem. In this work, we extended the visibility graphlet approach to investigate both discrete and continuous chaotic time series. We applied visibility graphlets to capture the reconstructed local states, so that each is treated as a node and tracked downstream to create a temporal chain link. Our empirical findings show that the approach accurately captures the dynamical properties of chaotic systems. Networks constructed from periodic dynamic phases all converge to regular networks and to unique network structures for each model in the chaotic zones. Furthermore, our results show that the characterization of chaotic and non-chaotic zones in the Lorenz system corresponds to the maximal Lyapunov exponent, thus providing a simple and straightforward way to analyze chaotic systems.

Nonlinear effects on Turing patterns: Time oscillations and chaos

KAUST Repository

Aragón, J. L.

2012-08-08

We show that a model reaction-diffusion system with two species in a monostable regime and over a large region of parameter space produces Turing patterns coexisting with a limit cycle which cannot be discerned from the linear analysis. As a consequence, the patterns oscillate in time. When varying a single parameter, a series of bifurcations leads to period doubling, quasiperiodic, and chaotic oscillations without modifying the underlying Turing pattern. A Ruelle-Takens-Newhouse route to chaos is identified. We also examine the Turing conditions for obtaining a diffusion-driven instability and show that the patterns obtained are not necessarily stationary for certain values of the diffusion coefficients. These results demonstrate the limitations of the linear analysis for reaction-diffusion systems. © 2012 American Physical Society.

Chaotic amplification of neutrino chemical potentials by neutrino oscillations in big bang nucleosynthesis

International Nuclear Information System (INIS)

Shi, X.

1996-01-01

We investigate in detail the parameter space of active-sterile neutrino oscillations that amplifies neutrino chemical potentials at the epoch of big bang nucleosynthesis. We calculate the magnitude of the amplification and show evidence of chaos in the amplification process. We also discuss the implications of the neutrino chemical potential amplification in big bang nucleosynthesis. It is shown that with a ∼1 eV ν e , the amplification of its chemical potential by active-sterile neutrino oscillations can lower the effective number of neutrino species at big bang nucleosynthesis to significantly below three. copyright 1996 The American Physical Society

Chaotic amplification of neutrino chemical potentials by neutrino oscillations in big bang nucleosynthesis

Energy Technology Data Exchange (ETDEWEB)

Shi, X. [Department of Physics, Queen`s University, Kingston, Ontario, K7L 3N6 (CANADA)

1996-08-01

We investigate in detail the parameter space of active-sterile neutrino oscillations that amplifies neutrino chemical potentials at the epoch of big bang nucleosynthesis. We calculate the magnitude of the amplification and show evidence of chaos in the amplification process. We also discuss the implications of the neutrino chemical potential amplification in big bang nucleosynthesis. It is shown that with a {approximately}1 eV {nu}{sub {ital e}}, the amplification of its chemical potential by active-sterile neutrino oscillations can lower the effective number of neutrino species at big bang nucleosynthesis to significantly below three. {copyright} {ital 1996 The American Physical Society.}

Oscillating Bianchi IX universe in Horava-Lifshitz gravity

International Nuclear Information System (INIS)

Misonoh, Yosuke; Maeda, Kei-ichi; Kobayashi, Tsutomu

2011-01-01

We study a vacuum Bianchi IX universe in the context of Horava-Lifshitz gravity. In particular, we focus on the classical dynamics of the universe and analyze how anisotropy changes the history of the universe. For small anisotropy, we find an oscillating universe as well as a bounce universe just as the case of the Friedmann-Lemaitre-Robertson-Walker spacetime. However, if the initial anisotropy is large, we find the universe which ends up with a big crunch after oscillations if a cosmological constant Λ is zero or negative. For Λ>0, we find a variety of histories of the universe, that is a de Sitter expanding universe after oscillations in addition to the oscillating solution and the previous big crunch solution. This fate of the universe shows sensitive dependence of initial conditions, which is one of the typical properties of a chaotic system. If the initial anisotropy is near the upper bound, we find the universe starting from a big bang and ending up with a big crunch for Λ≤0, and a de Sitter expanding universe starting from a big bang for Λ>0.

Multi-Gbit/s optical phase chaos communications using a time-delayed optoelectronic oscillator with a three-wave interferometer nonlinearity.

Science.gov (United States)

Oden, Jérémy; Lavrov, Roman; Chembo, Yanne K; Larger, Laurent

2017-11-01

We propose a chaos communication scheme based on a chaotic optical phase carrier generated with an optoelectronic oscillator with nonlinear time-delay feedback. The system includes a dedicated non-local nonlinearity, which is a customized three-wave imbalanced interferometer. This particular feature increases the complexity of the chaotic waveform and thus the security of the transmitted information, as these interferometers are characterized by four independent parameters which are part of the secret key for the chaos encryption scheme. We first analyze the route to chaos in the system, and evidence a sequence of period doubling bifurcations from the steady-state to fully developed chaos. Then, in the chaotic regime, we study the synchronization between the emitter and the receiver, and achieve chaotic carrier cancellation with a signal-to-noise ratio up to 20 dB. We finally demonstrate error-free chaos communications at a data rate of 3 Gbit/s.

Multi-Gbit/s optical phase chaos communications using a time-delayed optoelectronic oscillator with a three-wave interferometer nonlinearity

Science.gov (United States)

Oden, Jérémy; Lavrov, Roman; Chembo, Yanne K.; Larger, Laurent

2017-11-01

We propose a chaos communication scheme based on a chaotic optical phase carrier generated with an optoelectronic oscillator with nonlinear time-delay feedback. The system includes a dedicated non-local nonlinearity, which is a customized three-wave imbalanced interferometer. This particular feature increases the complexity of the chaotic waveform and thus the security of the transmitted information, as these interferometers are characterized by four independent parameters which are part of the secret key for the chaos encryption scheme. We first analyze the route to chaos in the system, and evidence a sequence of period doubling bifurcations from the steady-state to fully developed chaos. Then, in the chaotic regime, we study the synchronization between the emitter and the receiver, and achieve chaotic carrier cancellation with a signal-to-noise ratio up to 20 dB. We finally demonstrate error-free chaos communications at a data rate of 3 Gbit/s.

Nanopore Current Oscillations: Nonlinear Dynamics on the Nanoscale.

Science.gov (United States)

Hyland, Brittany; Siwy, Zuzanna S; Martens, Craig C

2015-05-21

In this Letter, we describe theoretical modeling of an experimentally realized nanoscale system that exhibits the general universal behavior of a nonlinear dynamical system. In particular, we consider the description of voltage-induced current fluctuations through a single nanopore from the perspective of nonlinear dynamics. We briefly review the experimental system and its behavior observed and then present a simple phenomenological nonlinear model that reproduces the qualitative behavior of the experimental data. The model consists of a two-dimensional deterministic nonlinear bistable oscillator experiencing both dissipation and random noise. The multidimensionality of the model and the interplay between deterministic and stochastic forces are both required to obtain a qualitatively accurate description of the physical system.

Synchronous implementation of optoelectronic NOR and XNOR logic gates using parallel synchronization of three chaotic lasers

International Nuclear Information System (INIS)

Yan Sen-Lin

2014-01-01

The parallel synchronization of three chaotic lasers is used to emulate optoelectronic logic NOR and XNOR gates via modulating the light and the current. We deduce a logical computational equation that governs the chaotic synchronization, logical input, and logical output. We construct fundamental gates based on the three chaotic lasers and define the computational principle depending on the parallel synchronization. The logic gate can be implemented by appropriately synchronizing two chaotic lasers. The system shows practicability and flexibility because it can emulate synchronously an XNOR gate, two NOR gates, and so on. The synchronization can still be deteceted when mismatches exist with a certain range. (general)

A compact chaotic laser device with a two-dimensional external cavity structure

International Nuclear Information System (INIS)

Sunada, Satoshi; Adachi, Masaaki; Fukushima, Takehiro; Shinohara, Susumu; Arai, Kenichi; Harayama, Takahisa

2014-01-01

We propose a compact chaotic laser device, which consists of a semiconductor laser and a two-dimensional (2D) external cavity for delayed optical feedback. The overall size of the device is within 230 μm × 1 mm. A long time delay sufficient for chaos generation can be achieved with the small area by the multiple reflections at the 2D cavity boundary, and the feedback strength is controlled by the injection current to the external cavity. We experimentally demonstrate that a variety of output properties, including chaotic output, can be selectively generated by controlling the injection current to the external cavity.

Studies in Chaotic adiabatic dynamics

International Nuclear Information System (INIS)

Jarzynski, C.

1994-01-01

Chaotic adiabatic dynamics refers to the study of systems exhibiting chaotic evolution under slowly time-dependent equations of motion. In this dissertation the author restricts his attention to Hamiltonian chaotic adiabatic systems. The results presented are organized around a central theme, namely, that the energies of such systems evolve diffusively. He begins with a general analysis, in which he motivates and derives a Fokker-Planck equation governing this process of energy diffusion. He applies this equation to study the open-quotes goodnessclose quotes of an adiabatic invariant associated with chaotic motion. This formalism is then applied to two specific examples. The first is that of a gas of noninteracting point particles inside a hard container that deforms slowly with time. Both the two- and three-dimensional cases are considered. The results are discussed in the context of the Wall Formula for one-body dissipation in nuclear physics, and it is shown that such a gas approaches, asymptotically with time, an exponential velocity distribution. The second example involves the Fermi mechanism for the acceleration of cosmic rays. Explicit evolution equations are obtained for the distribution of cosmic ray energies within this model, and the steady-state energy distribution that arises when this equation is modified to account for the injection and removal of cosmic rays is discussed. Finally, the author re-examines the multiple-time-scale approach as applied to the study of phase space evolution under a chaotic adiabatic Hamiltonian. This leads to a more rigorous derivation of the above-mentioned Fokker-Planck equation, and also to a new term which has relevance to the problem of chaotic adiabatic reaction forces (the forces acting on slow, heavy degrees of freedom due to their coupling to light, fast chaotic degrees)

Bifurcation of Safe Basins and Chaos in Nonlinear Vibroimpact Oscillator under Harmonic and Bounded Noise Excitations

Directory of Open Access Journals (Sweden)

Rong Haiwu

2014-01-01

Full Text Available The erosion of the safe basins and chaotic motions of a nonlinear vibroimpact oscillator under both harmonic and bounded random noise is studied. Using the Melnikov method, the system’s Melnikov integral is computed and the parametric threshold for chaotic motions is obtained. Using the Monte-Carlo and Runge-Kutta methods, the erosion of the safe basins is also discussed. The sudden change in the character of the stochastic safe basins when the bifurcation parameter of the system passes through a critical value may be defined as an alternative stochastic bifurcation. It is founded that random noise may destroy the integrity of the safe basins, bring forward the occurrence of the stochastic bifurcation, and make the parametric threshold for motions vary in a larger region, hence making the system become more unsafely and chaotic motions may occur more easily.

Synchronization of chaotic and nonchaotic oscillators: Application to bipolar disorder

Energy Technology Data Exchange (ETDEWEB)

Nono Dueyou Buckjohn, C., E-mail: bucknono@yahoo.f [Laboratoire de Mecanique, Departement de Physique, Faculte des Sciences, Universite de Yaounde I, B.P. 812 Yaounde (Cameroon); Siewe Siewe, M., E-mail: martinsiewesiewe@yahoo.f [Laboratoire de Mecanique, Departement de Physique, Faculte des Sciences, Universite de Yaounde I, B.P. 812 Yaounde (Cameroon); Tchawoua, C., E-mail: ctchawa@yahoo.f [Laboratoire de Mecanique, Departement de Physique, Faculte des Sciences, Universite de Yaounde I, B.P. 812 Yaounde (Cameroon); Kofane, T.C., E-mail: tckofane@yahoo.co [Laboratoire de Mecanique, Departement de Physique, Faculte des Sciences, Universite de Yaounde I, B.P. 812 Yaounde (Cameroon)

2010-08-02

In this Letter, we use a synchronization scheme on two bipolar disorder models consisting of a strong nonlinear system with multiplicative excitation and a nonlinear oscillator without parametric harmonic forcing. The stability condition following our control function is analytically demonstrated using the Lyapunov theory and Routh-Hurwitz criteria, we then have the condition for the existence of a feedback gain matrix. A convenient demonstration of the accuracy of the method is complemented by the numerical simulations from which we illustrate the synchronized dynamics between the two non-identical bipolar disorder patients.

Synchronization of chaotic and nonchaotic oscillators: Application to bipolar disorder

International Nuclear Information System (INIS)

Nono Dueyou Buckjohn, C.; Siewe Siewe, M.; Tchawoua, C.; Kofane, T.C.

2010-01-01

In this Letter, we use a synchronization scheme on two bipolar disorder models consisting of a strong nonlinear system with multiplicative excitation and a nonlinear oscillator without parametric harmonic forcing. The stability condition following our control function is analytically demonstrated using the Lyapunov theory and Routh-Hurwitz criteria, we then have the condition for the existence of a feedback gain matrix. A convenient demonstration of the accuracy of the method is complemented by the numerical simulations from which we illustrate the synchronized dynamics between the two non-identical bipolar disorder patients.

Synchronization of chaotic and nonchaotic oscillators: Application to bipolar disorder

Science.gov (United States)

Nono Dueyou Buckjohn, C.; Siewe Siewe, M.; Tchawoua, C.; Kofane, T. C.

2010-08-01

In this Letter, we use a synchronization scheme on two bipolar disorder models consisting of a strong nonlinear system with multiplicative excitation and a nonlinear oscillator without parametric harmonic forcing. The stability condition following our control function is analytically demonstrated using the Lyapunov theory and Routh-Hurwitz criteria, we then have the condition for the existence of a feedback gain matrix. A convenient demonstration of the accuracy of the method is complemented by the numerical simulations from which we illustrate the synchronized dynamics between the two non-identical bipolar disorder patients.

Characterizing chaotic melodies in automatic music composition

Science.gov (United States)

Coca, Andrés E.; Tost, Gerard O.; Zhao, Liang

2010-09-01

In this paper, we initially present an algorithm for automatic composition of melodies using chaotic dynamical systems. Afterward, we characterize chaotic music in a comprehensive way as comprising three perspectives: musical discrimination, dynamical influence on musical features, and musical perception. With respect to the first perspective, the coherence between generated chaotic melodies (continuous as well as discrete chaotic melodies) and a set of classical reference melodies is characterized by statistical descriptors and melodic measures. The significant differences among the three types of melodies are determined by discriminant analysis. Regarding the second perspective, the influence of dynamical features of chaotic attractors, e.g., Lyapunov exponent, Hurst coefficient, and correlation dimension, on melodic features is determined by canonical correlation analysis. The last perspective is related to perception of originality, complexity, and degree of melodiousness (Euler's gradus suavitatis) of chaotic and classical melodies by nonparametric statistical tests.

Complex-enhanced chaotic signals with time-delay signature suppression based on vertical-cavity surface-emitting lasers subject to chaotic optical injection

Science.gov (United States)

Chen, Jianjun; Duan, Yingni; Zhong, Zhuqiang

2018-03-01

A chaotic system is constructed on the basis of vertical-cavity surface-emitting lasers (VCSELs), where a slave VCSEL subject to chaotic optical injection (COI) from a master VCSEL with the external feedback. The complex degree (CD) and time-delay signature (TDS) of chaotic signals generated by this chaotic system are investigated numerically via permutation entropy (PE) and self-correlation function (SF) methods, respectively. The results show that, compared with master VCSEL subject to optical feedback, complex-enhanced chaotic signals with TDS suppression can be achieved for S-VCSEL subject to COI. Meanwhile, the influences of several controllable parameters on the evolution maps of CD of chaotic signals are carefully considered. It is shown that the CD of chaotic signals for S-VCSEL is always higher than that for M-VCSEL due to the CIO effect. The TDS of chaotic signals can be significantly suppressed by choosing the reasonable parameters in this system. Furthermore, TDS suppression and high CD chaos can be obtained simultaneously in the specific parameter ranges. The results confirm that this chaotic system may effectively improve the security of a chaos-based communication scheme.

Oscillations Excited by Plasmoids Formed During Magnetic Reconnection in a Vertical Gravitationally Stratified Current Sheet

Science.gov (United States)

Jelínek, P.; Karlický, M.; Van Doorsselaere, T.; Bárta, M.

2017-10-01

Using the FLASH code, which solves the full set of the 2D non-ideal (resistive) time-dependent magnetohydrodynamic (MHD) equations, we study processes during the magnetic reconnection in a vertical gravitationally stratified current sheet. We show that during these processes, which correspond to processes in solar flares, plasmoids are formed due to the tearing mode instability of the current sheet. These plasmoids move upward or downward along the vertical current sheet and some of them merge into larger plasmoids. We study the density and temperature structure of these plasmoids and their time evolution in detail. We found that during the merging of two plasmoids, the resulting larger plasmoid starts to oscillate with a period largely determined by L/{c}{{A}}, where L is the size of the plasmoid and c A is the Alfvén speed in the lateral parts of the plasmoid. In our model, L/{c}{{A}} evaluates to ˜ 25 {{s}}. Furthermore, the plasmoid moving downward merges with the underlying flare arcade, which causes oscillations of the arcade. In our model, the period of this arcade oscillation is ˜ 35 {{s}}, which also corresponds to L/{c}{{A}}, but here L means the length of the loop and c A is the average Alfvén speed in the loop. We also show that the merging process of the plasmoid with the flare arcade is a complex process as presented by complex density and temperature structures of the oscillating arcade. Moreover, all these processes are associated with magnetoacoustic waves produced by the motion and merging of plasmoids.

A non-correlator-based digital communication system using interleaved chaotic differential peaks keying (I-CDPK) modulation and chaotic synchronization

International Nuclear Information System (INIS)

Chien, T.-I; Hung, Y.-C.; Liao, T.-L.

2006-01-01

This paper presents a novel non-correlator-based digital communication system with the application of interleaved chaotic differential peaks keying (I-CDPK) modulation technique. The proposed communication system consists of four major modules: I-CDPK modulator (ICM), frequency modulation (FM) transmitter, FM receiver and I-CDPK demodulator (ICDM). In the ICM module, there are four components: a chaotic circuit to generate the chaotic signals, A/D converter, D/A converter and a digital processing mechanism to control all signal flows and performs I-CDPK modulation corresponding to the input digital bits. For interleaving every input digital bit set, every state of the chaotic system is used to represent one portion of it, but only a scalar state variable (i.e. the system output) is sent to the ICDM's chaotic circuit through both FM transmitter and FM receiver. An observer-based chaotic synchronization scheme is designed to synchronize the chaotic circuits of the ICM and ICDM. Meanwhile, the bit detector in ICDM is devoted to recover the transmitted input digital bits. Some numerical simulations of an illustrative communication system are given to demonstrate its theoretical effectiveness. Furthermore, the performance of bit error rate of the proposed system is analyzed and compared with those of the correlator-based communication systems adopting coherent binary phase shift keying (BPSK) and coherent differential chaotic shift keying (DCSK) schemes

Regular and irregular patterns of self-localized excitation in arrays of coupled phase oscillators

Energy Technology Data Exchange (ETDEWEB)

Wolfrum, Matthias; Omel' chenko, Oleh E. [Weierstrass Institute, Mohrenstrasse 39, Berlin 10117 (Germany); Sieber, Jan [College of Engineering, Mathematics and Physical Sciences, University of Exeter, North Park Road, Exeter EX4 4QF (United Kingdom)

2015-05-15

We study a system of phase oscillators with nonlocal coupling in a ring that supports self-organized patterns of coherence and incoherence, called chimera states. Introducing a global feedback loop, connecting the phase lag to the order parameter, we can observe chimera states also for systems with a small number of oscillators. Numerical simulations show a huge variety of regular and irregular patterns composed of localized phase slipping events of single oscillators. Using methods of classical finite dimensional chaos and bifurcation theory, we can identify the emergence of chaotic chimera states as a result of transitions to chaos via period doubling cascades, torus breakup, and intermittency. We can explain the observed phenomena by a mechanism of self-modulated excitability in a discrete excitable medium.

Approximating chaotic saddles for delay differential equations.

Science.gov (United States)

Taylor, S Richard; Campbell, Sue Ann

2007-04-01

Chaotic saddles are unstable invariant sets in the phase space of dynamical systems that exhibit transient chaos. They play a key role in mediating transport processes involving scattering and chaotic transients. Here we present evidence (long chaotic transients and fractal basins of attraction) of transient chaos in a "logistic" delay differential equation. We adapt an existing method (stagger-and-step) to numerically construct the chaotic saddle for this system. This is the first such analysis of transient chaos in an infinite-dimensional dynamical system, and in delay differential equations in particular. Using Poincaré section techniques we illustrate approaches to visualizing the saddle set, and confirm that the saddle has the Cantor-like fractal structure consistent with a chaotic saddle generated by horseshoe-type dynamics.

Approximating chaotic saddles for delay differential equations

Science.gov (United States)

Taylor, S. Richard; Campbell, Sue Ann

2007-04-01

Chaotic saddles are unstable invariant sets in the phase space of dynamical systems that exhibit transient chaos. They play a key role in mediating transport processes involving scattering and chaotic transients. Here we present evidence (long chaotic transients and fractal basins of attraction) of transient chaos in a “logistic” delay differential equation. We adapt an existing method (stagger-and-step) to numerically construct the chaotic saddle for this system. This is the first such analysis of transient chaos in an infinite-dimensional dynamical system, and in delay differential equations in particular. Using Poincaré section techniques we illustrate approaches to visualizing the saddle set, and confirm that the saddle has the Cantor-like fractal structure consistent with a chaotic saddle generated by horseshoe-type dynamics.

New robust chaotic system with exponential quadratic term

International Nuclear Information System (INIS)

Bao Bocheng; Li Chunbiao; Liu Zhong; Xu Jianping

2008-01-01

This paper proposes a new robust chaotic system of three-dimensional quadratic autonomous ordinary differential equations by introducing an exponential quadratic term. This system can display a double-scroll chaotic attractor with only two equilibria, and can be found to be robust chaotic in a very wide parameter domain with positive maximum Lyapunov exponent. Some basic dynamical properties and chaotic behaviour of novel attractor are studied. By numerical simulation, this paper verifies that the three-dimensional system can also evolve into periodic and chaotic behaviours by a constant controller. (general)

Chaotic scattering and quantum dynamics

International Nuclear Information System (INIS)

Doron, Eyal.

1992-11-01

The main concern of this thesis is the application of the semiclassical approximation to quantum chaotic scattering systems. We deal with two separate, although interconnected, subjects. The first subject dealt with is the semiclassical characterization of the fluctuations of the S matrix. A particular important parameter is the magnetic field B, and we show how the correlation length and line shape of S matrix elements under a change of B may be derived. An effect which is present in many physical wave systems is absorption of energy flux. We show how absorption affects both the reflectivity and the scattering phase and time delay of a scattering system. In the second part of the thesis, we show how the formalism and results obtained from chaotic scattering can be applied to the investigation of closed chaotic systems, and in particular to chaotic billiards. The semiclassical expansion for billiards is presented. In the last part of the thesis we deal with the statistics of S matrices of chaotic scattering systems. The main message of this work is that scattering matrix, and its classical counterpart the Poincare Scattering Map can be used to yield a powerful formulation of the quantum mechanical dynamics of bounded systems. (author)

On dynamics analysis of a new chaotic attractor

International Nuclear Information System (INIS)

Zhou Wuneng; Xu Yuhua; Lu Hongqian; Pan Lin

2008-01-01

In this Letter, a new chaotic system is discussed. Some basic dynamical properties, such as Lyapunov exponents, Poincare mapping, fractal dimension, bifurcation diagram, continuous spectrum and chaotic dynamical behaviors of the new chaotic system are studied, either numerically or analytically. The obtained results show clearly that the system discussed in this Letter is a new chaotic system and deserves a further detailed investigation

Influence of magnetic arc oscillation and current pulsing on microstructure and high temperature tensile strength of alloy 718 TIG weldments

International Nuclear Information System (INIS)

Sivaprasad, K.; Ganesh Sundara Raman, S.; Mastanaiah, P.; Madhusudhan Reddy, G.

2006-01-01

The aim of the present work is to study the effect of magnetic arc oscillation and current pulsing on the microstructure and high temperature tensile strength of alloy 718 tungsten inert gas weldments. The magnetic arc oscillation technique resulted in refined Laves phase with lesser interconnectivity. The full benefits of current pulsing in breaking the dendrites could not be realized in the present study due to relatively higher heat input used in the welding process. In the direct aged condition weldments prepared using magnetic arc oscillation technique exhibited higher tensile strength due to the presence of refined and lesser-interconnected Laves particles. In the solution treated and aged condition, magnetic arc oscillated weldments exhibited lower tensile strength compared with the weldments made without arc oscillation due to the presence of large amounts of finer δ needles

Energy dissipation in fragmented geomaterials associated with impacting oscillators

Science.gov (United States)

Khudyakov, Maxim; Pasternak, Elena; Dyskin, Arcady

2016-04-01

In wave propagation through fragmented geomaterials forced by periodic loadings, the elements (fragments) strike against each other when passing through the neutral position (position with zero mutual rotation), quickly damping the oscillations. Essentially the impacts act as shock absorbers albeit localised at the neutral points. In order to analyse the vibrations of and wave propagation in such structures, a differential equation of a forced harmonic oscillator was investigated, where the each time the system passes through the neutral point the velocity gets reduced by multiplying it with the restitution coefficient which characterise the impact of the fragments. In forced vibrations the impact times depend on both the forced oscillations and the restitution coefficient and form an irregular sequence. Numerical solution of the differential equation was performed using Mathematica software. Along with vibration diagrams, the dependence of the energy dissipation on the ratio of the forcing frequency to the natural frequency was obtained. For small positive values of the restitution coefficient (less than 0.5), the asymmetric oscillations were found, and the phase of the forced vibrations determined the direction of the asymmetry. Also, at some values of the forcing frequencies and the restitution coefficient chaotic behaviour was found.

Hypogenetic chaotic jerk flows

International Nuclear Information System (INIS)

Li, Chunbiao; Sprott, Julien Clinton; Xing, Hongyan

2016-01-01

Removing the amplitude or polarity information in the feedback loop of a jerk structure shows that special nonlinearities with partial information in the variable can also lead to chaos. Some striking properties are found for this kind of hypogenetic chaotic jerk flow, including multistability of symmetric coexisting attractors from an asymmetric structure, hidden attractors with respect to equilibria but with global attraction, easy amplitude control, and phase reversal which is convenient for chaos applications. - Highlights: • Hypogenetic chaotic jerk flows with incomplete feedback of amplitude or polarity are obtained. • Multistability of symmetric coexisting attractors from an asymmetric structure is found. • Some jerk systems have hidden attractors with respect to equilibria but have global attraction. • These chaotic jerk flows have the properties of amplitude control and phase reversal.

Symmetric encryption algorithms using chaotic and non-chaotic generators: A review.

Science.gov (United States)

Radwan, Ahmed G; AbdElHaleem, Sherif H; Abd-El-Hafiz, Salwa K

2016-03-01

This paper summarizes the symmetric image encryption results of 27 different algorithms, which include substitution-only, permutation-only or both phases. The cores of these algorithms are based on several discrete chaotic maps (Arnold's cat map and a combination of three generalized maps), one continuous chaotic system (Lorenz) and two non-chaotic generators (fractals and chess-based algorithms). Each algorithm has been analyzed by the correlation coefficients between pixels (horizontal, vertical and diagonal), differential attack measures, Mean Square Error (MSE), entropy, sensitivity analyses and the 15 standard tests of the National Institute of Standards and Technology (NIST) SP-800-22 statistical suite. The analyzed algorithms include a set of new image encryption algorithms based on non-chaotic generators, either using substitution only (using fractals) and permutation only (chess-based) or both. Moreover, two different permutation scenarios are presented where the permutation-phase has or does not have a relationship with the input image through an ON/OFF switch. Different encryption-key lengths and complexities are provided from short to long key to persist brute-force attacks. In addition, sensitivities of those different techniques to a one bit change in the input parameters of the substitution key as well as the permutation key are assessed. Finally, a comparative discussion of this work versus many recent research with respect to the used generators, type of encryption, and analyses is presented to highlight the strengths and added contribution of this paper.

'Oscillator-wave' model: properties and heuristic instances

International Nuclear Information System (INIS)

Damgov, Vladimir; Trenchev, Plamen; Sheiretsky, Kostadin

2003-01-01

The article considers a generalized model of an oscillator, subjected to the influence of an external wave. It is shown that the systems of diverse physical background, which this model encompasses by their nature, should belong to the broader, proposed in previous works class of 'kick-excited self-adaptive dynamical systems'. The theoretical treatment includes an analytic approach to the conditions for emergence of small and large amplitudes, i.e. weak and strong non-linearity of the system. Derived also are generalized conditions for the transition of systems of this 'oscillator-wave' type to non-regular and chaotic behaviour. For the purpose of demonstrating the heuristic properties of the generalized oscillator-wave model from this point of view are considered the relevant systems and phenomena of the quantized cyclotron resonance and the megaquantum resonance-wave model of the Solar System. We point to a number of other natural and scientific phenomena, which can be effectively analyzed from the point of view of the developed approach. In particular we stress on the possibility for development and the wide applicability of specific wave influences, for example for the improvement and the speeding up of technological processes

Fractional order control and synchronization of chaotic systems

CERN Document Server

Vaidyanathan, Sundarapandian; Ouannas, Adel

2017-01-01

The book reports on the latest advances in and applications of fractional order control and synchronization of chaotic systems, explaining the concepts involved in a clear, matter-of-fact style. It consists of 30 original contributions written by eminent scientists and active researchers in the field that address theories, methods and applications in a number of research areas related to fractional order control and synchronization of chaotic systems, such as: fractional chaotic systems, hyperchaotic systems, complex systems, fractional order discrete chaotic systems, chaos control, chaos synchronization, jerk circuits, fractional chaotic systems with hidden attractors, neural network, fuzzy logic controllers, behavioral modeling, robust and adaptive control, sliding mode control, different types of synchronization, circuit realization of chaotic systems, etc. In addition to providing readers extensive information on chaos fundamentals, fractional calculus, fractional differential equations, fractional contro...

Chaotic interactions of self-replicating RNA.

Science.gov (United States)

Forst, C V

1996-03-01

A general system of high-order differential equations describing complex dynamics of replicating biomolecules is given. Symmetry relations and coordinate transformations of general replication systems leading to topologically equivalent systems are derived. Three chaotic attractors observed in Lotka-Volterra equations of dimension n = 3 are shown to represent three cross-sections of one and the same chaotic regime. Also a fractal torus in a generalized three-dimensional Lotka-Volterra Model has been linked to one of the chaotic attractors. The strange attractors are studied in the equivalent four-dimensional catalytic replicator network. The fractal torus has been examined in adapted Lotka-Volterra equations. Analytic expressions are derived for the Lyapunov exponents of the flow in the replicator system. Lyapunov spectra for different pathways into chaos has been calculated. In the generalized Lotka-Volterra system a second inner rest point--coexisting with (quasi)-periodic orbits--can be observed; with an abundance of different bifurcations. Pathways from chaotic tori, via quasi-periodic tori, via limit cycles, via multi-periodic orbits--emerging out of periodic doubling bifurcations--to "simple" chaotic attractors can be found.

Eigenfunctions in chaotic quantum systems

Energy Technology Data Exchange (ETDEWEB)

Baecker, Arnd

2007-07-01

The structure of wavefunctions of quantum systems strongly depends on the underlying classical dynamics. In this text a selection of articles on eigenfunctions in systems with fully chaotic dynamics and systems with a mixed phase space is summarized. Of particular interest are statistical properties like amplitude distribution and spatial autocorrelation function and the implication of eigenfunction structures on transport properties. For systems with a mixed phase space the separation into regular and chaotic states does not always hold away from the semiclassical limit, such that chaotic states may completely penetrate into the region of the regular island. The consequences of this flooding are discussed and universal aspects highlighted. (orig.)

Eigenfunctions in chaotic quantum systems

International Nuclear Information System (INIS)

Baecker, Arnd

2007-01-01

The structure of wavefunctions of quantum systems strongly depends on the underlying classical dynamics. In this text a selection of articles on eigenfunctions in systems with fully chaotic dynamics and systems with a mixed phase space is summarized. Of particular interest are statistical properties like amplitude distribution and spatial autocorrelation function and the implication of eigenfunction structures on transport properties. For systems with a mixed phase space the separation into regular and chaotic states does not always hold away from the semiclassical limit, such that chaotic states may completely penetrate into the region of the regular island. The consequences of this flooding are discussed and universal aspects highlighted. (orig.)

Stochastic process of pragmatic information for 2D spiral wave turbulence in globally and locally coupled Alief-Panfilov oscillators

Science.gov (United States)

Kuwahara, Jun; Miyata, Hajime; Konno, Hidetoshi

2017-09-01

Recently, complex dynamics of globally coupled oscillators have been attracting many researcher's attentions. In spite of their numerous studies, their features of nonlinear oscillator systems with global and local couplings in two-dimension (2D) are not understood fully. The paper focuses on 2D states of coherent, clustered and chaotic oscillation especially under the effect of negative global coupling (NGC) in 2D Alief-Panfilov model. It is found that the tuning NGC can cause various new coupling-parameter dependency on the features of oscillations. Then quantitative characterization of various states of oscillations (so called spiral wave turbulence) is examined by using the pragmatic information (PI) which have been utilized in analyzing multimode laser, solar activity and neuronal systems. It is demonstrated that the dynamics of the PI for various oscillations can be characterized successfully by the Hyper-Gamma stochastic process.

Smart control application in the oscillations using FACTS (STATCOM and SVC

Directory of Open Access Journals (Sweden)

Alfonso James Alzate Gomez

2017-07-01

Full Text Available Context: Reducing the oscillations of the electrical power systems is an important task in order to maintain their stability. This paper presents a methodology for adjusting the parameters of a fuzzy oscillations controller with a Static Var Compensator (SVC and a Static Synchronous Compensator (STATCOM. Methodology: The methodology consists of tuning a fuzzy controller to dampen oscillations in an electrical power system, with different optimization techniques such as: Genetic Algorithms (GA, Particle Swarm Optimization (PSO, and Chaotic Optimization Algorithm (COA. Results: The voltage and speed oscillations of a system composed of a synchronous machine connected to an infinite bus bar (SMIB are obtained through simulations. There is data before and after connecting a SVC and a STATCOM, installed independently and in different operating conditions. The results obtained show that using a technique for adjusting parameters in the fuzzy controller is better than the adjustment of trial and error. Conclusion: With the obtained results, it is possible to verify the effectiveness of the fuzzy controller using Flexible AC Transmissions Systems (FACTS.

On synchronization of three chaotic systems

International Nuclear Information System (INIS)

Yan Jianping; Li Changpin

2005-01-01

In this paper, a simple but efficient method is applied to the synchronization of three chaotic systems, i.e., the chaotic Lorenz, Chua, and Chen systems. Numerical simulations show this method works very well

Low-sensitivity, low-bounce, high-linearity current-controlled oscillator suitable for single-supply mixed-mode instrumentation system.

Science.gov (United States)

Hwang, Yuh-Shyan; Kung, Che-Min; Lin, Ho-Cheng; Chen, Jiann-Jong

2009-02-01

A low-sensitivity, low-bounce, high-linearity current-controlled oscillator (CCO) suitable for a single-supply mixed-mode instrumentation system is designed and proposed in this paper. The designed CCO can be operated at low voltage (2 V). The power bounce and ground bounce generated by this CCO is less than 7 mVpp when the power-line parasitic inductance is increased to 100 nH to demonstrate the effect of power bounce and ground bounce. The power supply noise caused by the proposed CCO is less than 0.35% in reference to the 2 V supply voltage. The average conversion ratio KCCO is equal to 123.5 GHz/A. The linearity of conversion ratio is high and its tolerance is within +/-1.2%. The sensitivity of the proposed CCO is nearly independent of the power supply voltage, which is less than a conventional current-starved oscillator. The performance of the proposed CCO has been compared with the current-starved oscillator. It is shown that the proposed CCO is suitable for single-supply mixed-mode instrumentation systems.

Hash function based on piecewise nonlinear chaotic map

International Nuclear Information System (INIS)

Akhavan, A.; Samsudin, A.; Akhshani, A.

2009-01-01

Chaos-based cryptography appeared recently in the early 1990s as an original application of nonlinear dynamics in the chaotic regime. In this paper, an algorithm for one-way hash function construction based on piecewise nonlinear chaotic map with a variant probability parameter is proposed. Also the proposed algorithm is an attempt to present a new chaotic hash function based on multithreaded programming. In this chaotic scheme, the message is connected to the chaotic map using probability parameter and other parameters of chaotic map such as control parameter and initial condition, so that the generated hash value is highly sensitive to the message. Simulation results indicate that the proposed algorithm presented several interesting features, such as high flexibility, good statistical properties, high key sensitivity and message sensitivity. These properties make the scheme a suitable choice for practical applications.

Chaotic Zones around Rotating Small Bodies

Energy Technology Data Exchange (ETDEWEB)

Lages, José; Shevchenko, Ivan I. [Institut UTINAM, Observatoire des Sciences de l’Univers THETA, CNRS, Université de Franche-Comté, Besançon F-25030 (France); Shepelyansky, Dima L., E-mail: jose.lages@utinam.cnrs.fr [Laboratoire de Physique Théorique du CNRS, IRSAMC, Université de Toulouse, UPS, Toulouse F-31062 (France)

2017-06-01

Small bodies of the solar system, like asteroids, trans-Neptunian objects, cometary nuclei, and planetary satellites, with diameters smaller than 1000 km usually have irregular shapes, often resembling dumb-bells or contact binaries. The spinning of such a gravitating dumb-bell creates around it a zone of chaotic orbits. We determine its extent analytically and numerically. We find that the chaotic zone swells significantly if the rotation rate is decreased; in particular, the zone swells more than twice if the rotation rate is decreased 10 times with respect to the “centrifugal breakup” threshold. We illustrate the properties of the chaotic orbital zones in examples of the global orbital dynamics about asteroid 243 Ida (which has a moon, Dactyl, orbiting near the edge of the chaotic zone) and asteroid 25143 Itokawa.

Chaotic spectra: How to extract dynamic information

International Nuclear Information System (INIS)

Taylor, H.S.; Gomez Llorente, J.M.; Zakrzewski, J.; Kulander, K.C.

1988-10-01

Nonlinear dynamics is applied to chaotic unassignable atomic and molecular spectra with the aim of extracting detailed information about regular dynamic motions that exist over short intervals of time. It is shown how this motion can be extracted from high resolution spectra by doing low resolution studies or by Fourier transforming limited regions of the spectrum. These motions mimic those of periodic orbits (PO) and are inserts into the dominant chaotic motion. Considering these inserts and the PO as a dynamically decoupled region of space, resonant scattering theory and stabilization methods enable us to compute ladders of resonant states which interact with the chaotic quasi-continuum computed in principle from basis sets placed off the PO. The interaction of the resonances with the quasicontinuum explains the low resolution spectra seen in such experiments. It also allows one to associate low resolution features with a particular PO. The motion on the PO thereby supplies the molecular movements whose quantization causes the low resolution spectra. Characteristic properties of the periodic orbit based resonances are discussed. The method is illustrated on the photoabsorption spectrum of the hydrogen atom in a strong magnetic field and on the photodissociation spectrum of H 3 + . Other molecular systems which are currently under investigation using this formalism are also mentioned. 53 refs., 10 figs., 2 tabs

Unified Subharmonic Oscillation Conditions for Peak or Average Current Mode Control

OpenAIRE

Fang, Chung-Chieh

2013-01-01

This paper is an extension of the author's recent research in which only buck converters were analyzed. Similar analysis can be equally applied to other types of converters. In this paper, a unified model is proposed for buck, boost, and buck-boost converters under peak or average current mode control to predict the occurrence of subharmonic oscillation. Based on the unified model, the associated stability conditions are derived in closed forms. The same stability condition can be applied to ...

Oscillations of disks

CERN Document Server

Kato, Shoji

2016-01-01

This book presents the current state of research on disk oscillation theory, focusing on relativistic disks and tidally deformed disks. Since the launch of the Rossi X-ray Timing Explorer (RXTE) in 1996, many high-frequency quasiperiodic oscillations (HFQPOs) have been observed in X-ray binaries. Subsequently, similar quasi-periodic oscillations have been found in such relativistic objects as microquasars, ultra-luminous X-ray sources, and galactic nuclei. One of the most promising explanations of their origin is based on oscillations in relativistic disks, and a new field called discoseismology is currently developing. After reviewing observational aspects, the book presents the basic characteristics of disk oscillations, especially focusing on those in relativistic disks. Relativistic disks are essentially different from Newtonian disks in terms of several basic characteristics of their disk oscillations, including the radial distributions of epicyclic frequencies. In order to understand the basic processes...

Observation and analysis of oscillations in linear accelerators

International Nuclear Information System (INIS)

Seeman, J.T.

1991-11-01

This report discusses the following on oscillation in linear accelerators: Betatron Oscillations; Betatron Oscillations at High Currents; Transverse Profile Oscillations; Transverse Profile Oscillations at High Currents.; Oscillation and Profile Transient Jitter; and Feedback on Transverse Oscillations

Unstable periodic orbits and chaotic economic growth

International Nuclear Information System (INIS)

Ishiyama, K.; Saiki, Y.

2005-01-01

We numerically find many unstable periodic solutions embedded in a chaotic attractor in a macroeconomic growth cycle model of two countries with different fiscal policies, and we focus on a special type of the unstable periodic solutions. It is confirmed that chaotic behavior represented by the model is qualitatively and quantitatively related to the unstable periodic solutions. We point out that the structure of a chaotic solution is dissolved into a class of finite unstable periodic solutions picked out among a large number of periodic solutions. In this context it is essential for the unstable periodic solutions to be embedded in the chaotic attractor

Cryptography with chaotic mixing

International Nuclear Information System (INIS)

Oliveira, Luiz P.L. de; Sobottka, Marcelo

2008-01-01

We propose a cryptosystem based on one-dimensional chaotic maps of the form H p (x)=r p -1 0G0r p (x) defined in the interval [0, 10 p ) for a positive integer parameter p, where G(x)=10x(mod10) and r p (x)= p √(x), which is a topological conjugacy between G and the shift map σ on the space Σ of the sequences with 10 symbols. There are three advantages in comparison with the recently proposed cryptosystem based on chaotic logistic maps F μ (x)=μx(1-x) with 3 p is always chaotic for all parameters p, (b) the knowledge of an ergodic measure allows assignments of the alphabetic symbols to equiprobable sites of H p 's domain and (c) for each p, the security of the cryptosystem is manageable against brute force attacks

Qualitative feature extractions of chaotic systems

International Nuclear Information System (INIS)

Vicha, T.; Dohnal, M.

2008-01-01

The theory of chaos offers useful tools for systems analysis. However, models of complex systems are based on a network of inconsistent, space and uncertain knowledge items. Traditional quantitative methods of chaos analysis are therefore not applicable. The paper by the same authors [Vicha T, Dohnal M. Qualitative identification of chaotic systems behaviours. Chaos, Solitons and Fractals, in press, [Log. No. 601019] ] presents qualitative interpretation of some chaos concepts. There are only three qualitative values positive/increasing, negative/decreasing and zero/constant. It means that any set of qualitative multidimensional descriptions of unsteady state behaviours is discrete and finite. A finite upper limit exists for the total number of qualitatively distinguishable scenarios. A set of 21 published chaotic models is solved qualitatively and 21 sets of all existing qualitative scenarios are presented. The intersection of all 21 scenario sets is empty. There is no such a behaviour which is common for all 21 models. The set of 21 qualitative models (e.g. Lorenz, Roessler) can be used to compare chaotic behaviours of an unknown qualitative model with them to evaluate if its chaotic behaviours is close to e.g. Lorenz chaotic model and how much

Chaos and catastrophes in quadrupole oscillations of nuclei

Energy Technology Data Exchange (ETDEWEB)

Bolotin, Yu L; Gonchar, V Yu; Inopin, I V

1987-02-01

Dynamics of quadrupole oscillations of atomic nuclei is investigated. A possibility of the transition from the regular regime to the chaotic one is studied; critical energy of this transition for different potential parameters is determined. The obtained results permit to state that for all the considered cases there exists a relatively narrow energy range, where the character of motion varies from regular to chaotic. The determined values of critical energy comply with the following regularities: a) the critical energy for potentials with common central minimum for all the values of parameters coincides with that found by the criterion of negative curvature; b) in the case of potentials with two minia (0 < a < 1/4 b/sup 2/) the critical energy for the central well having several elliptic fixed points coincides with that found by the criterion of negative curvature; for minima corresponding to non-spherical equilibrium states and having only one elliptic fixed point the critical energy coincides with saddle energy; c) similar relation between the number of fixed elliptic points and critical energy of transition to chaos takes place at a < 0.

Normal form and synchronization of strict-feedback chaotic systems

International Nuclear Information System (INIS)

Wang, Feng; Chen, Shihua; Yu Minghai; Wang Changping

2004-01-01

This study concerns the normal form and synchronization of strict-feedback chaotic systems. We prove that, any strict-feedback chaotic system can be rendered into a normal form with a invertible transform and then a design procedure to synchronize the normal form of a non-autonomous strict-feedback chaotic system is presented. This approach needs only a scalar driving signal to realize synchronization no matter how many dimensions the chaotic system contains. Furthermore, the Roessler chaotic system is taken as a concrete example to illustrate the procedure of designing without transforming a strict-feedback chaotic system into its normal form. Numerical simulations are also provided to show the effectiveness and feasibility of the developed methods

Heteroclinic Bifurcation Behaviors of a Duffing Oscillator with Delayed Feedback

Directory of Open Access Journals (Sweden)

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.

Chaotic secure content-based hidden transmission of biometric templates

International Nuclear Information System (INIS)

Khan, Muhammad Khurram; Zhang Jiashu; Tian Lei

2007-01-01

The large-scale proliferation of biometric verification systems creates a demand for effective and reliable security and privacy of its data. Like passwords and PIN codes, biometric data is also not secret and if it is compromised, the integrity of the whole verification system could be at high risk. To address these issues, this paper presents a novel chaotic secure content-based hidden transmission scheme of biometric data. Encryption and data hiding techniques are used to improve the security and secrecy of the transmitted templates. Secret keys are generated by the biometric image and used as the parameter value and initial condition of the chaotic map, and each transaction session has different secret keys to protect from the attacks. Two chaotic maps are incorporated for the encryption to resolve the finite word length effect and to improve the system's resistance against attacks. Encryption is applied on the biometric templates before hiding into the cover/host images to make them secure, and then templates are hidden into the cover image. Experimental results show that the security, performance, and accuracy of the presented scheme are encouraging comparable with other methods found in the current literature

Chaotic secure content-based hidden transmission of biometric templates

Energy Technology Data Exchange (ETDEWEB)

Khan, Muhammad Khurram [Research Group for Biometrics and Security, Sichuan Province Key Lab of Signal and Information Processing, Southwest Jiaotong University, Chengdu 610031, Sichuan (China)]. E-mail: khurram.khan@scientist.com; Zhang Jiashu [Research Group for Biometrics and Security, Sichuan Province Key Lab of Signal and Information Processing, Southwest Jiaotong University, Chengdu 610031, Sichuan (China); Tian Lei [Research Group for Biometrics and Security, Sichuan Province Key Lab of Signal and Information Processing, Southwest Jiaotong University, Chengdu 610031, Sichuan (China)

2007-06-15

The large-scale proliferation of biometric verification systems creates a demand for effective and reliable security and privacy of its data. Like passwords and PIN codes, biometric data is also not secret and if it is compromised, the integrity of the whole verification system could be at high risk. To address these issues, this paper presents a novel chaotic secure content-based hidden transmission scheme of biometric data. Encryption and data hiding techniques are used to improve the security and secrecy of the transmitted templates. Secret keys are generated by the biometric image and used as the parameter value and initial condition of the chaotic map, and each transaction session has different secret keys to protect from the attacks. Two chaotic maps are incorporated for the encryption to resolve the finite word length effect and to improve the system's resistance against attacks. Encryption is applied on the biometric templates before hiding into the cover/host images to make them secure, and then templates are hidden into the cover image. Experimental results show that the security, performance, and accuracy of the presented scheme are encouraging comparable with other methods found in the current literature.

Nonlinear chaotic model for predicting storm surges

Directory of Open Access Journals (Sweden)

M. Siek

2010-09-01

Full Text Available This paper addresses the use of the methods of nonlinear dynamics and chaos theory for building a predictive chaotic model from time series. The chaotic model predictions are made by the adaptive local models based on the dynamical neighbors found in the reconstructed phase space of the observables. We implemented the univariate and multivariate chaotic models with direct and multi-steps prediction techniques and optimized these models using an exhaustive search method. The built models were tested for predicting storm surge dynamics for different stormy conditions in the North Sea, and are compared to neural network models. The results show that the chaotic models can generally provide reliable and accurate short-term storm surge predictions.

Indirect adaptive control of discrete chaotic systems

International Nuclear Information System (INIS)

Salarieh, Hassan; Shahrokhi, Mohammad

2007-01-01

In this paper an indirect adaptive control algorithm is proposed to stabilize the fixed points of discrete chaotic systems. It is assumed that the functionality of the chaotic dynamics is known but the system parameters are unknown. This assumption is usually applicable to many chaotic systems, such as the Henon map, logistic and many other nonlinear maps. Using the recursive-least squares technique, the system parameters are identified and based on the feedback linearization method an adaptive controller is designed for stabilizing the fixed points, or unstable periodic orbits of the chaotic maps. The stability of the proposed scheme has been shown and the effectiveness of the control algorithm has been demonstrated through computer simulations

Optimized chaotic Brillouin dynamic grating with filtered optical feedback.

Science.gov (United States)

Zhang, Jianzhong; Li, Zhuping; Wu, Yuan; Zhang, Mingjiang; Liu, Yi; Li, Mengwen

2018-01-16

Chaotic Brillouin dynamic gratings (BDGs) have special advantages such as the creation of single, permanent and localized BDG. However, the periodic signals induced by conventional optical feedback (COF) in chaotic semiconductor lasers can lead to the generation of spurious BDGs, which will limit the application of chaotic BDGs. In this paper, filtered optical feedback (FOF) is proposed to eliminate spurious BDGs. By controlling the spectral width of the optical filter and its detuning from the laser frequency, semiconductor lasers with FOF operate in the suppression region of the time-delay signature, and chaotic outputs serving as pump waves are then utilized to generate the chaotic BDG in a polarization maintaining fiber. Through comparative analysis of the COF and FOF schemes, it has been demonstrated that spurious BDGs are effectively eliminated and that the reflection characterization of the chaotic BDG is improved. The influence of FOF on the reflection and gain spectra of the chaotic BDG is analyzed as well.

Chaplygin sleigh with periodically oscillating internal mass

Science.gov (United States)

Bizyaev, Ivan A.; Borisov, Alexey V.; Kuznetsov, Sergey P.

2017-09-01

We consider the movement of Chaplygin sleigh on a plane that is a solid body with imposed nonholonomic constraint, which excludes the possibility of motions transversal to the constraint element (“knife-edge”), and complement the model with an attached mass, periodically oscillating relatively to the main platform of the sleigh. Numerical simulations indicate the occurrence of either unrestricted acceleration of the sleigh, or motions with bounded velocities and momenta, depending on parameters. We note the presence of phenomena characteristic to nonholonomic systems with complex dynamics; in particular, attractors occur responsible for chaotic motions. In addition, quasiperiodic regimes take place similar to those observed in conservative nonlinear dynamics.

Chaotic phenomena in plasmas

International Nuclear Information System (INIS)

Kawai, Y.

1991-08-01

It has recently been recognized that the research on various aspects of chaotic dynamics grows rapidly as one of some areas in nonlinear science. On the other hands, the plasma has long been called a treasure-house of nonlinear phenomena, so it is easy to imagine that the plasma is abundant in chaotic phenomena. In fact, the research on plasma chaos is going on, such as the research on the stochastic magnetic field and the chaotic orbit in the toroidal helical system, as well as the research in other experiments. To review the present status of the research on plasma chaos and to make clear the basic common physics, a working group was organized in 1990 as a collaboration research of National Institute for Fusion Science. This is the report on its activity in 1990, with a stress on experimental data obtained in basic plasma experiments and RFP, and on the relaxed theories and computer simulations. (author)

A time-delayed method for controlling chaotic maps

International Nuclear Information System (INIS)

Chen Maoyin; Zhou Donghua; Shang Yun

2005-01-01

Combining the repetitive learning strategy and the optimality principle, this Letter proposes a time-delayed method to control chaotic maps. This method can effectively stabilize unstable periodic orbits within chaotic attractors in the sense of least mean square. Numerical simulations of some chaotic maps verify the effectiveness of this method

Intermittent Switching between Soliton Dynamic States in a Perturbed Sine-Gordon Model

DEFF Research Database (Denmark)

Sørensen, Mads Peter; Arley, N.; Christiansen, Peter Leth

1983-01-01

Chaotic intermittency between soliton dynamic states has been found in a perturbed sine-Gordon system in the absence of an external ac driving term. The system is a model of a long Josephson oscillator with constant loss and bias current in an external magnetic field. The results predict the exis......Chaotic intermittency between soliton dynamic states has been found in a perturbed sine-Gordon system in the absence of an external ac driving term. The system is a model of a long Josephson oscillator with constant loss and bias current in an external magnetic field. The results predict...

Deterministic and stochastic control of chimera states in delayed feedback oscillator

Energy Technology Data Exchange (ETDEWEB)

Semenov, V. [Department of Physics, Saratov State University, Astrakhanskaya Str. 83, 410012 Saratov (Russian Federation); Zakharova, A.; Schöll, E. [Institut für Theoretische Physik, TU Berlin, Hardenbergstraße 36, 10623 Berlin (Germany); Maistrenko, Y. [Institute of Mathematics and Center for Medical and Biotechnical Research, NAS of Ukraine, Tereschenkivska Str. 3, 01601 Kyiv (Ukraine)

2016-06-08

Chimera states, characterized by the coexistence of regular and chaotic dynamics, are found in a nonlinear oscillator model with negative time-delayed feedback. The control of these chimera states by external periodic forcing is demonstrated by numerical simulations. Both deterministic and stochastic external periodic forcing are considered. It is shown that multi-cluster chimeras can be achieved by adjusting the external forcing frequency to appropriate resonance conditions. The constructive role of noise in the formation of a chimera states is shown.

On the chaoticity of active-sterile neutrino oscillations in the early universe

DEFF Research Database (Denmark)

Braad, Poul-Erik; Hannestad, Steen

2000-01-01

We have investigated the evolution of the neutrino asymmetry in active-sterile neutrino oscillations in the early universe. We find that there are large regions of parameter space where the asymmetry is extremely sensitive to variations in the initial asymmetry as well as the external parameters ...... asymmetry is stochastic. We discuss the implications of our findings for Big Bang nucleosynthesis (BBN) and the cosmic microwave background (CMB)....

Empirically characteristic analysis of chaotic PID controlling particle swarm optimization

Science.gov (United States)

Yan, Danping; Lu, Yongzhong; Zhou, Min; Chen, Shiping; Levy, David

2017-01-01

Since chaos systems generally have the intrinsic properties of sensitivity to initial conditions, topological mixing and density of periodic orbits, they may tactfully use the chaotic ergodic orbits to achieve the global optimum or their better approximation to given cost functions with high probability. During the past decade, they have increasingly received much attention from academic community and industry society throughout the world. To improve the performance of particle swarm optimization (PSO), we herein propose a chaotic proportional integral derivative (PID) controlling PSO algorithm by the hybridization of chaotic logistic dynamics and hierarchical inertia weight. The hierarchical inertia weight coefficients are determined in accordance with the present fitness values of the local best positions so as to adaptively expand the particles’ search space. Moreover, the chaotic logistic map is not only used in the substitution of the two random parameters affecting the convergence behavior, but also used in the chaotic local search for the global best position so as to easily avoid the particles’ premature behaviors via the whole search space. Thereafter, the convergent analysis of chaotic PID controlling PSO is under deep investigation. Empirical simulation results demonstrate that compared with other several chaotic PSO algorithms like chaotic PSO with the logistic map, chaotic PSO with the tent map and chaotic catfish PSO with the logistic map, chaotic PID controlling PSO exhibits much better search efficiency and quality when solving the optimization problems. Additionally, the parameter estimation of a nonlinear dynamic system also further clarifies its superiority to chaotic catfish PSO, genetic algorithm (GA) and PSO. PMID:28472050

Empirically characteristic analysis of chaotic PID controlling particle swarm optimization.

Science.gov (United States)

Yan, Danping; Lu, Yongzhong; Zhou, Min; Chen, Shiping; Levy, David

2017-01-01

Since chaos systems generally have the intrinsic properties of sensitivity to initial conditions, topological mixing and density of periodic orbits, they may tactfully use the chaotic ergodic orbits to achieve the global optimum or their better approximation to given cost functions with high probability. During the past decade, they have increasingly received much attention from academic community and industry society throughout the world. To improve the performance of particle swarm optimization (PSO), we herein propose a chaotic proportional integral derivative (PID) controlling PSO algorithm by the hybridization of chaotic logistic dynamics and hierarchical inertia weight. The hierarchical inertia weight coefficients are determined in accordance with the present fitness values of the local best positions so as to adaptively expand the particles' search space. Moreover, the chaotic logistic map is not only used in the substitution of the two random parameters affecting the convergence behavior, but also used in the chaotic local search for the global best position so as to easily avoid the particles' premature behaviors via the whole search space. Thereafter, the convergent analysis of chaotic PID controlling PSO is under deep investigation. Empirical simulation results demonstrate that compared with other several chaotic PSO algorithms like chaotic PSO with the logistic map, chaotic PSO with the tent map and chaotic catfish PSO with the logistic map, chaotic PID controlling PSO exhibits much better search efficiency and quality when solving the optimization problems. Additionally, the parameter estimation of a nonlinear dynamic system also further clarifies its superiority to chaotic catfish PSO, genetic algorithm (GA) and PSO.

Empirically characteristic analysis of chaotic PID controlling particle swarm optimization.

Directory of Open Access Journals (Sweden)

Danping Yan

Full Text Available Since chaos systems generally have the intrinsic properties of sensitivity to initial conditions, topological mixing and density of periodic orbits, they may tactfully use the chaotic ergodic orbits to achieve the global optimum or their better approximation to given cost functions with high probability. During the past decade, they have increasingly received much attention from academic community and industry society throughout the world. To improve the performance of particle swarm optimization (PSO, we herein propose a chaotic proportional integral derivative (PID controlling PSO algorithm by the hybridization of chaotic logistic dynamics and hierarchical inertia weight. The hierarchical inertia weight coefficients are determined in accordance with the present fitness values of the local best positions so as to adaptively expand the particles' search space. Moreover, the chaotic logistic map is not only used in the substitution of the two random parameters affecting the convergence behavior, but also used in the chaotic local search for the global best position so as to easily avoid the particles' premature behaviors via the whole search space. Thereafter, the convergent analysis of chaotic PID controlling PSO is under deep investigation. Empirical simulation results demonstrate that compared with other several chaotic PSO algorithms like chaotic PSO with the logistic map, chaotic PSO with the tent map and chaotic catfish PSO with the logistic map, chaotic PID controlling PSO exhibits much better search efficiency and quality when solving the optimization problems. Additionally, the parameter estimation of a nonlinear dynamic system also further clarifies its superiority to chaotic catfish PSO, genetic algorithm (GA and PSO.

Synchronization of two different chaotic systems via nonlinear ...

African Journals Online (AJOL)

ADOWIE PERE

ABSTRACT: This work reports the synchronization of a pair of four chaotic systems via nonlinear control technique. This method has been found to be easy to implement and effective especially on two different chaotic systems. We paired four chaotic systems out of which one is new and we have six possible pairs.

Effect of external magnetic field on critical current for the onset of virtual cathode oscillations in relativistic electron beams

International Nuclear Information System (INIS)

Hramov, Alexander; Koronovskii, Alexey; Morozov, Mikhail; Mushtakov, Alexander

2008-01-01

In this Letter we research the space charge limiting current value at which the oscillating virtual cathode is formed in the relativistic electron beam as a function of the external magnetic field guiding the beam electrons. It is shown that the space charge limiting (critical) current decreases with growth of the external magnetic field, and that there is an optimal induction value of the magnetic field at which the critical current for the onset of virtual cathode oscillations in the electron beam is minimum. For the strong external magnetic field the space charge limiting current corresponds to the analytical relation derived under the assumption that the motion of the electron beam is one-dimensional [D.J. Sullivan, J.E. Walsh, E. Coutsias, in: V.L. Granatstein, I. Alexeff (Eds.), Virtual Cathode Oscillator (Vircator) Theory, in: High Power Microwave Sources, vol. 13, Artech House Microwave Library, 1987, Chapter 13]. Such behavior is explained by the characteristic features of the dynamics of electron space charge in the longitudinal and radial directions in the drift space at the different external magnetic fields

Video encryption using chaotic masks in joint transform correlator

Science.gov (United States)

Saini, Nirmala; Sinha, Aloka

2015-03-01

A real-time optical video encryption technique using a chaotic map has been reported. In the proposed technique, each frame of video is encrypted using two different chaotic random phase masks in the joint transform correlator architecture. The different chaotic random phase masks can be obtained either by using different iteration levels or by using different seed values of the chaotic map. The use of different chaotic random phase masks makes the decryption process very complex for an unauthorized person. Optical, as well as digital, methods can be used for video encryption but the decryption is possible only digitally. To further enhance the security of the system, the key parameters of the chaotic map are encoded using RSA (Rivest-Shamir-Adleman) public key encryption. Numerical simulations are carried out to validate the proposed technique.

Video encryption using chaotic masks in joint transform correlator

International Nuclear Information System (INIS)

Saini, Nirmala; Sinha, Aloka

2015-01-01

A real-time optical video encryption technique using a chaotic map has been reported. In the proposed technique, each frame of video is encrypted using two different chaotic random phase masks in the joint transform correlator architecture. The different chaotic random phase masks can be obtained either by using different iteration levels or by using different seed values of the chaotic map. The use of different chaotic random phase masks makes the decryption process very complex for an unauthorized person. Optical, as well as digital, methods can be used for video encryption but the decryption is possible only digitally. To further enhance the security of the system, the key parameters of the chaotic map are encoded using RSA (Rivest–Shamir–Adleman) public key encryption. Numerical simulations are carried out to validate the proposed technique. (paper)

B-periodic oscillations in the Hall-resistance induced by a dc-current-bias under combined microwave-excitation and dc-current bias in the GaAs/AlGaAs 2D system.

Science.gov (United States)

Liu, Han-Chun; Reichl, C; Wegscheider, W; Mani, R G

2018-05-18

We report the observation of dc-current-bias-induced B-periodic Hall resistance oscillations and Hall plateaus in the GaAs/AlGaAs 2D system under combined microwave radiation- and dc bias excitation at liquid helium temperatures. The Hall resistance oscillations and plateaus appear together with concomitant oscillations also in the diagonal magnetoresistance. The periods of Hall and diagonal resistance oscillations are nearly identical, and source power (P) dependent measurements demonstrate sub-linear relationship of the oscillation amplitude with P over the span 0 < P ≤ 20 mW.

Theory and practice of chaotic cryptography

International Nuclear Information System (INIS)

Amigo, J.M.; Kocarev, L.; Szczepanski, J.

2007-01-01

In this Letter we address some basic questions about chaotic cryptography, not least the very definition of chaos in discrete systems. We propose a conceptual framework and illustrate it with different examples from private and public key cryptography. We elaborate also on possible limits of chaotic cryptography

Dynamics of chaotic strings

International Nuclear Information System (INIS)

Schaefer, Mirko

2011-01-01

The main topic of this thesis is the investigation of dynamical properties of coupled Tchebycheff map networks. The results give insights into the chaotic string model and its network generalization from a dynamical point of view. As a first approach, discrete symmetry transformations of the model are studied. These transformations are formulated in a general way in order to be also applicable to similar dynamics on bipartite network structures. The dynamics is studied numerically via Lyapunov measures, spatial correlations, and ergodic properties. It is shown that the zeros of the interaction energy are distinguished only with respect to this specific observable, but not by a more general dynamical principle. The original chaotic string model is defined on a one-dimensional lattice (ring-network) as the underlying network topology. This thesis studies a modification of the model based on the introduction of tunable disorder. The effects of inhomogeneous coupling weights as well as small-world perturbations of the ring-network structure on the interaction energy are discussed. Synchronization properties of the chaotic string model and its network generalization are studied in later chapters of this thesis. The analysis is based on the master stability formalism, which relates the stability of the synchronized state to the spectral properties of the network. Apart from complete synchronization, where the dynamics at all nodes of the network coincide, also two-cluster synchronization on bipartite networks is studied. For both types of synchronization it is shown that depending on the type of coupling the synchronized dynamics can display chaotic as well as periodic or quasi-periodic behaviour. The semi-analytical calculations reveal that the respective synchronized states are often stable for a wide range of coupling values even for the ring-network, although the respective basins of attraction may inhabit only a small fraction of the phase space. To provide

Robust synchronization of chaotic systems via feedback

Energy Technology Data Exchange (ETDEWEB)

Femat, Ricardo [IPICYT, San Luis Potosi (Mexico). Dept. de Matematicas Aplicadas; Solis-Perales, Gualberto [Universidad de Guadalajara, Centro Univ. de Ciencias Exactas e Ingenierias (Mexico). Div. de Electronica y Computacion

2008-07-01

This volume includes the results derived during last ten years about both suppression and synchronization of chaotic -continuous time- systems. Along this time, the concept was to study how the intrinsic properties of dynamical systems can be exploited to suppress and to synchronize the chaotic behaviour and what synchronization phenomena can be found under feedback interconnection. A compilation of these findings is described in this book. This book shows a perspective on synchronization of chaotic systems. (orig.)

Non-linear thermal engineering, chaotic advection and mixing; Thermique non-lineaire, melange et advection chaotique

Energy Technology Data Exchange (ETDEWEB)

NONE

1999-12-31

This conference day was jointly organized by the `university group of thermal engineering (GUT)` and the French association of thermal engineers. This book of proceedings contains 7 papers entitled: `energy spectra of a passive scalar undergoing advection by a chaotic flow`; `analysis of chaotic behaviours: from topological characterization to modeling`; `temperature homogeneity by Lagrangian chaos in a direct current flow heat exchanger: numerical approach`; ` thermal instabilities in a mixed convection phenomenon: nonlinear dynamics`; `experimental characterization study of the 3-D Lagrangian chaos by thermal analogy`; `influence of coherent structures on the mixing of a passive scalar`; `evaluation of the performance index of a chaotic advection effect heat exchanger for a wide range of Reynolds numbers`. (J.S.)

Non-linear thermal engineering, chaotic advection and mixing; Thermique non-lineaire, melange et advection chaotique

Energy Technology Data Exchange (ETDEWEB)

NONE

1998-12-31

This conference day was jointly organized by the `university group of thermal engineering (GUT)` and the French association of thermal engineers. This book of proceedings contains 7 papers entitled: `energy spectra of a passive scalar undergoing advection by a chaotic flow`; `analysis of chaotic behaviours: from topological characterization to modeling`; `temperature homogeneity by Lagrangian chaos in a direct current flow heat exchanger: numerical approach`; ` thermal instabilities in a mixed convection phenomenon: nonlinear dynamics`; `experimental characterization study of the 3-D Lagrangian chaos by thermal analogy`; `influence of coherent structures on the mixing of a passive scalar`; `evaluation of the performance index of a chaotic advection effect heat exchanger for a wide range of Reynolds numbers`. (J.S.)

Preliminary oscillating fluxes current drive experiment in DIII-D tokamak

International Nuclear Information System (INIS)

Yamaguchi, S.; Schaffer, M.; Kondoh, Y.

1995-01-01

A preliminary oscillating flux helicity injection experiment was done on DIII-D tokamak. The toroidal flux was modulated by programming the plasma elongation. Instead of programming the surface voltage directly, the plasma current was programmed with a periodic modulation at some phase shift. The theoretical basis of this modulation is discussed in terms of the helicity injection and also introduced by cross-field motion of the modulated plasma. Because the primary winding is well coupled with the plasma current and the power supply is strong, the plasma current behaves as programmed. However, as the plasma shape is not coupled strongly with the shaping and equilibrium coils, the elongation amplitude and phase are affected by the change of plasma current and do not behave as programmed. Because of this, the voltage induced by the helicity injection is low, and the experiment did not test the principle of helicity injection. The injection powers of helicity and energy, and the electric field intensity of the helicity injection model and the cross-field motion of plasma are compared with each other experimentally. The improvement necessary to do the experiment is also proposed. ((orig.))

Chaotic correlations in barrier billiards with arbitrary barriers

International Nuclear Information System (INIS)

Osbaldestin, A H; Adamson, L N C

2013-01-01

We study autocorrelation functions in symmetric barrier billiards for golden mean trajectories with arbitrary barriers. Renormalization analysis reveals the presence of a chaotic invariant set and thus that, for a typical barrier, there are chaotic correlations. The chaotic renormalization set is the analogue of the so-called orchid that arises in a generalized Harper equation. (paper)

Computer Modelling of Functional Aspects of Noise in Endogenously Oscillating Neurons

Science.gov (United States)

Huber, M. T.; Dewald, M.; Voigt, K.; Braun, H. A.; Moss, F.

1998-03-01

Membrane potential oscillations are a widespread feature of neuronal activity. When such oscillations operate close to the spike-triggering threshold, noise can become an essential property of spike-generation. According to that, we developed a minimal Hodgkin-Huxley-type computer model which includes a noise term. This model accounts for experimental data from quite different cells ranging from mammalian cortical neurons to fish electroreceptors. With slight modifications of the parameters, the model's behavior can be tuned to bursting activity, which additionally allows it to mimick temperature encoding in peripheral cold receptors including transitions to apparently chaotic dynamics as indicated by methods for the detection of unstable periodic orbits. Under all conditions, cooperative effects between noise and nonlinear dynamics can be shown which, beyond stochastic resonance, might be of functional significance for stimulus encoding and neuromodulation.

Image Encryption and Chaotic Cellular Neural Network

Science.gov (United States)

Peng, Jun; Zhang, Du

Machine learning has been playing an increasingly important role in information security and assurance. One of the areas of new applications is to design cryptographic systems by using chaotic neural network due to the fact that chaotic systems have several appealing features for information security applications. In this chapter, we describe a novel image encryption algorithm that is based on a chaotic cellular neural network. We start by giving an introduction to the concept of image encryption and its main technologies, and an overview of the chaotic cellular neural network. We then discuss the proposed image encryption algorithm in details, which is followed by a number of security analyses (key space analysis, sensitivity analysis, information entropy analysis and statistical analysis). The comparison with the most recently reported chaos-based image encryption algorithms indicates that the algorithm proposed in this chapter has a better security performance. Finally, we conclude the chapter with possible future work and application prospects of the chaotic cellular neural network in other information assurance and security areas.

Implementation of chaotic secure communication systems based on OPA circuits

International Nuclear Information System (INIS)

Huang, C.-K.; Tsay, S.-C.; Wu, Y.-R.

2005-01-01

In this paper, we proposed a novel three-order autonomous circuit to construct a chaotic circuit with double scroll characteristic. The design idea is to use RLC elements and a nonlinear resistor. The one of salient features of the chaotic circuit is that the circuit with two flexible breakpoints of nonlinear element, and the advantage of the flexible breakpoint is that it increased complexity of the dynamical performance. Here, if we take a large and suitable breakpoint value, then the chaotic state can masking a large input signal in the circuit. Furthermore, we proposed a secure communication hyperchaotic system based on the proposed chaotic circuits, where the chaotic communication system is constituted by a chaotic transmitter and a chaotic receiver. To achieve the synchronization between the transmitter and the receiver, we are using a suitable Lyapunov function and Lyapunov theorem to design the feedback control gain. Thus, the transmitting message masked by chaotic state in the transmitter can be guaranteed to perfectly recover in the receiver. To achieve the systems performance, some basic components containing OPA, resistor and capacitor elements are used to implement the proposed communication scheme. From the viewpoints of circuit implementation, this proposed chaotic circuit is superior to the Chua chaotic circuits. Finally, the test results containing simulation and the circuit measurement are shown to demonstrate that the proposed method is correct and feasible

Chaotic behavior learning of Chua's circuit

International Nuclear Information System (INIS)

Sun Jian-Cheng

2012-01-01

Least-square support vector machines (LS-SVM) are applied for learning the chaotic behavior of Chua's circuit. The system is divided into three multiple-input single-output (MISO) structures and the LS-SVM are trained individually. Comparing with classical approaches, the proposed one reduces the structural complexity and the selection of parameters is avoided. Some parameters of the attractor are used to compare the chaotic behavior of the reconstructed and the original systems for model validation. Results show that the LS-SVM combined with the MISO can be trained to identify the underlying link among Chua's circuit state variables, and exhibit the chaotic attractors under the autonomous working mode

Fractional dynamics of globally slow transcription and its impact on deterministic genetic oscillation.

Directory of Open Access Journals (Sweden)

Kun Wei

Full Text Available In dynamical systems theory, a system which can be described by differential equations is called a continuous dynamical system. In studies on genetic oscillation, most deterministic models at early stage are usually built on ordinary differential equations (ODE. Therefore, gene transcription which is a vital part in genetic oscillation is presupposed to be a continuous dynamical system by default. However, recent studies argued that discontinuous transcription might be more common than continuous transcription. In this paper, by appending the inserted silent interval lying between two neighboring transcriptional events to the end of the preceding event, we established that the running time for an intact transcriptional event increases and gene transcription thus shows slow dynamics. By globally replacing the original time increment for each state increment by a larger one, we introduced fractional differential equations (FDE to describe such globally slow transcription. The impact of fractionization on genetic oscillation was then studied in two early stage models--the Goodwin oscillator and the Rössler oscillator. By constructing a "dual memory" oscillator--the fractional delay Goodwin oscillator, we suggested that four general requirements for generating genetic oscillation should be revised to be negative feedback, sufficient nonlinearity, sufficient memory and proper balancing of timescale. The numerical study of the fractional Rössler oscillator implied that the globally slow transcription tends to lower the chance of a coupled or more complex nonlinear genetic oscillatory system behaving chaotically.

Fractional dynamics of globally slow transcription and its impact on deterministic genetic oscillation.

Science.gov (United States)

Wei, Kun; Gao, Shilong; Zhong, Suchuan; Ma, Hong

2012-01-01

In dynamical systems theory, a system which can be described by differential equations is called a continuous dynamical system. In studies on genetic oscillation, most deterministic models at early stage are usually built on ordinary differential equations (ODE). Therefore, gene transcription which is a vital part in genetic oscillation is presupposed to be a continuous dynamical system by default. However, recent studies argued that discontinuous transcription might be more common than continuous transcription. In this paper, by appending the inserted silent interval lying between two neighboring transcriptional events to the end of the preceding event, we established that the running time for an intact transcriptional event increases and gene transcription thus shows slow dynamics. By globally replacing the original time increment for each state increment by a larger one, we introduced fractional differential equations (FDE) to describe such globally slow transcription. The impact of fractionization on genetic oscillation was then studied in two early stage models--the Goodwin oscillator and the Rössler oscillator. By constructing a "dual memory" oscillator--the fractional delay Goodwin oscillator, we suggested that four general requirements for generating genetic oscillation should be revised to be negative feedback, sufficient nonlinearity, sufficient memory and proper balancing of timescale. The numerical study of the fractional Rössler oscillator implied that the globally slow transcription tends to lower the chance of a coupled or more complex nonlinear genetic oscillatory system behaving chaotically.

A novel one equilibrium hyper-chaotic system generated upon Lü attractor

International Nuclear Information System (INIS)

Hong-Yan, Jia; Zeng-Qiang, Chen; Zhu-Zhi, Yuan

2010-01-01

By introducing an additional state feedback into a three-dimensional autonomous chaotic attractor Lü system, this paper presents a novel four-dimensional continuous autonomous hyper-chaotic system which has only one equilibrium. There are only 8 terms in all four equations of the new hyper-chaotic system, which may be less than any other four-dimensional continuous autonomous hyper-chaotic systems generated by three-dimensional (3D) continuous autonomous chaotic systems. The hyper-chaotic system undergoes Hopf bifurcation when parameter c varies, and becomes the 3D modified Lü system when parameter k varies. Although the hyper-chaotic system does not undergo Hopf bifurcation when parameter k varies, many dynamic behaviours such as periodic attractor, quasi periodic attractor, chaotic attractor and hyper-chaotic attractor can be observed. A circuit is also designed when parameter k varies and the results of the circuit experiment are in good agreement with those of simulation. (general)

Chaotic sedimentation of particle pairs in a vertical channel at low Reynolds number: Multiple states and routes to chaos

Science.gov (United States)

Verjus, Romuald; Guillou, Sylvain; Ezersky, Alexander; Angilella, Jean-Régis

2016-12-01

The sedimentation of a pair of rigid circular particles in a two-dimensional vertical channel containing a Newtonian fluid is investigated numerically, for terminal particle Reynolds numbers (ReT) ranging from 1 to 10, and for a confinement ratio equal to 4. While it is widely admitted that sufficiently inertial pairs should sediment by performing a regular DKT oscillation (Drafting-Kissing-Tumbling), the present analysis shows in contrast that a chaotic regime can also exist for such particles, leading to a much slower sedimentation velocity. It consists of a nearly horizontal pair, corresponding to a maximum effective blockage ratio, and performing a quasiperiodic transition to chaos while increasing the particle weight. For less inertial regimes, the classical oblique doublet structure and its complex behavior (multiple stable states and hysteresis, period-doubling cascade and chaotic attractor) are recovered, in agreement with previous work [Aidun, C. K. and Ding, E.-J., "Dynamics of particle sedimentation in a vertical channel: Period-doubling bifurcation and chaotic state," Phys. Fluids 15, 1612 (2003)]. As a consequence of these various behaviors, the link between the terminal Reynolds number and the non-dimensional driving force is complex: it contains several branches displaying hysteresis as well as various bifurcations. For the range of Reynolds number considered here, a global bifurcation diagram is given.

Design of the Chaotic Signal Generator Based on LABVIEW

Directory of Open Access Journals (Sweden)

Jian-Guo Zhang

2014-01-01

Full Text Available We introduces a new method that can achieve the generation of Colpitts chaotic signal The system is based on virtual instrument platform and combined with MATLAB calculation to achieve the generation of Colpitts chaotic signal and making it analysis with autocorrelation and power spectrum at the same time. Signal channel output of chaotic signal was realized through USB-6009 acquisition module extending DA5405 high-speed DAC (Digital-to-Analog Converter chip. The system can adjust parameters based on customers’ requirements to achieve different frequency chaotic signal generation. Compared with the traditional autonomy Colpitts chaotic signal generator, this generator is simple and clear in structure, simple to operate, strong stability, easy to achieve etc.

Synchronization of a class of chaotic signals via robust observer design

Energy Technology Data Exchange (ETDEWEB)

Aguilar-Lopez, Ricardo [Departamento de Energia, Universidad Autonoma Metropolitana - Azcapotzalco, San Pablo 180, Reynosa-Tamaulipas, Azcapotzalco 02200, Mexico, D.F. (Mexico)], E-mail: raguilar@correo.azc.uam.mx; Martinez-Guerra, Rafael [Departamento de Energia, Universidad Autonoma Metropolitana - Azcapotzalco, San Pablo 180, Reynosa-Tamaulipas, Azcapotzalco 02200, Mexico, D.F. (Mexico); Departamento de Control Automatico, CINVESTAV IPN, Apartado Postal 14-740, Mexico, D.F. C.P. 07360 (Mexico)], E-mail: rguerra@ctrl.cinvestav.mx

2008-07-15

In this paper the signal synchronization of a class of chaotic systems based on robust observer design is tackled. The task is the synchronization of the signals generated by two Chen oscillators with different initial condition. The proposed observer is robust against model uncertainties and noisy output measurements. An alternative system representation is proposed to transform the measured disturbance onto system disturbance, which leads a more adequate observer structure. The proposed methodology contains an uncertainty estimator based on the predictive contribution to infer the unobservable uncertainties and corrective contribution to estimate the observable uncertainties; which provides robustness against noisy measurements and model uncertainties. Convergence analysis of the proposed estimation methodology is realized, analyzing the dynamic equation of the estimation error, where asymptotic convergence is shown. Numerical experiments illustrate the good performance of the proposed methodology.

Synchronization of a class of chaotic signals via robust observer design

International Nuclear Information System (INIS)

Aguilar-Lopez, Ricardo; Martinez-Guerra, Rafael

2008-01-01

In this paper the signal synchronization of a class of chaotic systems based on robust observer design is tackled. The task is the synchronization of the signals generated by two Chen oscillators with different initial condition. The proposed observer is robust against model uncertainties and noisy output measurements. An alternative system representation is proposed to transform the measured disturbance onto system disturbance, which leads a more adequate observer structure. The proposed methodology contains an uncertainty estimator based on the predictive contribution to infer the unobservable uncertainties and corrective contribution to estimate the observable uncertainties; which provides robustness against noisy measurements and model uncertainties. Convergence analysis of the proposed estimation methodology is realized, analyzing the dynamic equation of the estimation error, where asymptotic convergence is shown. Numerical experiments illustrate the good performance of the proposed methodology

Identifying and Evaluating Chaotic Behavior in Hydro-Meteorological Processes

Directory of Open Access Journals (Sweden)

Soojun Kim

2015-01-01

Full Text Available The aim of this study is to identify and evaluate chaotic behavior in hydro-meteorological processes. This study poses the two hypotheses to identify chaotic behavior of the processes. First, assume that the input data is the significant factor to provide chaotic characteristics to output data. Second, assume that the system itself is the significant factor to provide chaotic characteristics to output data. For solving this issue, hydro-meteorological time series such as precipitation, air temperature, discharge, and storage volume were collected in the Great Salt Lake and Bear River Basin, USA. The time series in the period of approximately one year were extracted from the original series using the wavelet transform. The generated time series from summation of sine functions were fitted to each series and used for investigating the hypotheses. Then artificial neural networks had been built for modeling the reservoir system and the correlation dimension was analyzed for the evaluation of chaotic behavior between inputs and outputs. From the results, we found that the chaotic characteristic of the storage volume which is output is likely a byproduct of the chaotic behavior of the reservoir system itself rather than that of the input data.

The chaotic dynamical aperture

International Nuclear Information System (INIS)

Lee, S.Y.; Tepikian, S.

1985-01-01

Nonlinear magnetic forces become more important for particles in the modern large accelerators. These nonlinear elements are introduced either intentionally to control beam dynamics or by uncontrollable random errors. Equations of motion in the nonlinear Hamiltonian are usually non-integrable. Because of the nonlinear part of the Hamiltonian, the tune diagram of accelerators is a jungle. Nonlinear magnet multipoles are important in keeping the accelerator operation point in the safe quarter of the hostile jungle of resonant tunes. Indeed, all the modern accelerator design have taken advantages of nonlinear mechanics. On the other hand, the effect of the uncontrollable random multipoles should be evaluated carefully. A powerful method of studying the effect of these nonlinear multipoles is using a particle tracking calculation, where a group of test particles are tracing through these magnetic multipoles in the accelerator hundreds to millions of turns in order to test the dynamical aperture of the machine. These methods are extremely useful in the design of a large accelerator such as SSC, LEP, HERA and RHIC. These calculations unfortunately take tremendous amount of computing time. In this paper, we try to apply the existing method in the nonlinear dynamics to study the possible alternative solution. When the Hamiltonian motion becomes chaotic, the tune of the machine becomes undefined. The aperture related to the chaotic orbit can be identified as chaotic dynamical aperture. We review the method of determining chaotic orbit and apply the method to nonlinear problems in accelerator physics. We then discuss the scaling properties and effect of random sextupoles

Chaotic time series. Part II. System Identification and Prediction

Directory of Open Access Journals (Sweden)

Bjørn Lillekjendlie

1994-10-01

Full Text Available This paper is the second in a series of two, and describes the current state of the art in modeling and prediction of chaotic time series. Sample data from deterministic non-linear systems may look stochastic when analysed with linear methods. However, the deterministic structure may be uncovered and non-linear models constructed that allow improved prediction. We give the background for such methods from a geometrical point of view, and briefly describe the following types of methods: global polynomials, local polynomials, multilayer perceptrons and semi-local methods including radial basis functions. Some illustrative examples from known chaotic systems are presented, emphasising the increase in prediction error with time. We compare some of the algorithms with respect to prediction accuracy and storage requirements, and list applications of these methods to real data from widely different areas.

Cryptanalysis on a modified Baptista-type cryptosystem with chaotic masking algorithm

International Nuclear Information System (INIS)

Chen Yong; Liao Xiaofeng

2005-01-01

Based on chaotic masking algorithm, an enhanced Baptista-type cryptosystem is proposed by Li et al. to resist all known attacks [S. Li, X. Mou, Z. Ji, J. Zhang, Y. Cai, Phys. Lett. A 307 (2003) 22; S. Li, G. Chen, K.-W. Wong, X. Mou, Y. Cai, Phys. Lett. A 332 (2004) 368]. In this Letter, we show that the second class bit extracting function in [S. Li, X. Mou, Z. Ji, J. Zhang, Y. Cai, Phys. Lett. A 307 (2003) 22] still leak partial information on the current chaotic state and reduce the security of cryptosystem. So, this type bit extracting function is not a good candidate for the masking algorithm

Composing chaotic music from the letter m

Science.gov (United States)

Sotiropoulos, Anastasios D.

Chaotic music is composed from a proposed iterative map depicting the letter m, relating the pitch, duration and loudness of successive steps. Each of the two curves of the letter m is based on the classical logistic map. Thus, the generating map is xn+1 = r xn(1/2 - xn) for xn between 0 and 1/2 defining the first curve, and xn+1 = r (xn - 1/2)(1 - xn) for xn between 1/2 and 1 representing the second curve. The parameter r which determines the height(s) of the letter m varies from 2 to 16, the latter value ensuring fully developed chaotic solutions for the whole letter m; r = 8 yielding full chaotic solutions only for its first curve. The m-model yields fixed points, bifurcation points and chaotic regions for each separate curve, as well as values of the parameter r greater than 8 which produce inter-fixed points, inter-bifurcation points and inter-chaotic regions from the interplay of the two curves. Based on this, music is composed from mapping the m- recurrence model solutions onto actual notes. The resulting musical score strongly depends on the sequence of notes chosen by the composer to define the musical range corresponding to the range of the chaotic mathematical solutions x from 0 to 1. Here, two musical ranges are used; one is the middle chromatic scale and the other is the seven- octaves range. At the composer's will and, for aesthetics, within the same composition, notes can be the outcome of different values of r and/or shifted in any octave. Compositions with endings of non-repeating note patterns result from values of r in the m-model that do not produce bifurcations. Scores of chaotic music composed from the m-model and the classical logistic model are presented.

Economic dispatch using chaotic bat algorithm

International Nuclear Information System (INIS)

Adarsh, B.R.; Raghunathan, T.; Jayabarathi, T.; Yang, Xin-She

2016-01-01

This paper presents the application of a new metaheuristic optimization algorithm, the chaotic bat algorithm for solving the economic dispatch problem involving a number of equality and inequality constraints such as power balance, prohibited operating zones and ramp rate limits. Transmission losses and multiple fuel options are also considered for some problems. The chaotic bat algorithm, a variant of the basic bat algorithm, is obtained by incorporating chaotic sequences to enhance its performance. Five different example problems comprising 6, 13, 20, 40 and 160 generating units are solved to demonstrate the effectiveness of the algorithm. The algorithm requires little tuning by the user, and the results obtained show that it either outperforms or compares favorably with several existing techniques reported in literature. - Highlights: • The chaotic bat algorithm, a new metaheuristic optimization algorithm has been used. • The problem solved – the economic dispatch problem – is nonlinear, discontinuous. • It has number of equality and inequality constraints. • The algorithm has been demonstrated to be applicable on high dimensional problems.

Parametric Control on Fractional-Order Response for Lü Chaotic System

KAUST Repository

Moaddy, K; Radwan, A G; Salama, Khaled N.; Momani, S; Hashim, I

2013-01-01

This paper discusses the influence of the fractional order parameter on conventional chaotic systems. These fractional-order parameters increase the system degree of freedom allowing it to enter new domains and thus it can be used as a control for such dynamical systems. This paper investigates the behaviour of the equally-fractional-order Lü chaotic system when changing the fractional-order parameter and determines the fractional-order ranges for chaotic behaviour. Five different parameter values and six fractional-order cases are discussed through this paper. Unlike the conventional parameters, as the fractional-order increases the system response begins with stability, passing by chaotic behaviour then reaches periodic response. As the system parameter α increases, a shift in the fractional order is required to maintain chaotic response.Therefore, the range of chaotic response can be expanded or minimized by controlling the fractional-order parameter. The non-standard finite difference method is used to solve the fractional-order Lü chaotic system numerically to validate these responses.

Parametric Control on Fractional-Order Response for Lü Chaotic System

KAUST Repository

Moaddy, K

2013-04-10

This paper discusses the influence of the fractional order parameter on conventional chaotic systems. These fractional-order parameters increase the system degree of freedom allowing it to enter new domains and thus it can be used as a control for such dynamical systems. This paper investigates the behaviour of the equally-fractional-order Lü chaotic system when changing the fractional-order parameter and determines the fractional-order ranges for chaotic behaviour. Five different parameter values and six fractional-order cases are discussed through this paper. Unlike the conventional parameters, as the fractional-order increases the system response begins with stability, passing by chaotic behaviour then reaches periodic response. As the system parameter α increases, a shift in the fractional order is required to maintain chaotic response.Therefore, the range of chaotic response can be expanded or minimized by controlling the fractional-order parameter. The non-standard finite difference method is used to solve the fractional-order Lü chaotic system numerically to validate these responses.

A Hybrid Chaotic Quantum Evolutionary Algorithm

DEFF Research Database (Denmark)

Cai, Y.; Zhang, M.; Cai, H.

2010-01-01

A hybrid chaotic quantum evolutionary algorithm is proposed to reduce amount of computation, speed up convergence and restrain premature phenomena of quantum evolutionary algorithm. The proposed algorithm adopts the chaotic initialization method to generate initial population which will form a pe...... tests. The presented algorithm is applied to urban traffic signal timing optimization and the effect is satisfied....

Nuclear friction and chaotic motion

International Nuclear Information System (INIS)

Srokowski, T.; Szczurek, A.; Drozdz, S.

1990-01-01

The concept of nuclear friction is considered from the point of view of regular versus chaotic motion in an atomic nucleus. Using a realistic nuclear Hamiltonian it is explicitly shown that the frictional description of the gross features of nuclear collisions is adequate if the system behaves chaotically. Because of the core in the Hamiltonian, the three-body nuclear system already reveals a structure of the phase space rich enough for this concept to be applicable

Chaotic diagonal recurrent neural network

International Nuclear Information System (INIS)

Wang Xing-Yuan; Zhang Yi

2012-01-01

We propose a novel neural network based on a diagonal recurrent neural network and chaos, and its structure and learning algorithm are designed. The multilayer feedforward neural network, diagonal recurrent neural network, and chaotic diagonal recurrent neural network are used to approach the cubic symmetry map. The simulation results show that the approximation capability of the chaotic diagonal recurrent neural network is better than the other two neural networks. (interdisciplinary physics and related areas of science and technology)

Chaotic secure communication based on strong tracking filtering

International Nuclear Information System (INIS)

Li Xiongjie; Xu Zhengguo; Zhou Donghua

2008-01-01

A scheme for implementing secure communication based on chaotic maps and strong tracking filter (STF) is presented, and a modified STF algorithm with message estimation is developed for the special requirement of chaotic secure communication. At the emitter, the message symbol is modulated by chaotic mapping and is output through a nonlinear function. At the receiver, the driving signal is received and the message symbol is recovered dynamically by the STF with estimation of message symbol. Simulation results of Holmes map demonstrate that when message symbols are binary codes, STF can effectively recover the codes of the message from the noisy chaotic signals. Compared with the extended Kalman filter (EKF), STF has a lower bit error rate

A new transiently chaotic flow with ellipsoid equilibria

Science.gov (United States)

Panahi, Shirin; Aram, Zainab; Jafari, Sajad; Pham, Viet-Thanh; Volos, Christos; Rajagopal, Karthikeyan

2018-03-01

In this article, a simple autonomous transiently chaotic flow with cubic nonlinearities is proposed. This system represents some unusual features such as having a surface of equilibria. We shall describe some dynamical properties and behaviours of this system in terms of eigenvalue structures, bifurcation diagrams, time series, and phase portraits. Various behaviours of this system such as periodic and transiently chaotic dynamics can be shown by setting special parameters in proper values. Our system belongs to a newly introduced category of transiently chaotic systems: systems with hidden attractors. Transiently chaotic behaviour of our proposed system has been implemented and tested by the OrCAD-PSpise software. We have found a proper qualitative similarity between circuit and simulation results.

A novel 3D autonomous system with different multilayer chaotic attractors

International Nuclear Information System (INIS)

Dong Gaogao; Du Ruijin; Tian Lixin; Jia Qiang