Dynamical Behavior of a 3D Jerk System with a Generalized Memristive Device

As a new type of electronic components, a memristive device is receiving worldwide attention and can enrich the dynamical behaviors of the oscillating system. In this paper, we propose a 3D jerk system by introducing a generalized memristive device. It is found that the dynamical behaviors of the system are sensitive to the initial conditions even the system parameters are fixed, which results in the coexistence of multiple attractors. And there exists different transition behaviors depending on the selection of the parameters and initial values. Thereby, it is one important type of the candidate system for secure communication since the reconstruction of accurate state space becomes more difficult. Moreover, we build a hardware circuit and the experimental results effectively confirm the theoretical analyses.

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Circuit Implementation, Synchronization of Multistability, and Image Encryption of a Four-Wing Memristive Chaotic System

Journal of Electrical and Computer Engineering ◽

10.1155/2018/8649294 ◽

2018 ◽

Vol 2018 ◽

pp. 1-13 ◽

Cited By ~ 5

Author(s):

Guangya Peng ◽

Fuhong Min ◽

Enrong Wang

Keyword(s):

Image Encryption ◽

Chaotic System ◽

Secure Communication ◽

Secret Key ◽

Multiple Attractors ◽

Dynamical Behaviors ◽

Key Space ◽

Control Scheme ◽

Memristive System ◽

Coexistence Of Multiple Attractors

The four-wing memristive chaotic system used in synchronization is applied to secure communication which can increase the difficulty of deciphering effectively and enhance the security of information. In this paper, a novel four-wing memristive chaotic system with an active cubic flux-controlled memristor is proposed based on a Lorenz-like circuit. Dynamical behaviors of the memristive system are illustrated in terms of Lyapunov exponents, bifurcation diagrams, coexistence Poincaré maps, coexistence phase diagrams, and attraction basins. Besides, the modular equivalent circuit of four-wing memristive system is designed and the corresponding results are observed to verify its accuracy and rationality. A nonlinear synchronization controller with exponential function is devised to realize synchronization of the coexistence of multiple attractors, and the synchronization control scheme is applied to image encryption to improve secret key space. More interestingly, considering different influence of multistability on encryption, the appropriate key is achieved to enhance the antideciphering ability.

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Pre-inflation dynamical behavior of warm inflation in loop quantum cosmology

Modern Physics Letters A ◽

10.1142/s0217732320502934 ◽

2020 ◽

Vol 35 (35) ◽

pp. 2050293

Author(s):

Kui Xiao ◽

Sheng-Qin Wang

Keyword(s):

Quantum Cosmology ◽

Initial Conditions ◽

Dynamical Behavior ◽

Loop Quantum Cosmology ◽

Warm Inflation ◽

Dynamical Behaviors ◽

Slow Roll ◽

Dissipative Coefficient ◽

Slow Roll Inflation ◽

Three Phases

Considering a constant dissipative coefficient [Formula: see text], the pre-inflation dynamical behaviors of warm inflation in the loop quantum cosmology scenario are discussed. We consider three sets of initial conditions. The evolution of the background can always be divided into three phases, namely super-inflation, damping, and slow-roll inflation phases, with the duration of each phase depending on the initial conditions. As an example, we compare the background evolution between [Formula: see text] and [Formula: see text] under special initial conditions and find that there is no slow-roll inflation phase for [Formula: see text] while the number of e-folds is about 60.209 for [Formula: see text].

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Experimental Validation of Multiple Attractors in a Simple Chaotic Circuit

WSEAS TRANSACTIONS ON CIRCUITS AND SYSTEMS ◽

10.37394/23201.2020.19.19 ◽

2020 ◽

Vol 19 ◽

Keyword(s):

Theoretical Prediction ◽

Chaotic System ◽

Experimental Validation ◽

Complex Dynamics ◽

Initial Conditions ◽

Dynamical Behavior ◽

Experimental Results ◽

Equilibrium Analysis ◽

Tuning Parameter ◽

Multiple Attractors

In this paper, a simple jerk circuit that allows studying the dynamical behavior of a three-dimensional autonomous chaotic system with only one nonlinear term is further investigated by numerical simulations and experimental validation. Depending on a single tuning parameter, the chaotic system is theoretically studied using standard techniques such as equilibrium analysis, bifurcation diagram, and Lyapunov exponents. Subsequently, the circuit that models the chaotic system is implemented to validate theoretical prediction experimentally. Despite the simple structure of the jerk circuit, experimental study of Fourier spectra has shown that the jerk circuit displays complex dynamics characterized by periodic limit cycles and aperiodic strange attractors. In addition, the jerk circuit has exhibited a wide tuning range and experimental results have shown good agreement with theoretical prediction except for few cases where numerical simulation has failed to accurately match experimental results due to sensitivity to initial conditions which is a signature of chaotic nonlinear systems.

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Tristable Phenomenon in a Predator–Prey System Arising from Multiple Limit Cycles Bifurcation

International Journal of Bifurcation and Chaos ◽

10.1142/s0218127420501291 ◽

2020 ◽

Vol 30 (09) ◽

pp. 2050129

Author(s):

Jiao Jiang ◽

Wenjing Zhang ◽

Pei Yu

Keyword(s):

Limit Cycles ◽

Dynamical Behavior ◽

Predator Prey ◽

Dynamical Behaviors ◽

Prey System ◽

Stable Periodic ◽

New Type ◽

Stable Equilibria ◽

Ratio Dependent ◽

Parameter Values

In this paper, we consider a predator–prey system with Holling type III ratio-dependent functional response. Such a system can exhibit complex dynamical behavior such as bistable and tristable phenomena which contain equilibria and oscillating motions for certain parameter values. In particular, we show that the ratio-dependent predator–prey system can exhibit multiple limit cycles due to Hopf bifurcation, giving rise to coexistence of stable equilibria and stable periodic solutions. These solutions may reveal some new type of patterns of complex dynamical behaviors in predator–prey systems.

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Fractional-order chaotic system with hyperbolic function

Advances in Mechanical Engineering ◽

10.1177/1687814019872581 ◽

2019 ◽

Vol 11 (8) ◽

pp. 168781401987258

Author(s):

G Gugapriya ◽

Prakash Duraisamy ◽

Anitha Karthikeyan ◽

B Lakshmi

Keyword(s):

Fractional Order ◽

Chaotic System ◽

Secure Communication ◽

Sliding Mode ◽

Initial Conditions ◽

Dynamical Behavior ◽

Adomian Decomposition Method ◽

Adaptive Synchronization ◽

Hyperbolic Function ◽

Adomian Decomposition

In this article, we study bistability, multiscroll, and symmetric properties of fractional-order chaotic system with cubic nonlinearity. The system is configured with hyperbolic function consisting of a parameter “ g.” By varying the parameter “ g,” the dynamical behavior of the system is investigated. Multistability and multiscroll are identified, which makes the system suitable for secure communication applications. When the system is treated as fractional order, for the same parameter values and initial conditions and when the fractional order is varied from 0.96 to 0.99, multiscroll property is obtained. Symmetric property is obtained for the order of 0.99. The fractional system holds only single scroll until 0.965 order and when the order increases to more than 0.99, it is having two-scroll attractor. This property opens a variety of applications for the systems, especially in secure communication. Adaptive synchronization of the system using sliding mode control scheme is presented. For implementing the fractional-order system in field-programmable gate array, Adomian decomposition method is used, and the register-transfer level schematic of the system is presented.

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Dynamical Analysis and Simulation of a New Lorenz-Like Chaotic System

Mathematical Problems in Engineering ◽

10.1155/2021/6669956 ◽

2021 ◽

Vol 2021 ◽

pp. 1-18

Author(s):

You Li ◽

Ming Zhao ◽

Fengjie Geng

Keyword(s):

Chaotic System ◽

Equilibrium Points ◽

Dynamical Behavior ◽

Heteroclinic Orbits ◽

Dynamical Analysis ◽

Poincaré Compactification ◽

Stable And Unstable Manifolds ◽

Dynamical Behaviors ◽

New Chaotic System ◽

New Type

This work presents and investigates a new chaotic system with eight terms. By numerical simulation, the two-scroll chaotic attractor is found for some certain parameters. And, by theoretical analysis, we discuss the dynamical behavior of the new-type Lorenz-like chaotic system. Firstly, the local dynamical properties, such as the distribution and the local stability of all equilibrium points, the local stable and unstable manifolds, and the Hopf bifurcations, are all revealed as the parameters varying in the space of parameters. Secondly, by applying the way of Poincaré compactification in ℝ 3 , the dynamics at infinity are clearly analyzed. Thirdly, combining the dynamics at finity and those at infinity, the global dynamical behaviors are formulated. Especially, we have proved the existence of the infinite heteroclinic orbits. Furthermore, all obtained theoretical results in this paper are further verified by numerical simulations.

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Multiple attractors and strange nonchaotic dynamical behavior in a periodically forced system

Nonlinear Dynamics ◽

10.1007/s11071-021-06608-8 ◽

2021 ◽

Vol 105 (4) ◽

pp. 3615-3635

Author(s):

A. Chithra ◽

I. Raja Mohamed

Keyword(s):

Dynamical Behavior ◽

Multiple Attractors

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Behavior of a Self-Sustained Electromechanical Transducer and Routes to Chaos

Journal of Vibration and Acoustics ◽

10.1115/1.2172255 ◽

2005 ◽

Vol 128 (3) ◽

pp. 282-293 ◽

Cited By ~ 12

Author(s):

J. C. Chedjou ◽

K. Kyamakya ◽

I. Moussa ◽

H.-P. Kuchenbecker ◽

W. Mathis

Keyword(s):

Electronic Circuit ◽

Initial Conditions ◽

Dynamical Behavior ◽

Period Doubling ◽

Electromechanical System ◽

Phase Portraits ◽

Coupling Coefficients ◽

Oscillatory Solutions ◽

Electromechanical Transducer ◽

Design Engineers

This paper studies the dynamics of a self-sustained electromechanical transducer. The stability of fixed points in the linear response is examined. Their local bifurcations are investigated and different types of bifurcation likely to occur are found. Conditions for the occurrence of Hopf bifurcations are derived. Harmonic oscillatory solutions are obtained in both nonresonant and resonant cases. Their stability is analyzed in the resonant case. Various bifurcation diagrams associated to the largest one-dimensional (1-D) numerical Lyapunov exponent are obtained, and it is found that chaos can appear suddenly, through period doubling, period adding, or torus breakdown. The extreme sensitivity of the electromechanical system to both initial conditions and tiny variations of the coupling coefficients is also outlined. The experimental study of̱the electromechanical system is carried out. An appropriate electronic circuit (analog simulator) is proposed for the investigation of the dynamical behavior of the electromechanical system. Correspondences are established between the coefficients of the electromechanical system model and the components of the electronic circuit. Harmonic oscillatory solutions and phase portraits are obtained experimentally. One of the most important contributions of this work is to provide a set of reliable analytical expressions (formulas) describing the electromechanical system behavior. These formulas are of great importance for design engineers as they can be used to predict the states of the electromechanical systems and respectively to avoid their destruction. The reliability of the analytical formulas is demonstrated by the very good agreement with the results obtained by both the numeric and the experimental analysis.

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MATHEMATICAL MODEL OF THREE SPECIES FOOD CHAIN INTERACTION WITH MIXED FUNCTIONAL RESPONSE

International Journal of Modern Physics Conference Series ◽

10.1142/s2010194512005399 ◽

2012 ◽

Vol 09 ◽

pp. 334-340 ◽

Cited By ~ 2

Author(s):

MADA SANJAYA WS ◽

ISMAIL BIN MOHD ◽

MUSTAFA MAMAT ◽

ZABIDIN SALLEH

Keyword(s):

Mathematical Model ◽

Functional Response ◽

Food Chain ◽

Equilibrium Points ◽

Dynamical Behavior ◽

Bifurcation Points ◽

Dynamical Behaviors ◽

Practical Life ◽

Parameter Values ◽

Chain Interaction

In this paper, we study mathematical model of ecology with a tritrophic food chain composed of a classical Lotka-Volterra functional response for prey and predator, and a Holling type-III functional response for predator and super predator. There are two equilibrium points of the system. In the parameter space, there are passages from instability to stability, which are called Hopf bifurcation points. For the first equilibrium point, it is possible to find bifurcation points analytically and to prove that the system has periodic solutions around these points. Furthermore the dynamical behaviors of this model are investigated. Models for biologically reasonable parameter values, exhibits stable, unstable periodic and limit cycles. The dynamical behavior is found to be very sensitive to parameter values as well as the parameters of the practical life. Computer simulations are carried out to explain the analytical findings.

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