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

Кузнецов, А. П.; Кузнецов, С. П.; Mosekilde, Erik; Stankevich, Nataliya

doi:10.1088/1751-8113/48/12/125101

Cited by 110 publications

(44 citation statements)

References 28 publications

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“…For example, hidden attractors are attractors in the systems with no equilibria or with only one stable equilibrium (a special case of multistable systems and coexistence of attractors). 8 Recent examples of hidden attractors can be found in [10,28,34,52,57,58,65,66,79,80,83,84]. Multistability is often an undesired situation in many applications, however coexisting self-excited attractors can be found by the standard computational procedure.…”

Section: Numerical Simulation and Visualization Of Attractorsmentioning

confidence: 99%

On differences and similarities in the analysis of Lorenz, Chen, and Lu systems

Леонов

Kuznetsov

2015

Applied Mathematics and Computation

103

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Keywords:Lorenz-like systems Lorenz system Chen system Lu system Lyapunov exponent Chaotic analog of 16th Hilbert problem a b s t r a c t Currently it is being actively discussed the question of the equivalence of various Lorenzlike systems and the possibility of universal consideration of their behavior (Algaba et al., 2013a(Algaba et al., ,b, 2014bChen, 2013;Chen and Yang, 2013; Leonov, 2013a), in view of the possibility of reduction of such systems to the same form with the help of various transformations. In the present paper the differences and similarities in the analysis of the Lorenz, the Chen and the Lu systems are discussed. It is shown that the Chen and the Lu systems stimulate the development of new methods for the analysis of chaotic systems. Open problems are discussed.

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Section: Numerical Simulation and Visualization Of Attractorsmentioning

confidence: 99%

On differences and similarities in the analysis of Lorenz, Chen, and Lu systems

Леонов

Kuznetsov

2015

Applied Mathematics and Computation

103

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“…One can see from (3a)-(3c) can exhibit either chaotic or periodic attractor depending on the initial conditions. It is worth noting that coexistence of attractors has been observed in various nonlinear systems including laser [28,29], biological system [30], chemical reactions [31], Lorenz systems [32][33][34][35], and electrical circuits [36,37], just to name a few.…”

Section: Dynamical Behaviors Of the Linearmentioning

confidence: 99%

Analysis of a No Equilibrium Linear Resistive-Capacitive-Inductance Shunted Junction Model, Dynamics, Synchronization, and Application to Digital Cryptography in Its Fractional-Order Form

et al. 2017

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A linear resistive-capacitive-inductance shunted junction (LRCLSJ) model obtained by replacing the nonlinear piecewise resistance of a nonlinear resistive-capacitive-inductance shunted junction (NRCLSJ) model by a linear resistance is analyzed in this paper. The LRCLSJ model has two or no equilibrium points depending on the dc bias current. For a suitable choice of the parameters, the LRCLSJ model without equilibrium point can exhibit regular and fast spiking, intrinsic and periodic bursting, and periodic and chaotic behaviors. We show that the LRCLSJ model displays similar dynamical behaviors as the NRCLSJ model. Moreover the coexistence between periodic and chaotic attractors is found in the LRCLSJ model for specific parameters. The lowest order of the commensurate form of the no equilibrium LRCLSJ model to exhibit chaotic behavior is found to be 2.934. Moreover, adaptive finite-time synchronization with parameter estimation is applied to achieve synchronization of unidirectional coupled identical fractional-order form of chaotic no equilibrium LRCLSJ models. Finally, a cryptographic encryption scheme with the help of the finite-time synchronization of fractional-order chaotic no equilibrium LRCLSJ models is illustrated through a numerical example, showing that a high level security device can be produced using this system.

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“…An attractor is called rare if it has relatively small basin of attraction volume, while the basin of the hidden attractor does not intersect with the neighborhood of any fixed point [4]. Recently, many new examples of hidden attractors have been discovered [5][6][7][8][9] and this topic is gaining increasing interest. One of the challenging problems is to detect and localize rare and hidden attractors in multi-stable systems.…”

Section: Introductionmentioning

confidence: 99%

Experimental investigation of perpetual points in mechanical systems

Brzeski

Virgin

2017

Nonlinear Dyn

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In dissipative dynamical systems, equilibrium (stationary) points have a dominant organizing effect on transient motion in phase space, especially in nonlinear systems. These time-independent solutions are readily defined in the context of ordinary differential equations, that is, they occur when all the time derivatives are simultaneously zero. However, there has been some recent interest in perpetual points: points at which the higher time derivatives are zero, but not necessarily the first. Previous work has focused on analytic work (including simulation) and some experimental studies of electric circuits. This paper focuses attention on the occurrence of these points in a simple mechanical system, including experimental verification. Thus, points of zero acceleration can be found in which the corresponding velocity is a maximum or minimum, but not zero. Specifically, the rigid-arm pendulum is used to generate data for which acceleration (and its derivative) can be evaluated. In this paper an experimental (mechanical) setup is described, specifically designed to investigate perpetual points, including a description of the data analysis approaches developed to identify their location.

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

Cited by 110 publications

References 28 publications

On differences and similarities in the analysis of Lorenz, Chen, and Lu systems

On differences and similarities in the analysis of Lorenz, Chen, and Lu systems

Analysis of a No Equilibrium Linear Resistive-Capacitive-Inductance Shunted Junction Model, Dynamics, Synchronization, and Application to Digital Cryptography in Its Fractional-Order Form

Experimental investigation of perpetual points in mechanical systems

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