A family of conservative chaotic systems with cyclic symmetry

A novel three-dimensional conservative system without an equilibrium point is constructed by replacing the square term x2+y2 in the Vaidyanathan - Sundarapandian oscillator with a simple absolute value term |x|. The system is analyzed in detail by using time-domain waveform plots, bifurcation plots, Lyapunov exponent spectra, spectral entropy (SE), and C0 complexity. It is found that the system has rich dynamic behaviors: multiple phase trajectories can be tuned by only one parameter and multistability due to initial value sensitivity. The system shows that it can yield eight heterogeneous trajectories coexistent at different initial conditions, including periodic, quasi-periodic, and chaotic states. Additionally, the transient behavior was also observed. Finally, the experimental circuit was implemented, verifying both the physical realizability and the rich dynamic behaviors of the proposed system. With high complexity and sensitivity of parameter and initial condition, the proposed system is useful in image encryption and secure communication.

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“…Since, the new system is conservative [32,33]. Rearranging LE i (i = 1, 2, 3) from large to small, and finding a integer j that satisfies …”

Section: Basic Dynamic Propertiesmentioning

confidence: 99%

“…Kaplan York dimension (D KY ) can be obtained as equation (5) according to D KY calculation method [32]. Assuming, the system can be rewritten as…”

Section: Basic Dynamic Propertiesmentioning

confidence: 99%

A new 3D hidden conservative chaotic system with multistability and its circuit implementation

Wang

Tian

et al. 2023

Phys. Scr.

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“…Rajagopal et al, proposed a few years earlier a chaotic system with cyclic symmetry where the shown multistability of three attractors [14]. Gugapriya et al proposed a family of circulant systems with various dynamical properties of the circulant systems, such as, existence of periodic limit cycle, torus-2 and chaotic oscillations with field programmable gate array to show the hardware reliability [15]. Kengne et al, in 2021 designed a three dimentional labyrinth system using piecewise quadratic nonlinearity, the model generate a coexistence of up to twelve attractors between chaos and periodic attractors, with analog design [16].…”

Section: Introductionmentioning

confidence: 99%

Adjustable symmetry on the dynamics of a new chaotic system with cyclic symmetry: theoretical study, control and experimental investigation

Boya

Kengne

2023

Phys. Scr.

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In this study, we propose a new chaotic autonomous system with adjustable cyclic and central symmetries. The new 3D system, with rich dynamics, is constructed based on the Thomas model. A detailed study of the nonlinear dynamics arising from the model allows us to reveal complex behaviors of different phenomena such as hysteresis dynamics, offset boosting, total amplitude control, and coexistence of several homogeneous and heterogeneous attractors in both regimes (symmetric and asymmetric). The control of multistability of the new cyclic system is studied by following the technique of linear augmentation. An analog electronic version of the model is designed and then simulated using the Pspice software. Moreover, a physical implementation using the Arduino microcontroller makes it possible to validate the results of the theoretical analysis.

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“…Subsequently, in 1997 and 1999, Sprott and Thomas respectively gave the jerk conservative chaotic system and the conservative chaotic system with sine function [7][8] . Subsequent research on conservative chaotic characteristics is gradually attracting researchers' attention [9][10][11][12][13][14][15] .…”

Section: Introductionmentioning

confidence: 99%

Multi-stability and FPGA Implementation of a Conservative Chaotic System

Song¹

2022

Proceedings of International Conference on Artificial Life and Robotics

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The paper first studies the reason why a three-dimensional volume conservative chaotic system proposed by Vaidyanathan and Volos can generate chaos by analyzing mechanics and energy. Then, based on numerical methods including balance characteristics, Lyapunov exponents, bifurcation diagrams, phase trajectories and so on, multi-stability of the three-dimensional volume conservative chaotic system are discovered. In addition, the threedimensional volume conservative chaotic system is realized by using FPGA, and all the results from FPGA implementation are consistent with those from numerical analysis.

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A family of conservative chaotic systems with cyclic symmetry

Cited by 25 publications

References 41 publications

A new 3D hidden conservative chaotic system with multistability and its circuit implementation

A new 3D hidden conservative chaotic system with multistability and its circuit implementation

Adjustable symmetry on the dynamics of a new chaotic system with cyclic symmetry: theoretical study, control and experimental investigation

Multi-stability and FPGA Implementation of a Conservative Chaotic System

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