Constructing Chaotic System With Multiple Coexisting Attractors

Lai, Qiang; Chen, Chaoyang; Zhao, Xiao‐Wen; Kengne, Jacques; Volos, Christos

doi:10.1109/access.2019.2900367

Cited by 64 publications

(27 citation statements)

References 33 publications

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“…The parameter R is the resistance value in the simple arc circuits shown in Fig.2, whose mathematical model is given in Appendix B (see (2)). Thus, for any fixed value of R in the interval [5,25] we obtain the corresponding K value from the interval [0, 1]. The values of K close to 0 indicate periodic time series, while those close to 1 are obtained for chaotic ones.…”

Section: The 0-1 Test For Chaos With One Varying Parameter a Prementioning

confidence: 99%

Using the 0-1 Test for Chaos in Nonlinear Continuous Systems With Two Varying Parameters: Parallel Computations

2019

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Two-parameter diagrams obtained through the 0-1 test of chaos for nonlinear oscillatory continuous systems are presented in this paper. The diagrams are the results of a parallel approach to tackle enormous memory and computational time requirements due to the known oversampling problem associated with the use of the 0-1 test for chaos in continuous systems. Our rectangular diagrams with black-and-white shades of gray levels correspond to the numbers between 0 and 1 obtained as the result of the 0-1 test for chaos. A comparison between the two-parameter diagrams for the 0-1 test with the color bifurcation diagrams for oscillatory systems obtained from another method (period-n identification) is also considered. Illustrative examples are based on both the well-known Lorenz model and a model describing two equivalent electric arc circuits. INDEX TERMS The 0-1 test of chaos, two-parameter bifurcation diagrams, oscillatory continuous dynamics, parallel computation, electric arc circuits.

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Section: The 0-1 Test For Chaos With One Varying Parameter a Prementioning

confidence: 99%

Using the 0-1 Test for Chaos in Nonlinear Continuous Systems With Two Varying Parameters: Parallel Computations

2019

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“…A multistable system is a system with various coexisting stable states (chaotic, point, and periodic state) under the same system parameters, with different initial conditions. In recent years, the phenomenon of multistability phenomenon has been reported in many nonlinear dynamic systems [13,[36][37][38][39][40][41][42][43][44][45][46].…”

Section: Multistabilitymentioning

confidence: 99%

Coexistence of Multiple Points, Limit Cycles, and Strange Attractors in a Simple Autonomous Hyperjerk Circuit with Hyperbolic Sine Function

et al. 2020

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In this contribution, a new elegant hyperjerk system with three equilibria and hyperbolic sine nonlinearity is investigated. In contrast to other models of hyperjerk systems where either hidden or self-excited attractors are obtained, the case reported in this work represents a unique one which displays the coexistence of self-excited chaotic attractors and stable fixed points. The dynamic properties of the new system are explored in terms of equilibrium point analyses, symmetry and dissipation, and existence of attractors as well. Common analysis tools (i.e., bifurcation diagram, Lyapunov exponents, and phase portraits) are used to highlight some important phenomena such as period-doubling bifurcation, chaos, periodic windows, and symmetric restoring crises. More interestingly, the system under consideration shows the coexistence of several types of stable states, including the coexistence of two, three, four, six, eight, and ten coexisting attractors. In addition, the system is shown to display antimonotonicity and offset boosting. Laboratory experimental measurements show a very good coherence with the theoretical predictions.

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“…Because of the multi-stable line or plane equilibrium aroused by memristors, initial condition-relied extreme multistability with complex bifurcation routes was emerged in memristor-based chaotic circuits and systems [21]. By contrast, due to the infinitely many isolated equilibria caused by periodic nonlinearities, initial condition-boosting infinite attractors were found in some periodic function-based offset-boostable dynamical systems [22], [23]. Furthermore, by introducing a memristor with periodic memductance into an offset-boostable linear system, a new memristive chaotic system was presented [24], [25], from which extreme multistability with the initial condition-relied bifurcation route to chaos and boosting bifurcation dynamics were disclosed.…”

Section: Introductionmentioning

confidence: 99%

Extreme Multistability in Simple Area-Preserving Map

Bao

Zhu

et al. 2020

IEEE Access

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Initial condition-relied extreme multistability has been recently found in many continuous dynamical systems. However, such a specific phenomenon has not yet been discovered in a discrete iterative map. To investigate this phenomenon, this paper proposes a two-dimensional conservative map only with one sine nonlinearity. The proposed simple discrete map is area-preserving in the phase space and displays the coexistence of infinite chaotic and quasi-periodic orbits caused by infinite fixed points. Multiple numerical results indicate that the area-preserving chaotic and quasi-periodic orbits have the initial condition-relied quasi-periodic route to chaos and initial condition-boosting bifurcation dynamics, which allow the simple area-preserving map to emerge the complex phenomenon of extreme multistability. Furthermore, a microcontroller-based hardware platform is developed to implement the initial conditionboosting chaotic signals.

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Constructing Chaotic System With Multiple Coexisting Attractors

Cited by 64 publications

References 33 publications

Using the 0-1 Test for Chaos in Nonlinear Continuous Systems With Two Varying Parameters: Parallel Computations

Using the 0-1 Test for Chaos in Nonlinear Continuous Systems With Two Varying Parameters: Parallel Computations

Coexistence of Multiple Points, Limit Cycles, and Strange Attractors in a Simple Autonomous Hyperjerk Circuit with Hyperbolic Sine Function

Extreme Multistability in Simple Area-Preserving Map

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