Topological classification of periodic orbits in the Yang-Chen system

Dong, Chengwei

doi:10.1209/0295-5075/123/20005

Cited by 9 publications

(3 citation statements)

References 20 publications

(25 reference statements)

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“…This method is not only suitable for the determination of periodic orbits but also for the homoclinic and heteroclinic orbits [32]. In the previous work, the periodic orbits in various chaotic systems were calculated efficiently using the variational method [33][34][35][36], which illustrates the practicability of this method in the GLTS.…”

Section: Numerical Implementationmentioning

confidence: 89%

Unstable periodic orbits analysis in the generalized Lorenz-type system

Dong¹,

Liu²,

Li³

2020

J. Stat. Mech.

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In this paper, we investigated the unstable periodic orbits of a nonlinear chaotic generalized Lorenz-type system. By means of the variational method, appropriate symbolic dynamics are put forward, and the homotopy evolution approach, which can be used in the initialization of the cycle search, is introduced. Fourteen short unstable periodic orbits with different topological lengths, under specific parameter values, are calculated. We also explored the continuous deformation for part of the orbits while changing the parameter values, which provides a new approach to observe various bifurcations. The scale transformation of the generalized Lorenz-type system leads to a single parameter system known as the diffusionless Lorenz equations. By systematically calculating the periodic orbits in the diffusionless Lorenz equations, our research shows the efficiency of this topological classification method for the periodic solutions in the variants of a classical Lorenz system.

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Section: Numerical Implementationmentioning

confidence: 89%

Unstable periodic orbits analysis in the generalized Lorenz-type system

Dong¹,

Liu²,

Li³

2020

J. Stat. Mech.

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“…the system is dissipative under the condition −2z < 0, and converges at the exponential e −2 z . As t approaches infinity, every volume element containing the system trace exponentially shrinks to 0, indicating that the system can produce bounded attractors [22].…”

Section: The New 4d Hyperchaotic Systemmentioning

confidence: 99%

Dynamics, periodic orbits of a novel four-dimensional hyperchaotic system with hidden attractors

Wei,

Dong

2024

Phys. Scr.

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In recent years, the investigation of systems featuring hidden attractors and coexisting attractors has garnered significant attention. This paper presents a novel four-dimensional (4D) hyperchaotic system devoid of equilibrium points, achieved by formulating an equation without a solution or constructing a system without fixed points. Due to the complex shape of this attractor, a novel coding method is utilized to establish symbol dynamics using eight letters. The proposed system exhibits highly intricate dynamics, including variations in topological structure with alterations in system parameters, as well as an exploration and discussion of four types of coexisting attractors. Our extensive practice has led us to propose a new conjecture: hyperchaotic systems with parameters close to the bifurcation point frequently display multistable states. Furthermore, the unstable periodic orbits with different topological lengths in the hidden hyperchaotic attractor are calculated systematically using the variational method. Additionally, the DSP circuit implementation is employed to validate the numerical simulation results for this new 4D system. Finally, adaptive synchronization is successfully realized within the system, thereby confirming its feasibility.

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“…In addition to being densely embedded around strange attractors [26], the dynamical average values of chaotic systems can be calculated by cycle expansions [27,28], which express long-time averages over chaotic orbits in terms of averages over periodic orbits in a hierarchical manner. If the system is hyperbolic, long periodic orbits are shadowed by short ones, and cycle expansions converge rapidly with increased cycle length [29,30].…”

Section: Introductionmentioning

confidence: 99%

Symbolic Encoding of Periodic Orbits and Chaos in the Rucklidge System

Dong

Jia

et al. 2021

Complexity

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To describe and analyze the unstable periodic orbits of the Rucklidge system, a so-called symbolic encoding method is introduced, which has been proven to be an efficient tool to explore the topological properties concealed in these periodic orbits. In this work, the unstable periodic orbits up to a certain topological length in the Rucklidge system are systematically investigated via a proposed variational method. The dynamics in the Rucklidge system are explored by using phase portrait analysis, Lyapunov exponents, and Poincaré first return maps. Symbolic encodings of the periodic orbits with two and four letters based on the trajectory topology in the phase space are implemented under two sets of parameter values. Meanwhile, the bifurcations of the periodic orbits are explored, significantly improving the understanding of the dynamics of the Rucklidge system. The multiple-letter symbolic encoding method could also be applicable to other nonlinear dynamical systems.

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Topological classification of periodic orbits in the Yang-Chen system

Cited by 9 publications

References 20 publications

Unstable periodic orbits analysis in the generalized Lorenz-type system

Unstable periodic orbits analysis in the generalized Lorenz-type system

Dynamics, periodic orbits of a novel four-dimensional hyperchaotic system with hidden attractors

Symbolic Encoding of Periodic Orbits and Chaos in the Rucklidge System

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