Unstable periodic orbits analysis in the generalized Lorenz-type system

Dong, Chengwei; Liu, Huihui; Li, Hantao

doi:10.1088/1742-5468/ab9e5f

Cited by 15 publications

(7 citation statements)

References 37 publications

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“…This method is widely recognized for its reliability and effectiveness in capturing the complex dynamical behavior of unsteady periodic orbits in hyperchaotic systems. The basic concept in physics is to begin with a first assumption of the periodic orbit and progressively refine it through an iterative process to obtain the true cycle [53]. The following partial differential equation dominates the evolution of the cycle guess L(τ) to the real periodic orbit p [52]:…”

Section: The Variational Methods Is a Technique Utilized In Computingmentioning

confidence: 99%

A new four-dimensional hyperchaotic system with hidden attractors and multistablity

Yang,

Dong,

Sui

2023

Phys. Scr.

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This paper proposes a novel 4D hyperchaotic system with hidden attractors and coexisting attractors, which have no equilibrium points. The dynamic behavior of the system and five groups of coexisting attractors are analyzed by applying phase space diagrams, bifurcation diagrams and the Lyapunov exponents spectrum. Additionally, the system’s stable limit cycles and unstable periodic orbits were calculated through the variational method and then encoded using symbolic dynamics. The numerical results were verified via a circuit simulation, confirming the realizability of the novel hyperchaotic system in hardware facilities. Finally, we applied the active synchronization control method to the new system with remarkable results.

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Section: The Variational Methods Is a Technique Utilized In Computingmentioning

confidence: 99%

A new four-dimensional hyperchaotic system with hidden attractors and multistablity

Yang,

Dong,

Sui

2023

Phys. Scr.

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“…In this case, it is more convenient and effective to establish symbolic dynamics based on the topological structure of orbits [49][50][51], such as the number of rotations between periodic orbits and equilibrium points. Furthermore, continuous deformation of the cycles with the change of parameters can also be explored by the variational method, which can help us judge the parameter values when the number of cycles or stability changes, and thus confirm the corresponding bifurcation phenomenon [52][53][54].…”

Section: One-dimensional Symbolic Dynamics For Unstable Cycles Embedd...mentioning

confidence: 99%

Dynamic Analysis of a Novel 3D Chaotic System with Hidden and Coexisting Attractors: Offset Boosting, Synchronization, and Circuit Realization

Dong

2022

Fractal Fract

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To further understand the dynamical characteristics of chaotic systems with a hidden attractor and coexisting attractors, we investigated the fundamental dynamics of a novel three-dimensional (3D) chaotic system derived by adding a simple constant term to the Yang–Chen system, which includes the bifurcation diagram, Lyapunov exponents spectrum, and basin of attraction, under different parameters. In addition, an offset boosting control method is presented to the state variable, and a numerical simulation of the system is also presented. Furthermore, the unstable cycles embedded in the hidden chaotic attractors are extracted in detail, which shows the effectiveness of the variational method and 1D symbolic dynamics. Finally, the adaptive synchronization of the novel system is successfully designed, and a circuit simulation is implemented to illustrate the flexibility and validity of the numerical results. Theoretical analysis and simulation results indicate that the new system has complex dynamical properties and can be used to facilitate engineering applications.

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“…The banded lower-upper decomposition method can be used to accelerate the computation, and the Woodbury formula can be employed to deal with periodic and boundary terms [54]. The variational method can be effectively used to calculate the unstable periodic orbits of various chaotic systems [55][56][57]. In the next section, we utilize the variational method to locate the unstable periodic orbits in the hidden chaotic attractor of system (2).…”

Section: Andmentioning

confidence: 99%

A New Variable-Boostable 3D Chaotic System with Hidden and Coexisting Attractors: Dynamical Analysis, Periodic Orbit Coding, Circuit Simulation, and Synchronization

Wang

Dong

2022

Fractal Fract

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The study of hidden attractors plays a very important role in the engineering applications of nonlinear dynamical systems. In this paper, a new three-dimensional (3D) chaotic system is proposed in which hidden attractors and self-excited attractors appear as the parameters change. Meanwhile, asymmetric coexisting attractors are also found as a result of the system symmetry. The complex dynamical behaviors of the proposed system were investigated using various tools, including time-series diagrams, Poincaré first return maps, bifurcation diagrams, and basins of attraction. Moreover, the unstable periodic orbits within a topological length of 3 in the hidden chaotic attractor were calculated systematically by the variational method, which required six letters to establish suitable symbolic dynamics. Furthermore, the practicality of the hidden attractor chaotic system was verified by circuit simulations. Finally, offset boosting control and adaptive synchronization were used to investigate the utility of the proposed chaotic system in engineering applications.

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Unstable periodic orbits analysis in the generalized Lorenz-type system

Cited by 15 publications

References 37 publications

A new four-dimensional hyperchaotic system with hidden attractors and multistablity

A new four-dimensional hyperchaotic system with hidden attractors and multistablity

Dynamic Analysis of a Novel 3D Chaotic System with Hidden and Coexisting Attractors: Offset Boosting, Synchronization, and Circuit Realization

A New Variable-Boostable 3D Chaotic System with Hidden and Coexisting Attractors: Dynamical Analysis, Periodic Orbit Coding, Circuit Simulation, and Synchronization

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