Transient behaviors and equilibria-analysis-based boundary crisis analysis in a smooth 4D dynamical system

Yu, Haohui; Du, Shengzhi; Dong, Enzeng; Tong, Jigang

doi:10.1016/j.chaos.2022.112220

Cited by 5 publications

(2 citation statements)

References 41 publications

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“…For example, Tang et al [27] found a new kind of topological horseshoe in the phase space of a hyperchaotic system constructed by introducing memory element. Yu et al [28] addressed the transient behavior mechanism analysis of a new 4D chaotic system. The third line switches to systems with distinctive features.…”

Section: Related Workmentioning

confidence: 99%

Dynamic Analysis and FPGA Implementation of a New Linear Memristor-Based Hyperchaotic System with Strong Complexity

Chen,

Yu,

Luo

et al. 2024

Mathematics

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Chaotic or hyperchaotic systems have a significant role in engineering applications such as cryptography and secure communication, serving as primary signal generators. To ensure stronger complexity, memristors with sufficient nonlinearity are commonly incorporated into the system, suffering a limitation on the physical implementation. In this paper, we propose a new four-dimensional (4D) hyperchaotic system based on the linear memristor which is the most straightforward to implement physically. Through numerical studies, we initially demonstrate that the proposed system exhibits robust hyperchaotic behaviors under typical parameter conditions. Subsequently, we theoretically prove the existence of solid hyperchaos by combining the topological horseshoe theory with computer-assisted research. Finally, we present the realization of the proposed hyperchaotic system using an FPGA platform. This proposed system possesses two key properties. Firstly, this work suggests that the simplest memristor can also induce strong nonlinear behaviors, offering a new perspective for constructing memristive systems. Secondly, compared to existing systems, our system not only has the largest Kaplan-Yorke dimension, but also has clear advantages in areas related to engineering applications, such as the parameter range and signal bandwidth, indicating promising potential in engineering applications.

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Section: Related Workmentioning

confidence: 99%

Dynamic Analysis and FPGA Implementation of a New Linear Memristor-Based Hyperchaotic System with Strong Complexity

Chen,

Yu,

Luo

et al. 2024

Mathematics

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“…Transient phenomena are commonly found in nature. The transient behavior of linear systems or transient behavior of some weakly nonlinear systems can be predicted, but transient behavior of chaotic systems is basically unpredictable [48,72]. The transient behavior is highly uncertain because of its generation time and duration, which makes the conditions necessary for transient generation an essential issue in dynamic analysis [73].…”

Section: Transient Chaosmentioning

confidence: 99%

Finite-time synchronization of fractional-order chaotic system based on hidden attractors

Yan,

Zhang,

Jiang

et al. 2023

Phys. Scr.

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A new 3D fractional-order chaotic system is obtained by improving the Sprott-A system and introducing the definition of fractional calculus to it. Then the new system is certified to be chaotic by studying and analyzing the phase diagram, Lyapunov exponents, and smaller alignment index tests. Then the analysis of equilibrium points finds that the new system has virtually no equilibrium points and hidden attractors. The new system is dynamically analyzed by bifurcation diagram, time-domain waveform and complexity, it is indicated that the system is susceptible to initial conditions, and with the changes of different parameters the system produced different scroll types of attractors. In addition, to verify the feasibility of the system, a simulation circuit design based on Multisim is therefore carried out. Finally, the finite-time synchronization of the fractional-order system is successfully achieved by taking advantage of the high security of the hidden attractors.

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Complex dynamics of the passive biped robot with flat feet: Gait bifurcation, intermittency and crisis

Liu,

Gao,

Rao

et al. 2024

Mechanism and Machine Theory

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Transient behaviors and equilibria-analysis-based boundary crisis analysis in a smooth 4D dynamical system

Cited by 5 publications

References 41 publications

Dynamic Analysis and FPGA Implementation of a New Linear Memristor-Based Hyperchaotic System with Strong Complexity

Dynamic Analysis and FPGA Implementation of a New Linear Memristor-Based Hyperchaotic System with Strong Complexity

Finite-time synchronization of fractional-order chaotic system based on hidden attractors

Complex dynamics of the passive biped robot with flat feet: Gait bifurcation, intermittency and crisis

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