Energy analysis of Sprott-A system and generation of a new Hamiltonian conservative chaotic system with coexisting hidden attractors

Conservative chaos systems have been investigated owing to their special advantages. Taking symmetry as a starting point, this study proposes a class of five-dimensional(5D) conservative hyperchaotic systems by constructing a generalized Hamiltonian conservative system. The proposed systems can have different types of coordinate-transformation and time-reversal symmetries. Also, the constructed systems are conservative in both volume and energy. The constructed systems are analyzed, and their conservative and chaotic properties are verified by relevant analysis methods, including the equilibrium points, phase diagram, Lyapunov exponent diagram, bifurcation diagram, and two-parameter Lyapunov exponent diagram. An interesting phenomenon, namely, that the proposed systems have multistable features when the initial values are changed, is observed. Furthermore, a detailed multistable characteristic analysis of two systems is performed, and it is found that the two systems have different numbers of coexisting orbits under the same energy. And, this type of system can also exhibit the coexistence of infinite orbits of different energies. Finally, the National Institute of Standards and Technology tests confirmed that the proposed systems can produce sequences with strong pseudo-randomness.

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“…According to (2), first, the Hamiltonian function [43] of a class of 5D conservative systems is assumed by equation (3).…”

Section: Construction Processmentioning

confidence: 99%

A class of 5D Hamiltonian conservative hyperchaotic systems with symmetry and multistability

et al. 2022

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“…Theoretically, the phase space volume of dissipative chaos is collapsed. [6][7][8] Different from the dissipative chaos, each trajectory in phase space of conservative chaos does not approach the equilibrium points finally with passage of time, which indicates there is no attractor in conservative chaos. [9] Moreover, there are some interesting discoveries on conservative chaos.…”

Section: Introductionmentioning

confidence: 99%

A multi-directional controllable multi-scroll conservative chaos generator: Modelling, analysis, and FPGA implementation*

Dong¹,

Li²,

Du³

2021

Chinese Phys. B

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Combing with the generalized Hamiltonian system theory, by introducing a special form of sinusoidal function, a class of n-dimensional (n = 1,2,3) controllable multi-scroll conservative chaos with complicated dynamics is constructed. The dynamics characteristics including bifurcation behavior and coexistence of the system are analyzed in detail, the latter reveals abundant coexisting flows. Furthermore, the proposed system passes the NIST tests and has been implemented physically by FPGA. Compared to the multi-scroll dissipative chaos, the experimental portraits of the proposed system show better ergodicity, which have potential application value in secure communication and image encryption.

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“…Positive LEs indicate a non-conservative system, while zerosum LEs suggest a conservative system. [20][21][22][23][24][25] Moreover, analyzing the dynamic evolution characteristics is another crucial aspect, which can be achieved through an improved method. In this paper, the thin plate oscillator is transformed into a three-dimensional (3D) autonomous system.…”

Section: Introductionmentioning

confidence: 99%

Dynamic modelling and chaos control for a thin plate oscillator using Bubnov–Galerkin integral method

Jiao

Wang

Jin³

et al. 2023

Chinese Phys. B

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The utilization of thin plate systems based on acoustic vibration holds significant importance in micro-nano manipulation and the exploration of nonlinear science. This paper focuses on the analysis of an actual thin plate system driven by acoustic wave signals. By combining the mechanical analysis of thin plate microelements with the Bubnov-Galerkin integral method, the governing equation for the forced vibration of a square thin plate is derived. Notably, the reaction force of the thin plate vibration system is defined as $f = \alpha \left| w \right|$, resembling Hooke's law. The energy function and energy level curve of the system are also analyzed. Subsequently, the amplitude-frequency response function of the thin plate oscillator is solved using the harmonic balance method. Through numerical simulations, the amplitude-frequency curves are analyzed for different vibration modes under the influence of various parameters. Furthermore, the paper demonstrates the occurrence of conservative chaotic motions in the thin plate oscillator using theoretical and numerical methods. Dynamics maps illustrating the system's states are presented to reveal the evolution laws of the system. By exploring the effects of force fields and system energy, the underlying mechanism of chaos is interpreted. Additionally, the phenomenon of chaos in the oscillator can be controlled through the method of velocity and displacement states feedback, which holds significance for engineering applications.

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Energy analysis of Sprott-A system and generation of a new Hamiltonian conservative chaotic system with coexisting hidden attractors

Cited by 37 publications

References 31 publications

A class of 5D Hamiltonian conservative hyperchaotic systems with symmetry and multistability

A class of 5D Hamiltonian conservative hyperchaotic systems with symmetry and multistability

A multi-directional controllable multi-scroll conservative chaos generator: Modelling, analysis, and FPGA implementation*

Dynamic modelling and chaos control for a thin plate oscillator using Bubnov–Galerkin integral method

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