Spatiotemporal chaos in a conservative Duffing-type system

Reis, Eduardo Villela Machado dos; Savi, Marcelo A.

doi:10.1016/j.chaos.2022.112776

Cited by 2 publications

(3 citation statements)

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Section: Introductionmentioning

confidence: 99%

“…Mechanical dynamical systems have several applications in chaos theory [1][2][3][4]. For instance, Reis and Savi [1] studied quasi-periodic and spatiotemporal chaotic responses in a conservative Duffing-type mechanical system with cubic nonlinearity. Using Lyapunov stability theory and power spectrum analysis, Cai et al [2] studied the periodic motion and chaos in the dynamics of a van der Pol (VDP) oscillator.…”

Section: Introductionmentioning

confidence: 99%

“…Regarding 3-D chaotic jerk systems, it is well-known that, in classical mechanics, an autonomous jerk differential equation has the general form given in (1), where "jerk" refers to the third-order derivative .…”

Section: Introductionmentioning

confidence: 99%

See 2 more Smart Citations

FPGA-Based Implementation of a New 3-D Multistable Chaotic Jerk System with Two Unstable Balance Points

et al. 2023

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Mechanical jerk systems have applications in several areas, such as oscillators, microcontrollers, circuits, memristors, encryption, etc. This research manuscript reports a new 3-D chaotic jerk system with two unstable balance points. It is shown that the proposed mechanical jerk system exhibits multistability with coexisting chaotic attractors for the same set of system constants but for different initial states. A bifurcation analysis of the proposed mechanical jerk system is presented to highlight the special properties of the system with respect to the variation of system constants. A field-programmable gate array (FPGA) implementation of the proposed mechanical jerk system is given by synthesizing the discrete equations that are obtained by applying one-step numerical methods. The hardware resources are reduced by performing pipeline operations, and, finally, the paper concludes that the experimental results of the proposed mechanical jerk system using FPGA-based design show good agreement with the MATLAB simulations of the same system.

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