Bursting patterns with complex structures in a parametrically and externally excited Jerk circuit system

Wei, Mengke; Han, Xiujing; Ma, Xindong; Zou, Yong; Bi, Qinsheng

doi:10.1140/epjs/s11734-022-00427-7

Cited by 9 publications

(4 citation statements)

References 46 publications

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“…with K > 0 and α z = 2E x + 2E y + E z exponentially stabilizes the new chaotic jerk systems (18) and ( 19) for all initial states in R 3 .…”

Section: Complete Synchronization Of the New Jerk Systems Using Backs...mentioning

confidence: 96%

“…Rajagopal et al [14] proposed a new dissipative chaotic jerk system with two quadratic nonlinearities, discussed its dynamic properties, and provided a circuit realization of the new jerk system. Chaotic jerk systems have applications in many areas, such as oscillators [3,15], microcontrollers [16], circuits [17,18], memristors [19,20], encryption [21], etc.…”

Section: Introductionmentioning

confidence: 99%

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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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“…with K > 0 and α z = 2E x + 2E y + E z exponentially stabilizes the new chaotic jerk systems (18) and ( 19) for all initial states in R 3 .…”

Section: Complete Synchronization Of the New Jerk Systems Using Backs...mentioning

confidence: 96%

Section: Introductionmentioning

confidence: 99%

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

et al. 2023

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“…Wen et al [ 22 ] reported several compound bursting patterns in a memristor-based Shimizu–Morioka system. Wei et al reported compound bursting dynamics in a parametrically and externally excited quintic nonlinear Rayleigh–Duffing system [ 23 ] and Jerk circuit system [ 24 ]. Yu et al [ 25 ] performed analytical investigations on symmetric jump phenomena reflecting multi-timescale dynamics in a nonlinear shape memory alloy oscillator with parametric and external cosinoidal excitations.…”

Section: Introductionmentioning

confidence: 99%

Improving the Performance of a Post-Buckled Beam Harvester under Combined External and Parametrical Slow Excitations

2023

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In this paper, we consider novel bursting energy harvesting under combined external and parametrical slow excitations, and a harvester is realized by employing an externally and parametrically excited post-buckled beam. Based on the method of fast–slow dynamics analysis, multiple-frequency oscillation, with two slow commensurate excitation frequencies, is used to observe complex bursting patterns, the behaviors of the bursting response are presented, and some novel one-parameter bifurcation patterns are observed. Furthermore, the bursting harvesting performances of the single and the two slow commensurate excitation frequencies are compared, and it was found that the two slow commensurate excitation frequencies can be used to improve the harvesting voltage.

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“…Recent studies on nonlinear dynamical systems with different nonlinear functions exhibiting chaos in their dynamics has led to several intriguing and surprising results. Most of the chaotic circuits studied in the literature are of autonomous in nature and are represented by a set of three coupled first-order differential equations [5][6][7][8][9] or an autonomous third or higher order ordinary differential equation system namely, the Jerk system [10][11][12][13][14], which is of great use in understanding the emergence of complex structures in non-autonomous chaotic systems [15] and memristor based systems [16]. Though generic third order autonomous chaotic circuit models were well studied the dynamical features associated with generic second-order non-autonomous circuit systems are limited to fewer systems [17][18][19][20][21] and has to be studied extensively.…”

Section: Introductionmentioning

confidence: 99%

Energy computation and multistability in a class of second-order chaotic systems with simple nonlinearities: numerical, experimental and analytical results

Sivaganesh¹,

Srinivasan²,

Fozin³

et al. 2022

Phys. Scr.

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The present work is aimed at the design, implementation and analysis of generic new second-order non-autonomous chaotic systems with simple nonlinear functions that have algebraically simple representations in mathematical form. These systems involve simple second-order non-autonomous ordinary differential equations with different simple nonlinearities like $G(x) (= x^2, |x|, max(x)$ and $min(x))$. The present study deals with numerical simulation, experimental analog circuit simulation results to demonstrate the ordered and chaotic phenomena being exhibited by these systems. Of most interest the striking phenomenon of multistability is uncovered for certain nonlinearities. Coexisting attractors are harnessed through the offset boosting approach. Also, the Hamilton energy is established through the Helmholtz theorem. It is found that both methods can be exploited as a non-bifurcation approach in characterizing multistability in the model. Further, analytical solutions developed for systems with certain nonlinearities are presented and the chaotic behavior of the systems studied using the solutions validating the numerical and experimental results are reported.

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Bursting patterns with complex structures in a parametrically and externally excited Jerk circuit system

Cited by 9 publications

References 46 publications

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

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

Improving the Performance of a Post-Buckled Beam Harvester under Combined External and Parametrical Slow Excitations

Energy computation and multistability in a class of second-order chaotic systems with simple nonlinearities: numerical, experimental and analytical results

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