2015
DOI: 10.1007/s11071-015-2364-y
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Dynamical analysis of a simple autonomous jerk system with multiple attractors

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Cited by 226 publications
(122 citation statements)
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“…It is worth noting that the stability depends on the memristor initial condition in a memristive dynamical circuit, leading to the occurrence of coexisting multiple attractors [9,13]. The coexistence of different kinds of attractors, called multistability, reveals a rich diversity of stable states in nonlinear dynamical systems [12,[24][25][26][27][28][29][30][31][32] and makes the system offer great flexibility, which can be used for image processing or taken as an additional source of randomness used for many information engineering applications [32][33][34][35][36][37]. Therefore, it is very attractive to seek for a simple memristive chaotic circuit that has the striking dynamical behavior of coexisting multiple attractors.…”
Section: Introductionmentioning
confidence: 99%
“…It is worth noting that the stability depends on the memristor initial condition in a memristive dynamical circuit, leading to the occurrence of coexisting multiple attractors [9,13]. The coexistence of different kinds of attractors, called multistability, reveals a rich diversity of stable states in nonlinear dynamical systems [12,[24][25][26][27][28][29][30][31][32] and makes the system offer great flexibility, which can be used for image processing or taken as an additional source of randomness used for many information engineering applications [32][33][34][35][36][37]. Therefore, it is very attractive to seek for a simple memristive chaotic circuit that has the striking dynamical behavior of coexisting multiple attractors.…”
Section: Introductionmentioning
confidence: 99%
“…It should be mentioned that just like the ideal flux/ voltage-controlled memristor-based chaotic circuits [4][5][6][7][8][9], the proposed memristor-based canonical Chua's circuit has a line equilibrium point with complicated stability distributions already depicted in Figures 2-4, whereas most of conventionally nonlinear dynamical systems with no equilibrium point [10], with only several determined equilibrium points [15][16][17][18][19][20][21], or with curves of equilibrium points [41][42][43] have relatively simple stability distributions with some divinable nonlinear dynamical behaviors.…”
Section: Coexisting Infinitely Many Attractors With Reference To Thementioning
confidence: 98%
“…Generally, multistability is confirmed in hardware experiments by randomly switching on and off experimental circuit supplies [9,[15][16][17][18][19][20][21] or by MATLAB numerical or PSPICE/PSIM circuit simulations [4][5][6][7][8][22][23][24][25][26][27][28]. Consequently, to direct the nonlinear dynamical circuit or system to a desired oscillating mode, an effective control approach should be proposed [12].…”
Section: Introductionmentioning
confidence: 99%
“…In that paper, they established a novel memristive hyperchaotic system with no equilibrium based on the newly proposed circuit realization scheme and investigated the phenomenon of extreme multistability with hidden oscillation that reveals the coexistence of infinitely many hidden attractors in the proposed memristive hyperchaotic system. Kengne et al [13] presented the basic dynamical properties of a simple autonomous jerk system including equilibria and stability, phase portraits, frequency spectra, bifurcation diagrams, and Lyapunov exponent plots. It is shown that the onset of chaos is achieved via the classical period-doubling and symmetryrestoring crisis scenarios.…”
Section: Complexitymentioning
confidence: 99%