Self-similar structures in a 2D parameter-space of an inductorless Chua's circuit

Albuquerque, Holokx A.; Rubinger, R. M.; Rech, Paulo C.

doi:10.1016/j.physleta.2008.05.036

Cited by 77 publications

(44 citation statements)

References 13 publications

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“…The above-mentioned models in these literatures are parameter spaces of the discrete system. Similar results are observed in [5][6][7], they demonstrate the complicated behaviors of the continuous system, which is also controlled by two different parameters numerically.…”

Section: P(t + 1) = H(t)[1 -Exp(-abp(t) 1+ah(t)supporting

confidence: 82%

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Bifurcation and chaos in a host-parasitoid model with a lower bound for the host

2018

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In this paper, a discrete-time biological model and its dynamical behaviors are studied in detail. The existence and stability of the equilibria of the model are qualitatively discussed. More precisely, the conditions for the existence of a flip bifurcation and a Neimark-Sacker bifurcation are derived by using the center manifold theorem and bifurcation theory. Numerical simulations are presented not only to validate our results with the theoretical analysis, but also to exhibit the complex dynamical behaviors. We also analyze the dynamic characteristics of the system in a two-dimensional parameter space. Numerical results indicate that we can more clearly and directly observe the chaotic phenomenon, period-doubling and period-adding, and the optimal parameters matching interval can also be found easily.

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Section: P(t + 1) = H(t)[1 -Exp(-abp(t) 1+ah(t)supporting

confidence: 82%

“…There have been some studies focusing on detailed treatments of this topic [2][3][4][5][6][7][8]. For example, in [2] Sun et al investigate the emergence of quasi-periodic and mode-locked states of an arbitrary period in pairs of coupled maps of a discrete system.…”

Section: P(t + 1) = H(t)[1 -Exp(-abp(t) 1+ah(t)mentioning

confidence: 99%

Bifurcation and chaos in a host-parasitoid model with a lower bound for the host

2018

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“…However, it was after the pioneering paper of Gallas 48 in 1993 studying the parameter space of the Hénon map that the parameter space attracted much attention, and since then, it has already been shown that such shrimp-shaped domains can be found in many theoretical models. [49][50][51][52][53][54][55][56][57][58] Very recently, they were also observed experimentally in a circuit of the Nishio-Inaba family. 59 A recent result from one of the pioneers of chaos theory, 60 was also devoted to this intriguing and rich parameter space structures.…”

Section: Introductionmentioning

confidence: 79%

Shrimp-shape domains in a dissipative kicked rotator

Oliveira

Robnik

Leonel

2011

Chaos

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Some dynamical properties for a dissipative kicked rotator are studied. Our results show that when dissipation is taken into account a drastic change happens in the structure of the phase space in the sense that the mixed structure is modified and attracting fixed points and chaotic attractors are observed. A detailed numerical investigation in a two-dimensional parameter space based on the behavior of the Lyapunov exponent is considered. Our results show the existence of infinite self-similar shrimp-shaped structures corresponding to periodic attractors, embedded in a large region corresponding to the chaotic regime. A strongly dissipative kicked rotator is studied. The investigation is based mainly on the asymptotic behavior of the Lyapunov exponents. Our results show that by reducing the two-dimensional map to a one-dimensional map in the limit of infinite kicks, the Feigenbaum's d is recovered. An investigation in the parameter space (the dissipation parameter and the kicking parameter) reveals the existence of infinite families of self-similar structures of shrimp-shape embedded in a large region corresponding to the chaotic regime. The organization of stability shrimps reported here for the discrete-time kicked rotator agrees well with the parameter space organization reported recently in the literature for several flows (continuous-time systems).

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“…In this work, we have studied a forced chaotic system that is a modified version of the Chua's circuit [8][9][10][11][12] with a very simple forcing mechanism, i.e., a series dc voltage source with the Chua's diode (see Fig. 1(a)) [12].…”

Section: Introductionmentioning

confidence: 99%

Periodicity detection on the parameter-space of a forced Chua’s circuit

et al. 2011

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We report a Periodicity-Detection algorithm, implemented in a LabVIEW routine for realtime data analysis on experimental chaos, to evaluate the periodicity P of experimental time series. The Periodicity-Detector (PD) algorithm was applied to the forced Chua's circuit with the aim to build the Periodicity-parameter-space (P -parameter-space). As results of the P -parameter-space, we could observe very complex dynamical behaviors, as regions of periodic structures, a new sequence of accumulation boundary, and the periodic structures organizing themselves in a period-adding bifurcation cascade. Those results agree with the maximal Lyapunov exponent and the bifurcation diagram analysis, presented in a previous work.

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Self-similar structures in a 2D parameter-space of an inductorless Chua's circuit

Cited by 77 publications

References 13 publications

Bifurcation and chaos in a host-parasitoid model with a lower bound for the host

Bifurcation and chaos in a host-parasitoid model with a lower bound for the host

Shrimp-shape domains in a dissipative kicked rotator

Periodicity detection on the parameter-space of a forced Chua’s circuit

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