Hyperchaos in convection with the Cattaneo-Christov heat-flux model

Daumann, Caio C.; Rech, Paulo C.

doi:10.1140/epjb/e2019-100081-6

Cited by 10 publications

(4 citation statements)

References 17 publications

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“…Compared with the chaotic state, the hyperchaotic state has more complex dynamical behaviors and is especially suitable for many security applications based on chaos [30][31][32][33]. However, there are at least two positive Lyapunov exponents to produce a hyperchaotic state.…”

Section: Introductionmentioning

confidence: 99%

Hyperchaotic maps of a discrete memristor coupled to trigonometric function

Liu¹,

Mou²,

Han³

et al. 2021

Phys. Scr.

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In this paper, a new chaotic map coupled with a memristor is constructed. Based on the proposed discrete maps of sine and cosine functions, the discrete memristor is introduced and used as input to enhance their chaotic performance. Then Lyapunov exponents spectra (LEs), bifurcation diagram, and other methods are used to evaluate their chaotic behaviors. Firstly, the fixed point of the new mapping is solved, and the stability of the fixed point is analyzed with different system parameters. The distinguishing feature of the discrete graph is the coexistence of multiple types such as chaos, quasiperiodic oscillation, and discrete periodic points. In particular, the coexistence of multiple chaotic and hyperchaotic attractors has been discovered, and the initial value can be adjusted to control the shift of the chaotic attractor. In addition, state transition phenomena such as chaos degeneration and the transformation of chaos into hyperchaos have been discovered. Finally, we designed and implemented the discrete map on the DSP platform. The research results provide guidance for the application and teaching of the chaotic map coupled discrete memristor.

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Section: Introductionmentioning

confidence: 99%

Hyperchaotic maps of a discrete memristor coupled to trigonometric function

Liu¹,

Mou²,

Han³

et al. 2021

Phys. Scr.

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“…Some miscellaneous topics of research in the control literature are the modelling, identification and control of systems (Leandro and Kienitz, 2019;Tirandaz, 2019;Habrache et al, 2019;Fadil et al, 2019;Wang, 2019;Abdelhedi and Derbel, 2019;Lien et al, 2019a,b;Vaidyanathan et al, 2019b). Significant research attention has been devoted to the modelling and applications of dynamical systems exhibiting chaos and hyperchaos (Xu et al, 2019;Gusso et al, 2019;Gatabazi et al, 2019;Singh and Roy, 2019;Cabanas et al, 2019;Ginoux et al, 2019;Jahanshahi et al, 2019;Rajagopal et al, 2019b;Daumann and Rech, 2019). Xu et al (2019) proposed a chaotic system based on a circuit design involving a memristor model and a meminductor model.…”

Section: Introductionmentioning

confidence: 99%

“…Rajagopal et al (2019) proposed a new van der Pol-Duffing (MVPD) snap oscillator exhibiting hyperchaos and implemented the hyperchaos system in FPGA. Daumann and Rech (2019) reported hyperchaos in a heat-flux convection model.…”

Section: Introductionmentioning

confidence: 99%

A new hyperjerk dynamical system with hyperchaotic attractor and two saddle-focus rest points exhibiting Hopf bifurcations, its hyperchaos synchronisation and circuit implementation

Vaidyanathan

Moroz

Sambas³

2019

IJMIC

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A new 4-D dynamical hyperjerk system with hyperchaos is reported in this work. The proposed nonlinear mechanical system with hyperchaos has two saddlefocus rest points exhibiting Hopf bifurcations. A detailed bifurcation analysis of the new hyperjerk plant with theory and simulations is discussed. As a control application, an integral sliding mode controller has been designed for the global hyperchaos synchronisation of the new hyperjerk system with itself. Finally, a circuit model using MultiSim of the new hyperjerk system with hyperchaos is designed for practical implementation.

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“…Layek and Pati include some numerical results including bifurcation transition diagrams, plots of the largest Lyapunov exponents, phase-space portraits, and routes to chaos via period-doubling bifurcations for r > 10 [6]. In 2019, Daumann and Rech used Lyapunov exponents spectra to characterize the dynamical behavior of system (1), and found numerically the existence of chaos in different parameter regions [2] (see the attractors in the phasespace of system (1) in Fig. 1).…”

mentioning

confidence: 99%

Codimension one and two bifurcations in Cattaneo-Christov heat flux model

Wei¹,

Zhang²,

Moroz³

et al. 2021

DCDS-B

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Layek and Pati (Phys. Lett. A, 2017) studied a nonlinear system of five coupled equations, which describe thermal relaxation in Rayleigh-Benard convection of a Boussinesq fluid layer, heated from below. Here we return to that paper and use techniques from dynamical systems theory to analyse the codimension-one Hopf bifurcation and codimension-two double-zero Bogdanov-Takens bifurcation. We determine the stability of the bifurcating limit cycle, and produce an unfolding of the normal form for codimension-two bifurcation for the Layek and Pati's model.

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Hyperchaos in convection with the Cattaneo-Christov heat-flux model

Cited by 10 publications

References 17 publications

Hyperchaotic maps of a discrete memristor coupled to trigonometric function

Hyperchaotic maps of a discrete memristor coupled to trigonometric function

A new hyperjerk dynamical system with hyperchaotic attractor and two saddle-focus rest points exhibiting Hopf bifurcations, its hyperchaos synchronisation and circuit implementation

Codimension one and two bifurcations in Cattaneo-Christov heat flux model

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