Dynamics and control in a novel hyperchaotic system

Matouk, A. E.

doi:10.1007/s40435-018-0439-6

Cited by 15 publications

(8 citation statements)

References 57 publications

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“…where the parameter set 4) is simple in comparison with similar types of 4D systems and reports studies of important problems [3,24,25]. It has the equilibria Eq (1) � (0, 0, 0, 0),…”

Section: The Systems' Descriptionmentioning

confidence: 99%

“…In [23], Singh and Roy showed the coexistence of selfexcited chaotic attractors in a new 3D chaotic system. In this work, we mainly focus on exploring hidden chaotic attractors and self-excited coexisting attractors in a novel hyperchaotic system given by Matouk [24]. e proposed system is described by a set of four coupled nonlinear integer or fractional-order differential equations [25] and is known here as Matouk's hyperchaotic system.…”

Section: Introductionmentioning

confidence: 99%

“…e proposed system is described by a set of four coupled nonlinear integer or fractional-order differential equations [25] and is known here as Matouk's hyperchaotic system. Matouk's system was applied to solve some potential engineering problems [3,24]. Here, the novel dynamical behaviors of Matouk's hyperchaotic systems have the following different types: (i) hidden chaotic attractors exist in the integer-order and the fractional-order Matouk's hyperchaotic systems with one saddle equilibrium point and two locally asymptotically stable equilibria; (ii) variety of selfexcited chaotic attractors exist in this system including the newly found one-eyed face attractors; (iii) coexistence of multihidden attractors, with different topological shapes, are also found in this system.…”

Section: Introductionmentioning

confidence: 99%

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Self‐Excited and Hidden Chaotic Attractors in Matouk’s Hyperchaotic Systems

Almatroud

Matouk

Mohammed

et al. 2022

Discrete Dynamics in Nature and Society

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Self-excited and hidden chaotic attractors are interesting complex dynamical phenomena. Here, Matouk’s hyperchaotic systems are shown to have self-excited and hidden chaotic attractors, respectively. Two case studies of hidden chaotic attractors are provided which are examined with orders 3.08 and 3.992, respectively. Moreover, self-excited chaotic attractors are found in the fractional-order system and its integer-order counterpart. The existence of one-eyed face self-excited chaotic attractors is also reported in this work. Our results show that the fractional derivative affects the appearances of hidden chaotic attractors in this system.

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“…where the parameter set 4) is simple in comparison with similar types of 4D systems and reports studies of important problems [3,24,25]. It has the equilibria Eq (1) � (0, 0, 0, 0),…”

Section: The Systems' Descriptionmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

See 1 more Smart Citation

Self‐Excited and Hidden Chaotic Attractors in Matouk’s Hyperchaotic Systems

Almatroud

Matouk

Mohammed

et al. 2022

Discrete Dynamics in Nature and Society

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“…Time delayed-feedback control is an efficient method for stabilizing unstable periodic orbits of chaotic systems (Leutcho et al, 2020;Fozin et al, 2019;Leutcho and Kengne, 2018;Matouk and Khan, 2020;Matouk, 2019;Njitacke et al, 2016). The method is based on applying feedback proportional to the deviation of the current state of the system from its state one period in the past so that the control signal vanished when the stabilization of the desired orbit is attained.…”

Section: Introductionmentioning

confidence: 99%

Bifurcation analysis and chaos control in Zhou's dynamical system

Aly

El-Dessoky

Yassen

et al. 2022

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PurposeThe purpose of the study is to obtain explicit formulas to determine the stability of periodic solutions to the new system and study the extent of the stability of those periodic solutions and the direction of bifurcated periodic solutions. More than that, the authors did a numerical simulation to confirm the results that the authors obtained and presented through numerical analysis are the periodic and stable solutions and when the system returns again to the state of out of control.Design/methodology/approachThe authors studied local bifurcation and verified its occurrence after choosing the delay as a parameter of control in Zhou 2019’s dynamical system with delayed feedback control. The authors investigated the normal form theory and the center manifold theorem.FindingsThe occurrence of local Hopf bifurcations at the Zhou's system is verified. By using the normal form theory and the center manifold theorem, the authors obtain the explicit formulas for determining the stability and direction of bifurcated periodic solutions. The theoretical results obtained and the corresponding numerical simulations showed that the chaos phenomenon in the Zhou's system can be controlled using a method of time-delay auto-synchronization.Originality/valueAs the delay increases further, the numerical simulations show that the periodic solution disappears, and the chaos attractor appears again. The obtained results can also be applied to the control and anti-control of chaos phenomena of system (1). There are still abundant and complex dynamical behaviors, and the topological structure of the new system should be completely and thoroughly investigated and exploited.

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“…Many chaotic systems have been developed such as Lorenz system [1], Rossler system [2], and Chen system [3]. As chaos theory progresses, many new chaotic systems [4][5][6][7][8] have been proposed, specially hyperchaotic systems [9][10][11][12][13][14][15]. A hyperchaotic system is usually characterized as a chaotic system with more than one positive Lyapunov exponent, implying that the dynamics expand in more than one direction, giving rise to more complex chaotic dynamics.…”

Section: Introductionmentioning

confidence: 99%

Numerical Simulation of a Class of Hyperchaotic System Using Barycentric Lagrange Interpolation Collocation Method

Zhou

Wang

et al. 2019

Complexity

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Hyperchaotic system, as an important topic, has become an active research subject in nonlinear science. Over the past two decades, hyperchaotic system between nonlinear systems has been extensively studied. Although many kinds of numerical methods of the system have been announced, simple and efficient methods have always been the direction that scholars strive to pursue. Based on this problem, this paper introduces another novel numerical method to solve a class of hyperchaotic system. Barycentric Lagrange interpolation collocation method is given and illustrated with hyperchaotic system (x˙=ax+dz-yz,y˙=xz-by, 0≤t≤T,z˙=cx-z+xy,w˙=cy-w+xz,) as examples. Numerical simulations are used to verify the effectiveness of the present method.

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Dynamics and control in a novel hyperchaotic system

Cited by 15 publications

References 57 publications

Self‐Excited and Hidden Chaotic Attractors in Matouk’s Hyperchaotic Systems

Self‐Excited and Hidden Chaotic Attractors in Matouk’s Hyperchaotic Systems

Bifurcation analysis and chaos control in Zhou's dynamical system

Numerical Simulation of a Class of Hyperchaotic System Using Barycentric Lagrange Interpolation Collocation Method

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