A Memristive Hyperchaotic System without Equilibrium

Pham, Viet–Thanh; Volos, Christos; Gambuzza, Lucia Valentina

doi:10.1155/2014/368986

Cited by 46 publications

(14 citation statements)

References 37 publications

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“…Recent examples of hidden attractors in the systems without equilibria can be found, e.g. in [59][60][61][62][62][63][64][65][66][67]. After the concepts of hidden chaotic attractors was introduced first in connection with discovery of the first hidden Chua attractors (see Fig.…”

Section: Self-excited and Hidden Attractorsmentioning

confidence: 99%

Hidden Attractors in Fundamental Problems and Engineering Models: A Short Survey

Kuznetsov

2016

Lecture Notes in Electrical Engineering

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Recently a concept of self-excited and hidden attractors was suggested: an attractor is called a self-excited attractor if its basin of attraction overlaps with neighborhood of an equilibrium, otherwise it is called a hidden attractor. For example, hidden attractors are attractors in systems with no equilibria or with only one stable equilibrium (a special case of multistability and coexistence of attractors). While coexisting self-excited attractors can be found using the standard computational procedure, there is no standard way of predicting the existence or coexistence of hidden attractors in a system. In this plenary survey lecture the concept of self-excited and hidden attractors is discussed, and various corresponding examples of self-excited and hidden attractors are considered. The material is mostly based on surveys [1-4].1 Analytical-numerical study of oscillations An oscillation dynamical system can generally be easily numerically localized if the initial data from its open neighborhood in the phase space (with the exception of a minor set of points) lead to a long-term behavior that approaches the oscillation. Such an oscillation (or a set of oscillations) is called an attractor, and its attracting set is called the basin of attraction (i.e., a set of initial data for which the trajectories tend to the attractor).When the theories of dynamical systems, oscillations, and chaos were first developed researchers mainly focused on analyzing equilibria stability, which can be easily done numerically or analytically, and on the birth of periodic or chaotic attractors from unstable equilibria. The structures of many physical dynamical International Conference on Advanced Engineering -Theory and Applications, 2015 (Ho Chi Minh City, Vietnam), http://icaeta.org/, plenary lecture arXiv:1510.04803v1 [nlin.CD] 16 Oct 2015 chaotic attractor in the Lorenz system with other parameters may be self-excited with respect to zero unstable equilibrium only, and the possible existence in the Lorenz system of a hidden chaotic attractor is an open problem.

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Section: Self-excited and Hidden Attractorsmentioning

confidence: 99%

Hidden Attractors in Fundamental Problems and Engineering Models: A Short Survey

Kuznetsov

2016

Lecture Notes in Electrical Engineering

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“…Other many hyperchaotic systems have come out of the Lorenz-like system [28][29][30][31]. Some other hyperchaotic ones have been proposed, including a memristive hyperchaotic system [32,33], fractional order hyperchaotic system [34,35] or hyperchaotic multi-wing system [36,37]. To the best of our knowledge, there is no relevant research on a hyperchaotic hidden attractor with geometric control.…”

Section: Introductionmentioning

confidence: 99%

A Symmetric Controllable Hyperchaotic Hidden Attractor

Zhang

Lei

et al. 2020

Symmetry

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“…Following up the first discovery of Wang et al, other hyperchaotic systems without equilibrium were presented [14][15][16][17]. Recent studies have attempted to explore special features of no-equilibrium hyperchaotic systems.…”

Section: Introductionmentioning

confidence: 99%

A No-Equilibrium Hyperchaotic System and Its Fractional-Order Form

Hoàng

Kingni

Pham

2017

Mathematical Problems in Engineering

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No-equilibrium system with chaotic behavior has attracted considerable attention recently because of its hidden attractor. We study a new four-dimensional system without equilibrium in this work. The new no-equilibrium system exhibits hyperchaos and coexisting attractors. Amplitude control feature of the system is also discovered. The commensurate fractional-order version of the proposed system is studied using numerical simulations. By tuning the commensurate fractional-order, the proposed system displays a wide variety of dynamical behaviors ranging from coexistence of quasiperiodic and chaotic attractors and bistable chaotic attractors to point attractor via transient chaos.

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A Memristive Hyperchaotic System without Equilibrium

Cited by 46 publications

References 37 publications

Hidden Attractors in Fundamental Problems and Engineering Models: A Short Survey

Hidden Attractors in Fundamental Problems and Engineering Models: A Short Survey

A Symmetric Controllable Hyperchaotic Hidden Attractor

A No-Equilibrium Hyperchaotic System and Its Fractional-Order Form

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