Hyperchaotic Memcapacitor Oscillator with Infinite Equilibria and Coexisting Attractors

Rajagopal, Karthikeyan; Jafari, Sajad; Karthikeyan, Anitha; Srinivasan, Ashokkumar; Ayele, Biniyam A.

doi:10.1007/s00034-018-0750-7

Cited by 51 publications

(11 citation statements)

References 81 publications

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“…When infinitely many attractors coexist for the same set of system parameters, multistability is referred to as extreme multistability [ 25 ]. The previously published literature have reported that the dynamical stability of memristive systems are heavily dependent on the initial conditions, which easily leads the system to generate multistability or even extreme multistability [ 26 , 27 , 28 , 29 ].…”

Section: Memcapacitor-based Chaotic Oscillator and Its Dynamicsmentioning

confidence: 99%

Complex Dynamics in a Memcapacitor-Based Circuit

Yuan

Wang

et al. 2019

Entropy

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In this paper, a new memcapacitor model and its corresponding circuit emulator are proposed, based on which, a chaotic oscillator is designed and the system dynamic characteristics are investigated, both analytically and experimentally. Extreme multistability and coexisting attractors are observed in this complex system. The basins of attraction, multistability, bifurcations, Lyapunov exponents, and initial-condition-triggered similar bifurcation are analyzed. Finally, the memcapacitor-based chaotic oscillator is realized via circuit implementation with experimental results presented.

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Section: Memcapacitor-based Chaotic Oscillator and Its Dynamicsmentioning

confidence: 99%

Complex Dynamics in a Memcapacitor-Based Circuit

Yuan

Wang

et al. 2019

Entropy

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“…bifurcations which are induced without varying the system parameters [Fiedler et al, 2000;Corinto & Forti, 2017]. More recently, FCAM has been extended to much broader classes of circuits containing more than one memristor [Corinto & Forti, 2018;Chen et al, 2020] as well as memcapacitors and meminductors [Corinto et al, 2019;Rajagopal et al, 2018;Yuan et al, 2016a;Yuan et al, 2016b]. Also in this case, it is shown that the original circuit can be equivalently described by a family of state space reduced-order systems indexed by a number of constant parameters, usually equal to the number of ideal memelements.…”

Section: Introductionmentioning

confidence: 99%

“…Several contributions make it clear that circuits containing memelements are able to display a rich variety of multistability phenomena [Li et al, 2014;Scarabello & Messias, 2014;Messias et al, 2010;Bao et al, 2016;Yuan et al, 2016a;Yuan et al, 2016b;Xu et al, 2017;Rajagopal et al, 2018;Varshney et al, 2018;Corinto et al, 2019;Yuan et al, 2019;Wang et al, 2019;Chang et al, 2019;Chen et al, 2020;Zhang et al, 2019]. To this respect, it is worth noting that multistability control is a field of general growing interest (see, e.g.…”

Section: Introductionmentioning

confidence: 99%

Input–Output Characterization of the Dynamical Properties of Circuits with a Memelement

Innocenti

Marco

Tesi

et al. 2020

Int. J. Bifurcation Chaos

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The paper proposes a novel input–output approach to characterize the dynamical properties of a class of circuits composed by a linear time-invariant two-terminal element coupled with one of the ideal memelements (memory elements) introduced by Prof. L. O. Chua, i.e. memristors, memcapacitors, and meminductors. The developed approach permits to readily determine the conditions under which the dynamics of any circuit of the class admits a first integral. It is also shown that the circuit dynamics can be obtained by collecting the dynamical behaviors displayed by a canonical reduced-order input–output system subject to a constant input of any amplitude. Notably, the reduced-order system exactly describes the dynamics of a circuit forced by a constant generator and with a nonlinear memoryless element in place of the memelement. The relation between the proposed input–output approach and the available state space ones (e.g. Flux-Charge Analysis Method (FCAM)) is also addressed. The main result is that explicit expressions of the invariant manifolds can be directly obtained in the voltage–current state space. Finally, it is shown how the approach also applies to circuits which contain forcing generators. It is believed that the proposed input–output approach can be a useful alternative to state space methods for studying multistability and control issues.

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“…In recent years, multistability [20][21][22][23][24][25] and extreme multistability [26][27][28][29][30][31][32] have become research hotspots in the field of chaotic systems. Multistability means that when the system parameters remain unchanged, the system can generate more than one attractor with different initial values.…”

Section: Introductionmentioning

confidence: 99%

Heterogeneous and Homogenous Multistabilities in a Novel 4D Memristor-Based Chaotic System with Discrete Bifurcation Diagrams

et al. 2020

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In this paper, a new 4D memristor-based chaotic system is constructed by using a smooth flux-controlled memristor to replace a resistor in the realization circuit of a 3D chaotic system. Compared with general chaotic systems, the chaotic system can generate coexisting infinitely many attractors. The proposed chaotic system not only possesses heterogeneous multistability but also possesses homogenous multistability. When the parameters of system are fixed, the chaotic system only generates two kinds of chaotic attractors with different positions in a very large range of initial values. Different from other chaotic systems with continuous bifurcation diagrams, this system has discrete bifurcation diagrams when the initial values change. In addition, this paper reveals the relationship between the symmetry of coexisting attractors and the symmetry of initial values in the system. The dynamic behaviors of the new system are analyzed by equilibrium point and stability, bifurcation diagrams, Lyapunov exponents, and phase orbit diagrams. Finally, the chaotic attractors are captured through circuit simulation, which verifies numerical simulation.

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Hyperchaotic Memcapacitor Oscillator with Infinite Equilibria and Coexisting Attractors

Cited by 51 publications

References 81 publications

Complex Dynamics in a Memcapacitor-Based Circuit

Complex Dynamics in a Memcapacitor-Based Circuit

Input–Output Characterization of the Dynamical Properties of Circuits with a Memelement

Heterogeneous and Homogenous Multistabilities in a Novel 4D Memristor-Based Chaotic System with Discrete Bifurcation Diagrams

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