Chaotic oscillator based on memcapacitor and meminductor

Wang, Xiaoyuan; Yu, Jun; Jin, Chenxi; Iu, Herbert Ho Ching; Yu, Simin

doi:10.1007/s11071-019-04781-5

Cited by 53 publications

(17 citation statements)

References 27 publications

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“…Memcapacitor or memristor can easily generates high-frequency chaotic oscillation signals in the circuit because of the characteristic of nonlinearity, and many chaotic circuits introduced them to obtain chaos [5][6][7][8][9]. The chaotic circuits can generate some unique phenomena, including transient chaos [10][11][12][13], steady-state chaos accompanied by burst period phenomenon [14], and multistable phenomenon [15][16][17][18].…”

Section: Introductionmentioning

confidence: 99%

A novel memcapacitor and its application in a chaotic circuit

et al. 2021

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In this paper, a novel memcapacitor is designed by SBT memristor and two capacitors. A fifth-order memcapacitor and memristor chaotic circuit is proposed. The stability of the equilibrium point of the system is analyzed theoretically. Lyapunov exponents spectra, bifurcation diagrams, poincaré maps and phase diagrams are used to analyze the dynamic behaviors of the system. The results show that under different initial values and parameters, the system produces rich dynamic behaviors such as stable points, limit cycles, chaos, and so on. Specially, coexisting attractors, transient chaos, and steady-state chaos accompanied by burst period phenomenon are also produced in the system. The proposed memcapacitor-based circuit expands the research methods of memcapacitor for application in chaotic circuits.

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Section: Introductionmentioning

confidence: 99%

A novel memcapacitor and its application in a chaotic circuit

et al. 2021

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“…By and large, the research on chaos, various types of strange attractors, coexisting attractors, synchronization control and their applications have became the hotspots [1][2][3][4][5]. Their interesting and complex dynamical phenomena are applied in various fields, for example chaos prediction in nonlinear viscoelastic plates [6], nonlinear resonances and multi-stability in simple neural circuits [7], synchronization control [8,33], grid multi-scroll chaotic attractors [4,5,9,30], multi-wing hyper chaotic system [10,30], electronic circuits [11][12][13][22][23][24], image encryption application [25,34], oscillator of memory elements [14,35,36,41], embedded implementation for digital systems [37][38][39][40] et al As well as we known, the chaotic application in electronic circuits began Chua circuit and generation of multiple scroll attractors started from Suykens and Vandewalle, beyond the double scroll [1]. Up to now, the main work and research on chaos theory, analysis methods and application fields are as follows: (i) chaotic systems and scroll attractors seem to have reached their maturity, i.e.…”

Section: Introductionmentioning

confidence: 99%

Bounded Orbits and Multiple Scroll Coexisting Attractors in a Dual System of Chua System

Liu

et al. 2020

IEEE Access

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A special three-dimensional chaotic system was proposed in 2016, as a dual system of Chua system, which is satisfied a 12 •a 21 < 0. The dynamics characteristics are different from the Jerk system (a 12 •a 21 =0) and Chua system (a 12 •a 21 > 0). In this paper, a method for generating M×N×L grid multiple scroll attractors is presented for this system. Also, in order to ensure the rigor of the theoretical results, we prove existence of the complex scenario of bounded orbits, such as homoclinic and heteroclinic orbits, and illustrate concurrent created and annihilated of symmetric orbits. Then, Shilnikov bifurcation and the possible relationship between the birth and death of the scroll attractors are studied. Furthermore, two theorems are demonstrated for these bounded orbits. Finally, the Lyapunov exponents, bifurcation diagrams, and multiple scroll coexisting attractors are displayed, which are related to the parameters and initial condition. INDEX TERMS Grid multiple scroll attractors; homoclinic and heteroclinic orbits; Shilnikov bifurcation; Coexisting attractors.

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“…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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Chaotic oscillator based on memcapacitor and meminductor

Cited by 53 publications

References 27 publications

A novel memcapacitor and its application in a chaotic circuit

A novel memcapacitor and its application in a chaotic circuit

Bounded Orbits and Multiple Scroll Coexisting Attractors in a Dual System of Chua System

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

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