Infinite Number of Hidden Attractors in Memristor-Based Autonomous Duffing Oscillator

Varshney, Vaibhav; Shanmugam, Sabarathinam; Prasad, Awadhesh; Thamilmaran, K.

doi:10.1142/s021812741850013x

Cited by 50 publications

(23 citation statements)

References 47 publications

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“…This means that the model is always stable in the x 4 direction. This kind of equilibrium gives the 'periodic line invariant' type of stability of the model, and the model is always stable for the x 4 line [54]. We evaluate the above matrix with two different sides of variable x 4 .…”

Section: System Stability Analysismentioning

confidence: 99%

Dynamical Analysis and Sampled-Data Stabilization of Memristor-Based Chua’s Circuits

et al. 2021

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In this paper, we investigate sampled-data stabilization of memristor nonlinearity in Chua's circuits. The system stability pertaining to its switching nonlinearity covers two situations of flux thresholds. Through the stability analysis, the multistability characteristic is proved by its periodic line invariant stable line. Moreover, the dynamical features of the considered system are examined in details by numerical and corresponding simulated experiments. Several statistical and analytical characteristic methods are used to confirm the existence of chaotic attractors. With the help of the Lyapunov stability theory, new sufficient conditions are formulated using the linear matrix inequality (LMI) method to ensure the robust stability and stabilization of closed-loop systems. Finally, we present a numerical example to ascertain the validity of the theoretical results obtained. INDEX TERMS Chua's circuits, Lyapunov stability, linear matrix inequality (LMI), memristor, sampleddata control.

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Section: System Stability Analysismentioning

confidence: 99%

Dynamical Analysis and Sampled-Data Stabilization of Memristor-Based Chua’s Circuits

et al. 2021

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“…Some hidden chaotic systems also have the characteristic of multistability, which is reported by many scholars [50]- [52]. Vaibhav Varshney and S. Sabarathinam et al found the hidden behavior due to 'periodic line invariant' and analyzed the causes of multistable state in the reference [53]. Since the initial value is one of the key factors that affect the state of memristor, the sensitivity of the memristive chaotic system includes the sensitivity to the initial value of the memristor itself.…”

Section: Introductionmentioning

confidence: 98%

Multiple Transient Transitions Behavior Analysis of a Double Memristor’s Hidden System and Its Circuit

Liu

Shi

et al. 2020

IEEE Access

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In this paper, a low-dimensional hidden nonlinear system is constructed by replacing two linear resistors of a simple integrating circuit with two active memristors. The system was analyzed in detail by using the Lyapunov exponent, 0-1 Test, Poincaré map, phase diagram, power spectral density diagram, timedomain waveform, and chaotic characteristic diagram. The results show that the system can oscillate by itself under zero initial conditions, and there are various transient transition behaviors, such as from chaos to limit cycle, chaos to quasi-periodic, quasi-periodic to another quasi-periodic transition, quasi-periodic to periodic transition. Besides, these transient processes themselves include 2, 3, 4, and 5 different states respectively, showing multiple transient transitions behavior, which are not reported in the related literature. It is also found that the initial states of these transition states have rich symmetrical attractors and the stable state is multistability. In addition, the global entropy analysis method is adopted to test the universal existence of transient behaviors, which demonstrates that the system has rich nonlinear characteristics. Finally, the memristive circuit verifies the system's physical feasibility and enriches the application of memristors in circuit theory. INDEX TERMS Active memristor, hidden attractor, multiple transient transitions, chaos, simple integrating circuit.

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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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Infinite Number of Hidden Attractors in Memristor-Based Autonomous Duffing Oscillator

Cited by 50 publications

References 47 publications

Dynamical Analysis and Sampled-Data Stabilization of Memristor-Based Chua’s Circuits

Dynamical Analysis and Sampled-Data Stabilization of Memristor-Based Chua’s Circuits

Multiple Transient Transitions Behavior Analysis of a Double Memristor’s Hidden System and Its Circuit

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

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