Hard and soft excitation of oscillations in memristor-based oscillators with a line of equilibria

Hard and soft excitation of oscillations in memristor-based oscillators with a line of equilibria A model of memristor-based Chua’s oscillator is studied. The considered system has infinitely many equilibrium points, which build a line of equilibria. Bifurcational mechanisms of oscillation excitation are explored for different forms of nonlinearity. Hard and soft excitation scenarios have principally different nature. The hard excitation is determined by the memristor piecewise-smooth characteristic and is a result of a border-collision bifurcation. The soft excitation is caused by addition of a smooth nonlinear function and has distinctive features of the supercritical Andronov–Hopf bifurcation. Mechanisms of instability and amplitude limitation are described for both two cases. Numerical modeling and theoretical analysis are combined with experiments on an electronic analog model of the system under study. The issues concerning physical realization of the dynamics of systems with a line of equilibria are considered. The question on whether oscillations in such systems can be classified as the self-sustained oscillations is raised. http://www.deepdyve.com/assets/images/DeepDyve-Logo-lg.png Nonlinear Dynamics Springer Journals

Hard and soft excitation of oscillations in memristor-based oscillators with a line of equilibria

Hard and soft excitation of oscillations in memristor-based oscillators with a line of equilibria

Nonlinear Dyn (2017) 89:2829–2843 DOI 10.1007/s11071-017-3628-5 ORIGINAL PAPER Hard and soft excitation of oscillations in memristor-based oscillators with a line of equilibria Ivan A. Korneev · Tatiana E. Vadivasova · Vladimir V. Semenov Received: 9 February 2017 / Accepted: 17 June 2017 / Published online: 17 July 2017 © Springer Science+Business Media B.V. 2017 Abstract A model of memristor-based Chua’s oscil- Keywords Memristor · Memristor-based oscillators · lator is studied. The considered system has infinitely Border-collision bifurcations · Line of equilibria · many equilibrium points, which build a line of equi- Bifurcational analysis · Analog experiment libria. Bifurcational mechanisms of oscillation exci- tation are explored for different forms of nonlinear- ity. Hard and soft excitation scenarios have principally 1 Introduction different nature. The hard excitation is determined by the memristor piecewise-smooth characteristic and is a There are well-known three fundamental two-terminal result of a border-collision bifurcation. The soft excita- passive electronic circuit elements: the resistor, the tion is caused by addition of a smooth nonlinear func- capacitor, and the inductor. The fourth element called tion and has distinctive features of the supercritical the memristor was postulated by Leon Chua [21]in Andronov–Hopf bifurcation. Mechanisms of instabil- 1971. Chua’s memristor relates the transferred electri- ity and amplitude limitation are described for both two cal charge, q(t ), and the magnetic flux linkage, ϕ(t ): cases. Numerical modeling and theoretical analysis are dϕ dϕ = M ·dq, whence it follows that M = M (q) = . dq combined with experiments on an electronic analog By using the formulas dϕ = Udt and dq = idt (U model of the system under study. The issues concerning is the voltage across the memristor, i is the current physical realization of the...
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Publisher
Springer Netherlands
Copyright
Copyright © 2017 by Springer Science+Business Media B.V.
Subject
Engineering; Vibration, Dynamical Systems, Control; Classical Mechanics; Mechanical Engineering; Automotive Engineering
ISSN
0924-090X
eISSN
1573-269X
D.O.I.
10.1007/s11071-017-3628-5
Publisher site
See Article on Publisher Site

Abstract

A model of memristor-based Chua’s oscillator is studied. The considered system has infinitely many equilibrium points, which build a line of equilibria. Bifurcational mechanisms of oscillation excitation are explored for different forms of nonlinearity. Hard and soft excitation scenarios have principally different nature. The hard excitation is determined by the memristor piecewise-smooth characteristic and is a result of a border-collision bifurcation. The soft excitation is caused by addition of a smooth nonlinear function and has distinctive features of the supercritical Andronov–Hopf bifurcation. Mechanisms of instability and amplitude limitation are described for both two cases. Numerical modeling and theoretical analysis are combined with experiments on an electronic analog model of the system under study. The issues concerning physical realization of the dynamics of systems with a line of equilibria are considered. The question on whether oscillations in such systems can be classified as the self-sustained oscillations is raised.

Journal

Nonlinear DynamicsSpringer Journals

Published: Jul 17, 2017

References

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