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Global dynamics of Chua Corsage Memristor circuit family: fixed-point loci, Hopf bifurcation, and coexisting dynamic attractors
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Global dynamics of Chua Corsage Memristor circuit family: fixed-point loci, Hopf bifurcation, and coexisting dynamic attractors
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Journal Article
Global dynamics of Chua Corsage Memristor circuit family: fixed-point loci, Hopf bifurcation, and coexisting dynamic attractors
2020
Overview
This paper presents an in-depth and rigorous mathematical analysis of a family of nonlinear dynamical circuits whose only nonlinear component is a
Chua Corsage Memristor (CCM)
characterized by an explicit seven-segment piecewise-linear equation. When connected across an external circuit powered by a DC battery, or a sinusoidal voltage source, the resulting circuits are shown to exhibit four asymptotically stable
equilibrium points
, a unique stable
limit cycle
spawn from a supercritical
Hopf bifurcation
along with three static attractors, four
coexisting dynamic attractors
of an associated
non-autonomous nonlinear differential equation,
and four corresponding
coexisting
pinched hysteresis loops. The
basin of attractions
of the above static and dynamic attractors is derived numerically via
global nonlinear analysis.
When driven by a battery, the resulting
CCM circuit
exhibits a
contiguous fixed-point loci
, along with its
DC V–I curve
described analytically by two explicit
parametric
equations. We also proved the
fundamental feature of the
edge of chaos
property; namely,
it is possible to destabilize a stable circuit
(i.e., without oscillation) and make it
oscillate
, by merely adding a
passive
circuit element, namely
L
>
0
. The
CCM circuit family
is one of the few known example of a strongly nonlinear dynamical system that is endowed with numerous coexisting static and dynamic attractors that can be studied both experimentally, and mathematically, via exact formulas.
Publisher
Springer Netherlands,Springer Nature B.V
Subject
