Journal
PHYSICS LETTERS A
Volume 380, Issue 38, Pages 3067-3072Publisher
ELSEVIER
DOI: 10.1016/j.physleta.2016.07.033
Keywords
Boundary equilibrium bifurcation; Discontinuous bifurcation; Piecewise-linear; Discontinuity map; Unimodal map; Bossier attractor
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An attractor of a piecewise-smooth continuous system of differential equations can bifurcate from a stable equilibrium to a more complicated invariant set when it collides with a switching manifold under parameter variation. Here numerical evidence is provided to show that this invariant set can be chaotic. The transition occurs locally (in a neighbourhood of a point) and instantaneously (for a single critical parameter value). This phenomenon is illustrated for the normal form of a boundary equilibrium bifurcation in three dimensions using parameter values adapted from of a piecewise-linear model of a chaotic electrical circuit. The variation of a secondary parameter reveals a period-doubling cascade to chaos with windows of periodicity. The dynamics is well approximated by a one-dimensional unimodal map which explains the bifurcation structure. The robustness of the attractor is also investigated by studying the influence of nonlinear terms. (C) 2016 Elsevier B.V. All rights reserved.
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