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Limit cycle bifurcation in 3D continuous piecewise linear systems with two zones. Application to Chua’s circuit. (English) Zbl 1093.34528

Summary: The generic case of three-dimensional continuous piecewise linear systems with two zones is analyzed. From a bounded linear center configuration, we prove that the periodic orbit which is tangent to the separation plane becomes a limit cycle under generic conditions. Expressions for the amplitude, period and characteristic multipliers of the bifurcating limit cycle are given. The results obtained are applied to the study of the onset of asymmetric periodic oscillations in Chua’s oscillator.

MSC:

34C23 Bifurcation theory for ordinary differential equations
34C05 Topological structure of integral curves, singular points, limit cycles of ordinary differential equations
37G15 Bifurcations of limit cycles and periodic orbits in dynamical systems
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