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On the existence and uniqueness of limit cycles in planar continuous piecewise linear systems without symmetry. (English) Zbl 1293.34047

Summary: Some techniques to show the existence and uniqueness of limit cycles, typically stated for smooth vector fields, are extended to continuous piecewise-linear differential systems.
New results are obtained for systems with three linearity zones without symmetry and having one equilibrium point in the central region. We also revisit the case of systems with only two linear zones, giving shorter proofs of known results.
A relevant application to the McKean piecewise linear model of single neuron activity is included.

MSC:

34C05 Topological structure of integral curves, singular points, limit cycles of ordinary differential equations
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