Abstract
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 a single neuron activity is included. © 2013 Elsevier Ltd. All rights reserved.
Original language | English |
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Pages (from-to) | 2002-2012 |
Journal | Nonlinear Analysis: Real World Applications |
Volume | 14 |
Issue number | 5 |
DOIs | |
Publication status | Published - 1 Oct 2013 |
Keywords
- Liénard equation
- Limit cycles
- Piecewise linear systems