In this paper we study a planar piecewise linear differential system formed by two regions separated by a straight line so that one system has a real unstable focus and the other a virtual stable focus which coincides with the real one. This system was introduced in a very recent paper (On the number of limit cycles in general planar piecewise linear systems, Discrete and Continuous Dynamical Systems-A 32, 2012, pp. 2147-2164) by S.-M. Huan and X.-S. Yang, who numerically showed that it can exhibit 3 limit cycles surrounding the real focus. This is the first example that a non-smooth piecewise linear differential system with two zones can have 3 nested limit cycles of crossing type surrounding a unique equilibrium. We provide a rigorous computer assisted proof of the quoted numerical result. Copyright © 2012 Watam Press.
|Journal||Dynamics of Continuous, Discrete and Impulsive Systems Series B: Applications and Algorithms|
|Publication status||Published - 28 May 2012|
- Limit cycle
- Non-Smooth differential system
- Piecewise linear differential system