On the number of limit cycles in discontinuous piecewise linear differential systems with two pieces separated by a straight line. (English) Zbl 1309.34039
Summary: We study the maximum number \(N\) of limit cycles that can exhibit a planar piecewise linear differential system formed by two pieces separated by a straight line. More precisely, we prove that this maximum number satisfies \(2\leq N\leq 4\) if one of the two linear differential systems has its equilibrium point on the straight line of discontinuity.
MSC:
| 34C05 | Topological structure of integral curves, singular points, limit cycles of ordinary differential equations |
| 34A36 | Discontinuous ordinary differential equations |
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