Existence of piecewise linear differential systems with exactly n limit cycles for all n∈N Original Research Article

In this paper, we prove that the piecewise linear differential system View the MathML source with ε≠0 and φ an odd piecewise linear periodic function of period 4, has exactly n limit cycles in the strip |x|⩽2(n+1). Consequently, there are piecewise linear differential systems having infinitely many limit cycles in the real plane. We also provide examples of piecewise linear differential systems having exactly n limit cycles for all View the MathML source.