Abstract:

The Melnikov functions can be used to find limit cycles for a piecewise smooth system. In the case where the separation manifold is non-linear we find an additional term in the second-order formula that was not predicted in classical theory. We will illustrate the result by showing that the piecewise linear systems separated by a cubic curve can have up to 7 limit cycles. We note that, as far as we know, the maximum number of known limit cycles for a piecewise linear system separated by a straight line is 3.