Limit cycles in piecewise smooth differential systems of focus-focus and saddle-saddle dynamics

In this paper, we obtained the Poincare return maps for the planar piecewise linear differential systems of the type focus-focus. Normal forms for planar piecewise smooth systems with two zones of the type focus-focus and saddle-saddle, separated by a straight line and with a center at the origin, are obtained. Upper bounds for the number of limit cycles bifurcated from the period annulus of these normal forms due to perturbation by polynomial functions of any degree are established.

کلیدواژه ها:

Piecewise linear differential system ، Piecewise smooth differential system ، Limit cycle ، Picard Fuch equations ، Poincare return map ، Melnikov function