Period-adding bifurcations in a class of one-dimensional discontinuous piecewise smooth maps

Abstract:

In this paper we consider the dynamics of a class of one-dimensional discontinuous nonlinear maps. We obtain the existence and stability conditions of fixed points in the parameter space. Then we study the existence and stability of period-m orbit of type $A^{m-1}B$. Analytical conditions for the existence and stability of such kind of periodic orbits are found. The period doubling and saddle-node bifurcations of those orbits are also studied.