Chaos in the simulation of systems with discontinuous derivatives

In this paper, a class of first order difference equations involving the nonlinearity sign[x(k)] is studied. The regions of steady state and chaos are indicated and the dynamical behavior is explained. Furthermore, the Euler simulation of a class of first order differential equations with discontinuous derivatives, involving the nonlinearity sign[x(t)], reduces to the above class of difference equations and displays similar behavior. Observations are made on what to expect in the simulation of discontinuous systems.