Discretization of non-Lipschitz continuous O.D.E. and chaos (Q1924878)

This article considers scalar autonomous ordinary differential equations with only one stable equilibrium point. It presents necessary and sufficient conditions under which the explicit Euler discretization is stable in a neighborhood of the equilibrium point. Furthermore, it gives sufficient conditions under which the Euler discretization has periodic orbits with period 2, and sufficient conditions under which it is chaotic.