Chaotic behavior of driven, second-order, piecewise linear systems

In this paper the chaotic behavior of second-order, discontinuous systems with a pseudo-equilibrium point on a discontinuity surface is analyzed. The discontinuous system is piecewise linear and approximated to a non-smooth continuous system. The discontinuous term is represented by a sign function that is replaced by a saturation function with high slope. Some of the conditions that determine the chaotic behavior of the approximate system are formally established. Besides, the convergence of its chaotic solutions to those of the discontinuous system is shown. Several bifurcation diagrams of both systems show the similarity of their dynamical behavior in a wide parameter range, and particularly for a parameter region determined from the application of the Melnikov technique to non-smooth systems, where a chaotic behavior can be displayed.