CLOSURES OF FRACTAL SETS IN NONLINEAR DYNAMICAL SYSTEMS WITH SWITCHED INPUTS

This paper studies closures of fractal sets observed in nonlinear dynamical systems excited stochastically by switched inputs. The Duffing oscillator and the forced dumped pendulum are analyzed as examples. The dynamics of the system is characterized by a fractal set in the phase space. We can numerically construct a closure that encloses the fractal set. Furthermore, it is shown that the closure is a limit cycle attractor of a dynamical system defined by the switching manifold.