Bifurcation in Discontinuous Dynamical Systems

Two dynamical systems are called topologically equivalent if their phase portraits are homeomorphic. The appearance of a topologically nonequivalent phase portrait under variation of parameters is called a bifurcation. Thus, a bifurcation is a change of the topological type of the system as its parameters pass through a bifurcation (critical) value. Many studies have been devoted to bifurcation in smooth and continuous dynamical systems. However, less is known about bifurcation of discontinuous dynamics. That is, with discontinuous trajectories and/or non-smooth trajectories. These dynamics model real world problems of mechanics, engineering sciences, neuroscience, population dynamics, finance and many others. Investigations will enrich theory of bifircations as well application power of mathematics.