The saw-like chaos in systems with hysteresis

Abstract:

We consider a dynamical system with hysteresis. The system is motivated by modifications of general-equilibrium macroeconomic models that attempt to capture risks and memory dependence of realistic economic agents. Global dynamics and bifurcations of this system are studied depending on two parameters. We show that for a certain open set of parameter values, the system exhibits chaotic behavior. To understand the nature of this type of chaos, we introduce a map, which we call the “saw map”, and discuss its properties.