Dynamics of Discrete Time Systems with a Hysteresis Stop Operator

TL;DR

This paper analyzes a two-dimensional discrete-time system combining linear dynamics with a hysteresis stop operator, exploring its global behavior and bifurcations influenced by parameters, motivated by economic models with memory effects.

Contribution

It introduces a novel coupled system with hysteresis, studying its global dynamics and bifurcations, inspired by macroeconomic models with frictions and memory.

Findings

Characterizes global dynamics and bifurcation structures

Identifies parameter conditions for different behaviors

Connects mathematical model to economic agent behavior

Abstract

We consider a piecewise linear two-dimensional dynamical system that couples a linear equation with the so-called stop operator. Global dynamics and bifurcations of this system are studied depending on two parameters. The system is motivated by modifications to general-equilibrium macroeconomic models that attempt to capture the frictions and memory-dependence of realistic economic agents.