Hysteresis in a simple V-shaped spring-mass system

This paper theoretically studies a simple system of two identical linear springs connected symmetrically to a mass in a V-shaped configuration, with an additional adjustable external force applied to the mass. As this force is varied, under certain conditions the equilibrium position of the mass demonstrates strong dependence on the history of changes in the external force, exhibiting hysteresis. Mathematically, variations of the external force cause the system to undergo two saddle-node bifurcations at two differing critical points, leading separately to the creation and destruction of branches of stable equilibria. Analysis of the bifurcation diagram shows that the saddle-node bifurcations cause hysteresis in the system, and the behavior is summarized in a hysteresis graph.