Complete asymptotic analysis of a two-nation arms race model with piecewise constant nonlinearities (Q764588)

Summary: A discrete time two-nation arms race model involving a piecewise constant nonlinear control function is formulated and studied. By elementary but novel arguments, we are able to give a complete analysis of its asymptotic behavior when the threshold parameter in the control function varies from \(0^+\) to \(\infty\). We show that all solutions originated from positive initial values tend to limit one or two cycles. An implication is that when devastating weapons are involved, ``terror equilibrium'' can be achieved and escalated race avoided. It is hoped that our analysis will provide motivation for further studying of discrete-time equations with piecewise smooth nonlinearities.