Bifurcation delay in nonlinear systems with time-scaling

The bifurcation delay in a dynamical system with time-dependent parameters is an important phenomenon. In general, dynamical systems with time-varying parameters show dynamic bifurcation. The dynamic bifurcations lead to bifurcation delay or bifurcation postponement, and they are dependent on the frequency of the time-varying parameter. This work presents numerical and analytical explanations of how the time-scaling in the dynamical system influences the dynamic bifurcation and thus the bifurcation delay. We show the results for two different nonlinear dynamical systems, such as an ecological system and a neuron model. We show a generic behavior in the bifurcation delay, that is, the delay follows an asymptotic expression as a function of time-scaling. Possible applications are highlighted.