The Ananthakrishna Model Under Non-synchronous Perturbation

The Ananthakrishna model,seeking to explain the Portevin-Le Chatelier effect,is studied with or without non-synchronous perturbations.For the unperturbed model,Bogdanov-Takens bifurcation and zeroHopf bifurcation are detected.For the perturbed model,rich dynamical behaviors are given by researching the Poincarémap,including solutions of different periods,quasi-periodic solutions,chaotic solutions,and bistability.Moreover,an augmented temperature-dependent perturbation amplitude induces a transition from non-serrated to serrated flow on the stress-time curve.Notably,on the stress-strain curve,the phenomenon of repeated yielding diminishes with an increase in the value of a temperature-dependent parameter,while it persists with an increase in the value of a temperature-independent parameter.Sensitivity analysis sheds light on the factors exerting the most significant influence on dislocation density.