[MS10] Model Bifurcations and Ecological Relevance

[MS10-02] Asymptotic and short-term responses of perturbation: A mathematical comparison of stability measures

*TAPAN KUMAR KAR¹ (1. Indian Institute of Engineering Science and Technology, Shibpur (India))

Keywords:

Asymptotic behaviour,Transient behaviour,Spatial heterogeneity,Resilience.

Dynamics is the subject that deals with change, with systems that evolve in time. Whether the system in question settles down to equilibrium, keeps repeating in cycles, or does something more complicated, it is dynamics that we use to analyze the behaviour. Asymptotic and transient solutions make up a dynamic system’s reaction to external disturbances. Stability and resilience characterize the asymptotic responses of perturbations of the equilibria. Short-term responses, however, can differ markedly from the asymptotic responses, and this short-term growth of a perturbation is often as important as its long-term decay. Studying how spatial heterogeneity affects transient behaviour in reaction-diffusion systems is also crucial. Viewed from the perspective of dynamics, in this talk, I shall present mathematical approaches to asymptotic and short-term responses to perturbation.