DMS Applied and Computational Mathematics Seminar

Time: Nov 11, 2022 (02:00 PM)
Location: 328 Parker Hall



Speaker: Susmitha Sadhu, Georgia College & State University

Title: A novel mechanism for detecting early warning signals of dramatic population changes and predicting a regime shift in a predator-prey model. 

Abstract: A regime shift refers to a significant change in the behavior of an ecosystem after a long period of apparently stable dynamics. Often an abrupt change in the state of an ecosystem may not be necessarily preceded by a noticeable change in the environment and hence the question of identifying an early warning signal and predicting a regime shift is challenging. In this talk, I will discuss a mechanism for detecting an early signal of a sudden dramatic population change as well as predicting a regime shift in a two-trophic ecosystem consisting of two species of predators competing for their common prey. With proper rescaling, the model can be written as a singularly perturbed system of equations, where the prey evolves on a faster timescale than its predators. In a parameter regime near a singular Hopf bifurcation, chaotic mixed-mode oscillations (MMOs), featuring concatenation of small and large-amplitude oscillations, are observed as long transients before the system approaches its asymptotic state and experiences a regime shift. To analyze the dynamical cause that initiates a large amplitude oscillation, the model is reduced to a suitable normal form near the singular-Hopf point. Exploiting the separation of timescales and properties of the solutions of the normal form, the transient dynamics are analyzed. The analysis yields a method for detecting the initiation of a large amplitude oscillation and predicting the onset of a transition to the asymptotic state. 
Faculty host: Hans-Werner van Wyk