Title: Optimal control of a discrete-time plant-herbivore/pest model with bistability in fluctuating environments
Abstract: Discrete-time plant-pest models with two different constant control strategies (i.e., removal versus reduction strategies) have been investigated to understand how to regulate the population of pest. The corresponding optimal control problem has been explored on three scenarios of bistability plant-pest dynamics where these dynamics are determined by the growth rate of the plant and the damage rate inflicted by pest. Furthermore, the impacts of fluctuating environments on discrete time plant-pest dynamics have been explored. Through analysis and simulations, we identify and evaluate the optimal controls and their impact on the plant-pest dynamics. There are critical factors to characterize the optimal controls and the corresponding plant-pest dynamics such as the control upper bound (the effectiveness level of the implementation of control measures) and the initial conditions of the plant and pest. The results show that the pest is hard to be eliminated when the control upper bound is not large enough or the initial conditions are chosen from the inner point of the basin of attractions. However, as the control upper bound is increased or the initial conditions are chosen from near the boundary of the basin of attractions, then the pest can be manageable regardless of fluctuating environments.
Speaker: Dr. Kang is a professor of Applied Mathematics in the sciences and mathematics faculty group of the College of Integrative Sciences and Arts (CISA) at Arizona State University. 
Date: 3:00pm-5:00pm 2024-6-13日 (Thursday)
Venue: Room 208, School of Mathematical Science
Inviter：Tao Feng

Students and teachers who are interested in Hopf algebras and tensor categoriesare welcome.