Lecture

Title. Stability analysis of a delayed population model.

Venue. 308 

Time. Part 1 (9.00 - 10.00 AM), Part 2 (12.00 - 1.00 PM)

Abstract. 

Nowadays mathematical, statistical, and simulation models play an important role to describing real-world problems. In particular, differential equations models are useful to understand ecological and epidemiological dynamics. We shall develop a predator-prey model with asymmetric functional and numerical responses. There is a time lag between consumption and digestion of prey biomass by the predators. Taking time delay as the bifurcation parameter, we shall identify four different dynamic behaviors, viz., one of the coexisting equilibria undergoes (1) no change in its stability for all time delay, (2) stability change, (3) stability switching, and (4) instability switching. Analytically we shall establish that a saddle equilibrium does not alter its stability due to varying delay. All these behavior will be explained in detail along with numerical examples. Simulations will be provided to visualize how the eigenvalues evolve with delay parameter and change stability nature. To the best of our knowledge, this is the only
population model revealing multiple dynamics with a single time delay. This contribution might be useful from mathematical and numerical view points.