Title: Game Theoretic Mathematical Modelling Approach for the Study of Honest Signalling
Description: This document focused on the evolution of honest signalling from prey to predator. The first two levels of quality and signalling strength were considered to study the evolution of honest signalling, elucidating the role of the handicapped principle. Then, continuous type signalling and quality were considered, and adaptive dynamics were studied.
Title: Stability and Bifurcation Analysis of Modified Lotka-Volterra Models
Description: In my master’s thesis, I explored Lotka-Volterra type models for competition and predator-prey dynamics. I examined the impact of small immigrations and migration on these interactions. Stability (asymptotic and Ulam’s type) and bifurcation analysis were performed for these models.
Title: Ulam’s Type Stability of Impulsive and Delay Differential Equations
Description: In this thesis, I worked on the qualitative theory of differential equations with a focus on stability analysis. Particularly, I proved several theorems concerning the existence, uniqueness, and Hyers-Ulam stability of higher-order impulsive and delay differential equations. I mainly used Banach’s contraction principle and integral inequalities of Gronwall type to prove these results.