Understanding the influence of prey odour in predator species: a three-species food chain study

Abstract

The odour emitted by prey is typically regarded as a crucial factor in an ecosystem. The objective of this study is to examine the stability and local bifurcations, specifically transcritical and Hopf bifurcation, of a food chain model that takes into account the influence of odour. The proposed model has been developed by incorporating a three-species food chain and an additional factor that is more representative of reality: the impact of prey odour on predator population and, consequently, on the food chain. The system’s solutions have been verified for positivity and boundedness. Subsequently, the conditions pertaining to the local stability and global stability of the equilibrium points of the proposed system, have been established. Additionally, the criteria for the emergence of bifurcations at certain equilibrium points are laid out. It has been observed that the equilibrium state of coexistence becomes unstable in the event of the absence of prey odour. The odour effect has been noted to play a role in promoting the coexistence of species within the food chain system, facilitated by the occurrence of two supercritical Hopf bifurcations. Furthermore, a comprehensive analysis of the impact of other different parameters within the system is presented. Subsequently, all the theoretical findings of this study are verified through a numerical analysis and outcomes are visually exhibited. The biological implications of the results are discussed and a conclusion has been drawn.