Dynamical Analysis of a Pest-Natural Enemy-Predator Model with Local Bifurcation Analysis

Abstract

Crop protection is vital for agriculture-dependent economies, where pest infestations significantly threaten crop yields. This study develops a pest–natural enemy–predator model based on the Smith growth function, which more accurately represents ecological dynamics than the traditional logistic model. We analyze the system’s equilibrium stability and bifurcation behaviour with respect to the pest-capturing rate (ϒ), establishing the existence of a Hopf bifurcation. Numerical simulations support our analytical results, while MATCONT-based bifurcation analysis identifies limit points, Hopf bifurcations, and branch points, offering deeper insights into the system’s dynamic behaviour.

Keywords: Pest Population; Natural Enemy; Smith Model; Local Bifurcation; Branch point; limit point.

2010 Mathematics Subject Classification. 32G34; 34C23