Prey-predator dynamics with additional food and Holling type-III response: application to Bemisia tabaci

Interactions between pests and their natural enemies play a central role in ecological balance and sustainable pest management. In the present work, we examine a prey-predator system in which the predator population experiences intra-specific competition and receives an external food supplement. The feeding mechanism of the predator follows a Holling type-III functional response. We demonstrate that the proposed formulation admits a unique, globally positive solution and investigate the stability of its equilibria. Analytical exploration reveals the occurrence of distinct bifurcation phenomena, including transcritical and saddle-node transitions. Numerical investigations further illustrate the emergence of hysteresis loops, indicating bistability within specific parameter ranges. Experimental observations concerning the predation of Bemisia tabaci by Orius albidipennis validate the Holling type-III assumption and serve to parameterize the theoretical model. The findings underscore the dual impact of additional food and predator competition in shaping biological control outcomes and improving pest suppression efficiency.