Modeling Biomass-Transfer Kleptoparasitism in a Predator-Prey System with Active Prey Defense

Abstract

This study proposes a three-dimensional predator-prey model incorporating a biomass-transfer formulation for kleptoparasitism and active prey antipredator behavior. The well-posedness of the system is established by confirming the existence, uniqueness, positivity, and boundedness of the solutions. Local and global stability analyses are performed to determine the analytical threshold conditions governing species persistence and extinction. Numerical simulations are subsequently conducted to verify the stability results and illustrate the system dynamics. The numerical observations indicate that a low kleptoparasitism intensity results in the extinction of the kleptoparasite due to insufficient energy gain. A moderate kleptoparasitism intensity permits stable coexistence but introduces bistability, making the long-term behavior dependent on initial population sizes. As the kleptoparasitism intensity increases further, the system loses its stable coexistence state and exhibits sustained population oscillations. At highly elevated kleptoparasitism intensity, the host predator population is significantly suppressed, which dampens the oscillations and allows the system to settle into a stable equilibrium. Numerical exploration of the parameter space suggests a trade-off between the interacting species: as prey defense strengthens, a higher stealing intensity is required for the kleptoparasite to survive, although the parameter region supporting stable coexistence remains narrow.