Study of the interactive effect of prey toxin and optimal foraging strategy on a predator-prey model

The optimal foraging theory predicts that predators choose prey with more net rate of energy intake and less energy costs if there are multiple food sources available. Toxins are found in many species in nature. Those toxins may be produced by prey as self- protection from predatory animals, or come from other sources such as pesticide residue. Therefore, it requires a balance between energy intake and toxicity damage. In order to study the interactive effect of prey toxin and optimal foraging strategy, we construct a predator-prey model with toxin-induced functional response and optimal foraging property. Dynamical analysis shows that the optimal strategy system presents more complex dynamical behavior than the fixed preference system. We conclude that optimal foraging strategy might play a key role in stabilizing or destabilizing the coexistence states of the species in the system, depending on the level of prey toxins.