Analysis of three species Lotka–Volterra food web models with omnivory

In this work, we consider a three species Lotka–Volterra food web model with omnivory which is defined as feeding on more than one trophic level. Based on a non-dimensional transformation, the model actually becomes a system of three first order ordinary differential equations with seven parameters. Analytically, we completely classify the parameter space into three categories containing eight cases, show the extinction results for five cases, and verify uniform persistence for the other three cases. Moreover, in the region of the parameter space where the system is uniformly persistent we prove the existence of periodic solutions via Hopf bifurcation and present the chaotic dynamics numerically. Biologically, the omnivory module blends the attributes of several well-studied community modules, such as food chains (food chain models), exploitative competition (two predators–one prey models), and apparent competition (one predator–two preys models). We try to point out the differences and similarities among these models quantitatively and give the biological interpretations.