Topological description of a non-differentiable bioeconomics model

A predator-prey model with non-differentiable functional response and with a Cobb-Douglas type production function is considered. We show that the non-differentiability has a strong influence on the dynamics of the model, locally and globally. We prove that there is not a uniqueness of solutions for any initial conditions on the coordinate axis. We conclude that for any conditions of the parameters, the dynamics of the model does not contain a globally attracting singularity. Finally, in the parameters space, we prove the existence of an open set such that, for all values in this set, the model has at least two small amplitude limit cycles generated by Hopf bifurcations.