Sliding Shilnikov Connection in Filippov-type Predator-Prey Model

TL;DR

This paper proves the existence of a Shilnikov sliding connection in a predator-prey model, analytically demonstrating chaotic behavior in a specific parameter region of a piecewise smooth differential system.

Contribution

It provides the first analytical proof of chaos via a Shilnikov sliding connection in a Filippov-type predator-prey model, extending previous numerical evidence.

Findings

Existence of a Shilnikov sliding connection in the model.

Chaotic behavior is analytically confirmed in an open parameter region.

The model exhibits complex dynamics due to the sliding connection.

Abstract

Recently, a piecewise smooth differential system was derived as a model of a 1 predator-2 prey interaction where the predator feeds adaptively on its preferred prey and an alternative prey. In such a model, strong evidence of chaotic behavior was numerically found. Here, we revisit this model and prove the existence of a Shilnikov sliding connection when the parameters are taken in a codimension one submanifold of the parameter space. As a consequence of this connection, we conclude, analytically, that the model behaves chaotically for an open region of the parameter space.