Dynamical and structural study of a generalized Caputo fractional order Lotka-Volterra model

Abstract

In this study, we generalize the Lotka-Volterra (LV) model. Our generalization is done via two simultaneous techniques. The first technique is done by incorporating a general term to model the immigrations to the predator or prey populace. The second technique is to utilize the Caputo fractional derivative. This study is done via different five cases. We show the impact of changing the fractional order to the proposed model response. We display that including a generalized immigration to the predator or prey populace produces stabilization of the LV model in context of Caputo fractional derivatives in all executed cases. In addition, we present the generalized model via graph and utilizing the graph theory concepts, we display several hidden features of the model.

Keywords

• Caputo fractional derivative
• Lotka-Volterra model
• Dynamical system graph
• Fractional stability
• Hermitian energy of model graph