Stability Analysis and Controlling Chaos of Fractional-Order Three-Species Food Chain Model with Fear

Abstract

In this article, stability analysis and chaos control of three species food chain model have been studied in the fractional order case. The fractional order three-species food chain model with fear term is the extension work of Panday et al. (Int J Bifurc Chaos 28:1850009, 2018), where they discussed the stability analysis and control of chaos of the model under several conditions. The stability analysis is done using Routh–Hurwitz condition and Matignon theorem for fractional order differential equations. The analysis has been done for the fractional-order of a three species food chain model with and without fear terms k1 and k2. If the fear terms are neglected in the considered model then the model is reduced to Hastings-Powell model. The chaos control is done using Lyapunov stability theory, the equilibrium points of the system are computed and stability is obtained in the system. The results are obtained through numerical simulation. © 2021, The Author(s), under exclusive licence to Springer Nature India Private Limited.