Chaotic dynamics in tritrophic interaction with volatile compounds in plants with power law kernel

Abstract

In this article, we study a fractional-order mathematical model representing tritrophic interaction amongst plants, herbivores, and carnivores with Caputo derivative. The existence and uniqueness of the system are investigated by fixed point theory, while the stability is studied by Hyers-Ulam and generalized Hyers-Ulam stability analysis. The Adams-Bashforth-Moulton scheme is used for numerical calculations. From numerical simulations, it is observed that when the fractional order decreases the system converges to a stable state. It is observed that for a small value of fractional order, the system approaches a stable state rapidly as compared to the integer order. The chaotic behaviour of the system is studied using the Lyapunov spectrum. It is noted that two positive exponents of the proposed model show that the system is hyper-chaotic. It is also observed that a small value of attraction constant disrupts the system due to volatile organic compounds.