Complex spatiotemporal dynamics in an eco-epidemic model: Turing instability, non-stationary patterns, and chaos control

This study presents the formulation of a spatiotemporal eco-epidemic model that takes into account an infectious disease affecting the prey population incorporating prey refugees and intraspecific competition of predators. In this work, we mainly focus on the interior equilibrium, which exists depending on the values of system parameters. In the absence of diffusion, our system shows rich dynamics, like Hopf bifurcation, chaos, etc. We analytically investigate the potential conditions for Turing instability in the context of diffusion. During numerical verification of our theoretical results, we see some non-stationary patterns along with the stationary pattern. By obtaining the Maximum Lyapunov exponent, we confirmed that the non-stationary pattern is chaotic. In addition, it is to be noted that maintaining ecosystem stability, preventing unpredictable population fluctuations, and ensuring the sustainability of species and resources all depend on controlling chaos in ecological models. For this purpose, we apply time-delay feedback control and successfully stabilize the spatiotemporal chaos.