Refuge-driven spatiotemporal chaos in a discrete predator-prey system

The driving mechanism of spatiotemporal chaos is one of the most important questions in the dynamics of predator-prey systems. In this paper, we investigate the spatiotemporal chaotic behaviors driven by refuge effect and their complexity in a Lotka-Volterra discrete predator-prey system. By choosing refuge effect as the bifurcation parameter, the existence conditions of Neimark-Sacker and flip bifurcations near the stable equilibrium point are analyzed. The bifurcation diagrams, maximum Lyapunov exponents, phase diagrams, diagrams of space-amplitude and space-time, spatial return maps and Kolmogorov-Sinai entropy are used to analyze the complex dynamical behaviors of the system. The results show that the refuge effect has a two-way effect on the stability of the system, and both Neimark-Sacker and flip bifurcations caused by it open the route to chaos. The increase in unpredictability of chaotic attractors makes the system increasingly chaotic characteristics. In addition, the characteristics of spatiotemporal dynamics on the route to chaos are captured. The chaotic behaviors of the system on the two types of bifurcations show transitions among several generic features, including frozen random pattern, defect chaotic diffusion pattern, pattern competition intermittency and fully developed turbulence. Our study promotes the understanding of the complex spatiotemporal dynamics of refuge-driven spatiotemporal chaos in predator-prey systems.