Exploring population oscillations: Cross-coupling and dispersal effects in prey–predator dynamics

Abstract

In this investigation, we explore the dynamics of a predator–prey metapopulation model with two identical patches, emphasizing the coupling mechanism through the predators’ dispersal. The coupling mechanism is a particular case of nearest-neighbor coupling, defined by cross-predation, which depicts the fact that the predators have alternative food resources. The study focuses on how dispersion rates and cross-predation affect species coexistence and system dynamics induced by different kinds of bifurcations associated with periodic orbits and stable states. We examined the structural organization of attractors using bifurcation theory and discovered a variety of intricate dynamics, such as symmetric, asymmetric, boundary, and asynchronous attractors. The onset of synchronous and asynchronous dynamical attractors associated with periodic orbits are analyzed by varying the level of coupling strength and the degree of dispersal rates. Another intriguing phenomenon that occurs in our system is the formation of chaotic attractors with asymmetric dynamics from quasi-periodicity as a result of the Neimark-Sacker (NS) bifurcation. We elucidate the emergence and suppression of chaos using the Poincare return map concept. Our system also exhibits intriguing phenomena, such as bistability and multistability, which indicate that it is capable of preserving ecological diversity and enhancing the level of population persistence. Finally, our findings demonstrate that the system’s dynamics are substantially diverse when the dispersal rate is low with limited coupling strengths. The conclusions have a significant impact on the fields of population and evolution science, improving our knowledge of the complex dynamics found in dispersed ecosystems.