Symmetry breaking in a metapopulation model with fitness-dependent dispersal

This study investigates the emergence of symmetry-breaking dynamics and the associated bifurcation behavior in an identically coupled Rosenzweig-MacArthur model with fitness-dependent dispersal between patches. We identify the occurrence of a symmetry-breaking (SB) state, characterized by the difference in the amplitude of oscillations across patches, signifying a form of desynchronization that supports species persistence. As the predator dispersal rate is varied, the SB state undergoes a sequence of dynamical transitions, alternating between chaotic symmetry breaking (CSB) and periodic symmetry breaking (PSB) states, and it includes the emergence of periodic windows that occur within chaotic windows across the dispersal rate. The alternating chaotic and periodic nature of SB dynamics is confirmed with the help of Lyapunov exponent analysis. In addition to the SB state, we observed antiphase synchronized (APS) and in-phase synchronized (IPS) states. To further understand the impact of initial conditions on distinct dynamical outcomes, we explore the basins of attraction within multistable regions. Finally, the stability of the APS, PSB, and IPS states is analyzed using Floquet analysis.