Dynamics and Bifurcations in a Two-Species Ricker Competition Model With Nonmonotonic Growth

This study investigates the dynamics of a discrete-time competition model involving two species with nonmonotonic growth rates. The system is formulated through coupled Ricker-type equations that incorporate both intraspecific and interspecific interactions. This part of the work deals with two fundamental properties: boundedness of the solutions and permanence of the system, which hold provided the parameters are chosen within suitable regimes. All equilibria are examined carefully for their local stability. For the interior equilibrium, explicit conditions are derived for the occurrence of flip and Neimark–Sacker bifurcations. Numerical simulations reveal a rich variety of dynamical behaviors, including stable period-two cycles, quasiperiodic oscillations, and chaotic dynamics arising through the period-doubling route, which are further verified by the corresponding maximum Lyapunov exponent (MLE) spectra. Unlike previous studies that mainly investigate isolated dynamical properties, the present work integrates rigorous persistence analysis, explicit bifurcation theory, global parameter-space exploration, period-two solution analysis, and numerical evidence of chaos within a unified framework, thereby providing a more comprehensive understanding of two-species Ricker competition dynamics with nonmonotonic growth.