Population dynamics of biological synchronous reproduction and the effects of synchronous reproductive cycle on population dynamics

Population dynamics and reproductive cycles are fundamental aspects of biological systems, with profound implications for species survival and ecosystem stability. Synchronous reproduction, a phenomenon observed across various taxa, optimizes breeding success and offspring survival but may also introduce complex dynamics under changing environmental conditions. However, there is a scarcity of reports on the impact of synchronous reproduction on population dynamics. This study investigates the influence of synchronous reproductive cycles on population dynamics, with a focus on bifurcation phenomena such as Hopf and period-doubling bifurcations. By employing a series of ordinary differential equation (ODE) models and their discrete difference equation (DDE) counterparts, we analyze the synergistic effects of the reproductive cycle and control parameters on population stability and oscillatory behavior. Numerical simulations demonstrate that synchronous reproduction induces systematic shifts in bifurcation diagrams within the parameter space. Specifically, an increase in reproductive cycle amplifies the displacement of bifurcation curves, revealing that reproductive cycle and control parameters jointly regulate population dynamics. Our results offer actionable guidance for ecosystem management by demonstrating that maintaining or adjusting reproductive synchrony could serve as a leverage point for stabilizing vulnerable populations. Specifically, conservation strategies targeting species with synchronized breeding cycles should prioritize habitat preservation during critical reproductive windows and incorporate climate-driven shifts in reproductive timing into adaptive management frameworks.