Partial Prey Migration as a Non-autonomous Harmonic Oscillator: Chaos-Order Transitions in a Forced Classical Lotka-Volterra Model

I investigate how partial prey migration cycles, analogous to a non-autonomous harmonic oscillator, force the classical Lotka-Volterra model and reshape predator-prey interactions. A 3D nonlinear system is introduced, into which the external forcing replicates the entry and exit of partial migrants from the ecosystem, devoid feedback loops. Numerical simulations reveal an elusive resilience contour of the species interplay under stationary migration cycles. Thus, quasi-periodic and chaotic fluctuations appear at a minimum migration magnitude, vanishing beyond a bifurcation-induced tipping point. However, resilient interactions surge in localized hotspots, i.e., narrow regions of phase space and forcing intensity. It is striking to note that the detected chaos exhibits a threefold complexity related to migration magnitude, initial conditions, and a functional response parameter, implying a basin of attraction intertwined at fractal boundaries. In contrast, the resilience non-monotonicity fades due to ascending cycles of partial prey migration involving recruitment of a cohort of migrants by its resident species. In this case, chaos is suppressed, leading to predictable oscillations and phase-locking. Even extreme predator-prey ratios (e.g., 10:1) do not endanger prey. Despite its parsimony, the framework offers a tractable prototype with broader ecological applicability for studying how exogenous forcings (e.g., climate-driven phenology), can alter ecosystems.