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 harmonicoscillator, force the classical Lotka-Volterra model and reshape predator-prey interactions. A 3D nonlinearsystem is introduced, into which the external forcing replicates the entry and exit of partial migrants from theecosystem, devoid feedback loops. Numerical simulations reveal an elusive resilience contour of the speciesinterplay under stationary migration cycles. Thus, quasi-periodic and chaotic fluctuations appear at a minimummigration magnitude, vanishing beyond a bifurcation-induced tipping point. However, resilient interactionssurge in localized hotspots, i.e., narrow regions of phase space and forcing intensity. It is striking to note thatthe detected chaos exhibits a threefold complexity related to migration magnitude, initial conditions, and afunctional response parameter, implying a basin of attraction intertwined at fractal boundaries. In contrast, theresilience non-monotonicity fades due to ascending cycles of partial prey migration involving recruitment of acohort of migrants by its resident species. In this case, chaos is suppressed, leading to predictable oscillationsand 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 exogenousforcings (e.g., climate-driven phenology), can alter ecosystems.