Demographic stochasticity in predator-prey (or activator-inhibitor) systems can generate persistent oscillations driven by intrinsic fluctuations, even when the corresponding deterministic mean-field descriptions exhibit only damped oscillations that vanish asymptotically as the system approaches a stable fixed point. Here we demonstrate that sustained stochastic oscillations may also emerge when the prey population responds deterministically to fluctuations in the predator population. In this framework, predator dynamics is governed by a stochastic process, whereas prey dynamics obeys an equation that is continuous in both time and population density, as expected in the limit of a large, homogeneous prey population. We compare the behavior of this hybrid stochastic-deterministic system with that of its mean-field counterpart and quantitatively characterize the resulting stochastic oscillatory regime, with particular emphasis on its dependence on the predator population size and the prey response time.

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• Fluctuations & noise
• Population dynamics
• Stochastic processes