Predator-Induced Fear Promotes Native Prey Synchrony and Stabilizes a Chaotic Food Chain under Apparent Competition

This study develops a three-species ecological model comprising a native prey, an invasive prey, and a common predator feeding on both prey populations. The model is designed to investigate the complex dynamics that may arise when a native species is exposed simultaneously to biological invasion and shared predation. The occurrence of chaos is examined through sensitive dependence on initial conditions and the maximum Lyapunov exponent, with a positive maximum Lyapunov exponent confirming chaotic dynamics.
Unlike conventional approaches that primarily consider refuge as a mechanism for prey persistence, this study investigates whether the native prey can persist in a chaotic environment through phase synchronization with the predator. In particular, we incorporate an adaptive response term in the native-prey growth dynamics to represent a predator-induced fear mechanism. Such an adaptive response allows the native population to modify its growth dynamics in accordance with variations in perceived predation risk and facilitate a coordinated temporal response to predator fluctuations.
Bifurcation analysis is employed to examine how the strength of this fear-mediated adaptive response influences the long-term dynamics of the system as key ecological parameters vary.  Numerical simulations show that the proposed mechanism can promote phase synchronization between the native prey and the predator, thereby preventing severe declines of the native population and supporting its persistence despite predation-driven apparent competition with the invasive prey. Importantly, the stabilization reported here refers to the maintenance of species persistence and coexistence rather than to the suppression of chaotic dynamics. The system may therefore remain dynamically chaotic while all three species continue to coexist within bounded population ranges. These findings suggest that predator-induced adaptive responses and synchronization may provide an alternative dynamical pathway for the persistence of native species in invasion-prone and complex ecological systems.

In particular, we incorporate an adaptive response term in the native-prey growth dynamics to represent a predator-induced fear mechanism. The term describes a phenomenological, fear-mediated adjustment of the native prey to changes in predator abundance, rather than implying cognitive intelligence.