Transitions induced by correlated Gaussian and non-Gaussian noises in a single-species model with Allee effect and aposematism

Stochastic forces can induce surprising dynamic phenomena that are absent in deterministic frameworks. In this study, we analyze a stochastic single-species model that integrates both the Allee effect and aposematism, subject to correlated non-Gaussian and Gaussian noises. By approximating the original non-Markovian system into a Markovian form, we derive an analytical expression for the stationary probability distribution (SPD). We then characterize state transitions through phenomenological bifurcation (P-bifurcation) and quantify extinction risks via the mean first passage time (MFPT). Our results show that both stochastic and biological parameters can qualitatively alter the SPD and induce P-bifurcations, independent of the noise correlation λ. Moreover, aposematism serves not only as an effective anti-predator strategy but also promotes population growth under λ≤0. Noise-induced bistability emerges only within specific parameter ranges, most notably at intermediate levels of aposematism. We further observe noise-enhanced stability (NES) under non-Gaussian noise with λ<0, indicating that moderate multiplicative noise can effectively prolong population persistence. Finally, based on the depth of the potential well, we evaluate the stability and resilience of the attractor.