Time-delayed and stochastic effects in a predator–prey model with ratio dependence and Holling type III functional response

In this article, we derive and analyze a novel predator–prey model with account for maturation delay in predators, ratio dependence, Holling type III functional response. The analysis of the system’s steady states reveals conditions on predation rate, predator growth time that can result prey-only equilibrium or facilitate simultaneous survival prey predators form stable coexistence state, sustain periodic oscillations around state. Demographic stochasticity is explored by means deriving delayed chemical master equation. Using system size expansion, study structure stochastic deterministically state analyzing dependence variance coherence parameters. Numerical simulations are performed to illustrate amplification, where individual realizations exhibit sustained case, approaches These results provide framework studying realistic systems response presence stochasticity, an important role played non-negligible delay.