A comparative study of deterministic and stochastic dynamics for a non-autonomous allelopathic phytoplankton model

In this paper, we investigate a non‐autonomous competitive phytoplankton model with periodic coefficients in deterministic and stochastic environment, respectively. We prove the existence of at least one positive periodic solution together with it’s global asymptotic stability. The existence of periodic solution has been obtained by using the continuation theorem of coincidence degree theory proposed by Gaines and Mawhin. We formulate the corresponding stochastic model by perturbing the growth rate parameters by white noise terms. We prove that all the higher order moments of the solution to the stochastic system is uniformly bounded which ensure that the solution of the stochastic system is stochastically bounded. We provide easily verifiable sufficient conditions for non‐persistence in mean, extinction and stochastic permanence of the stochastic system. Sufficient condition for permanence shows that if the noise intensity is very low then the solution of the stochastic system persists in the periodic coexistence domain of the deterministic system. We perform exhaustive numerical simulations to validate our analytical findings.