Fractional Order and Delay‐Induced Bifurcations in a Marine Ecosystem

ABSTRACT Using the memory effect of fractional derivatives, a new three‐dimensional fractional‐order marine ecosystem in the sense of the Caputo fractional derivative with a delay effect is excogitated, which can better understand the dynamics and interaction mechanisms of marine ecosystems. Firstly, we investigate the stability analysis of the equilibrium point and derive the transversal condition of Hopf bifurcation in such system by choosing the delay as a bifurcation parameter. Subsequently, some numerical simulations are performed to well substantiate the validity of our obtained theoretical results. We also show bifurcation diagrams of marine ecosystem with system parameter. The study reveals that fractional order and time delay play an important role in the bifurcation dynamics of marine ecosystems, especially Hopf bifurcation.