Global periodic solutions in a plankton-fish interaction model with toxication delay

Abstract

AbstractIn this paper, a plankton-fish interaction model is proposed and analyzed with the help of delay differential equations. Firstly, the elementary dynamical properties of the system in the absence of time delay is discussed. Then, we have established the existence of local Hopf-bifurcation as the time delay crosses its threshold value. The explicit results for stability and direction of the bifurcating periodic solution are derived by using normal form theory and center manifold arguments. In addition, special attention is paid to the global continuation of local Hopf bifurcations. Using the global Hopf-bifurcation result of [38] for functional differential equations, we establish the global existence of periodic solutions. The outcomes of the system are validated through numerical simulations in the concluding section.