Periodicity induced by state feedback controls and driven by disparate dynamics of a herbivore-plankton model with cannibalism

Plankton and herbivore in aquatic ecosystems are often deeply disturbed by human exploitations in impulsive patterns. In this paper, for a herbivore-plankton interaction model with cannibalism, firstly, the complex dynamic behaviors including the number, the existence and stability of internal equilibriums, the limit and homoclinic cycles, Hopf, saddle node, Pitchfork and Bogdanov-Takens bifurcations are investigated roughly. Furthermore, multiple state feedback controls are implemented so that three order-one periodic solutions (OOPSs) and heteroclinic bifurcation driven by disparate dynamics are induced, respectively. By the method of Bendixson theorem and successor function, the existences of OOPSs are proved. Finally, for the corresponding small parameter-perturbed system, B-convergent of OOPS and homoclinic bifurcation are investigated by the variational equation and the rotated vector, respectively.