Hopf Bifurcation and Stability Crossing Curve in a Planktonic Resource–Consumer System with Double Delays

Abstract

In this paper, a planktonic resource–consumer system with two delays is investigated and the coefficients depend on [Formula: see text] one of the two delays. Firstly, the property of solution and the existence of equilibrium are given. The dynamical analysis of the system including stability and Hopf bifurcation by using the delays as parameters is carried out. Both the single delay and two delays can cause the system to produce Hopf bifurcation and the stable switching phenomena may exist. Furthermore, using the crossing curve methods, we obtain the stable changes of equilibrium in two-delay parameter plane, which generalizes the results of the system that the coefficients do not depend on delay. Furthermore, the numerical simulation results show that the theoretical analyses are correct when the delays change.