A brief survey of persistence in dynamical systems
Delay differential equations and dynamical systems
Dynamic behaviors of a delay differential equation model of plankton allelopathy
Journal of Computational and Applied Mathematics
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Persistence and global stability of the coexistence equilibrium of a recently published model in biocontrol of crops are here shown both in the absence and the presence of delays, introduced to simulate the handling time of the prey. In the latter case, the system can behave in two different ways, in dependence of whether a suitably defined key parameter exceeds a certain threshold. Namely, below the threshold the delay is shown not to be able to influence the stability of the coexistence equilibrium; above it, existence of a Hopf bifurcation is analytically proven. Further, in this range, numerical simulations reveal a route to chaotic behavior as function of the size of the delay. Some operative conclusions for agroecosystem management are drawn, although they ultimately depend on each particular situation.