Species coexistence and chaotic behavior induced by multiple delays in a food chain system

In this paper, we present a food chain system composed of three species (resource, consumer and predator). Food digested periods corresponding to consumer-eat-resource and predator-eat-consumer are introduced for more realistic consideration, which are called resource digested delay (RDD) and consumer digested delay (CDD), respectively. In order to explore the combined influence of multiple delays on population dynamics, two different scenarios were explored, i.e. the intrinsic growth rate of resource is less/more than consumer and predator. In case 1, some types of species coexistence characterized by RDD and CDD independent are illustrated by the corresponding characteristic equation. Multiple delays can promote and suppress the recurrent bloom of species population, which is called the stability switching of species coexistence. In case 2, using RDD and CDD as the varying parameters, complex dynamical behaviors including multiple periodic motion and chaotic behavior are exhibited in detail by employing some numerical simulations, such as phase trajectory, power spectra, and bifurcation diagram. The population dynamics exhibit chaos behavior and then evolve into system collapse for species outbreak. Further, greater RDD and CDD make system population enter into system collapse easier.