Stability and Hopf bifurcation in a reaction–diffusion predator–prey system with interval biological parameters and stage structure

Abstract

This paper deals with a delayed reactiondiffusion predator-prey system combined with stage structure for prey and interval biological parameters. By taking the sum of delays as the bifurcation parameter, the local stability of the equilibrium points is investigated and the condition of Hopf bifurcation is obtained. In succession, using the normal form theory and the center manifold reduction for partial functional differential equations, we derive the explicit formulas determining stability, direction and other properties of bifurcating periodic solutions. Some numerical simulations are also included to illustrate our theoretical results.

Influence of impreciseness in designing tritrophic level complex food chain modeling in interval environment

“…For example, Pal et al [36] studied a predator-prey model with interval biological parameters; De et al [37] presented stability analysis of combined project of fish, broiler, and ducks in imprecise environment; Zhang and Zhao [38] studied a diffusive predator-prey system with delays and interval biological parameters to obtain a sustainable optimal harvesting policy; Sharma and Samanta [39] presented a two-species com- petition model where the model parameters are taken as interval numbers. Many other notable works in this regard can be found in [40][41][42][43][44][45].…”