Strong resonance bifurcations of a discrete Nicholson's blowf lies model with proportional delay
Population models have long been a focus of many researchers in the field of dynamical systems.Particularly,the discrete Nicholson's blowflies model with proportional delay have attracted much attention due to its periodic oscillation.For the stability and co-dim 1 bifurcation of this model,many references exist.In this paper,we further discuss the co-dim 2 bifurcation and resonance of this model.First,the stability of two fixed points of model is briefly described.Then the parameter conditions for the model undergoing reso-nances 1∶3 and 1∶4 at the positive fixed point and their normal form coefficients along with its scenario are dis-cussed by using the normal form theory.Finally,bifurcation of the model is illustrated.Here we mention that the study of bifurcation and resonance can help us understand the effect of interaction among species on biodi-versity and ecosystem stability and aid us predict and manage dynamic changes in ecosystems.
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