Bifurcation analysis in a predator–prey model for the effect of delay in prey

Abstract

In this paper, we study dynamics in a predator–prey model with delay, in which predator can be infected, with particular attention focused on nonresonant double Hopf bifurcation. By using center manifold reduction methods, we obtain the equivalent normal forms near a double Hopf critical point in this system. Moreover, bifurcations are classified in a two-dimensional parameter space near the critical point. Numerical simulations are presented to demonstrate the applicability of the theoretical results.

Dynamic Behaviors Analysis of Asymmetric Stochastic Delay Differential Equations with Noise and Application to Weak Signal Detection

“…It is seen from the relative errors that the theoretical analytical results agree quite well with those from numerical simulation. According to Equation (19), the amplitude of the weak signal of the asymmetric system (17) can be calculated as r = 0.01. Thus numerical simulation indicate the feasibility of using the asymmetric stochastic delay system with a Duffing oscillator to detect weak signal.…”

“…In addition, time delay is universal in nature. The dynamic analysis of the asymmetric delay differential system has attracted more and more scholarly attention [19][20][21][22]. However there is less research for asymmetric stochastic delay systems.…”