Abstract: In this paper, applying frequency domain approach, a
delayed competitive web-site system is investigated. By choosing
the parameter α as a bifurcation parameter, it is found that Hopf
bifurcation occurs as the bifurcation parameter α passes a critical
values. That is, a family of periodic solutions bifurcate from the
equilibrium when the bifurcation parameter exceeds a critical value.
Some numerical simulations are included to justify the theoretical
analysis results. Finally, main conclusions are given.
Abstract: In this paper, a FitzHugh-Nagumo model with time delays is investigated. The linear stability of the equilibrium and the existence of Hopf bifurcation with delay τ is investigated. By applying Nyquist criterion, the length of delay is estimated for which stability continues to hold. Numerical simulations for justifying the theoretical results are illustrated. Finally, main conclusions are given.
Abstract: In this paper, applying frequency domain approach, a delayed predator-prey fishery model with prey reserve is investigated. By choosing the delay τ as a bifurcation parameter, It is found that Hopf bifurcation occurs as the bifurcation parameter τ passes a sequence of critical values. That is, a family of periodic solutions bifurcate from the equilibrium when the bifurcation parameter exceeds a critical value. The length of delay which preserves the stability of the positive equilibrium is calculated. Some numerical simulations are included to justify the theoretical analysis results. Finally, main conclusions are given.