Junjie Wei

TL;DR: In this paper, the dynamics of a reaction-diffusion predator-prey system with strong Allee effect in the prey population is considered and nonexistence of nonconstant positive steady state solutions are identified.

TL;DR: In this paper, a reaction-diffusion population model with a general time-delayed growth rate per capita is considered, and the stability of the positive steady state solution and the existence of forward Hopf bifurcation from the positive stable state solution are obtained via the implicit function theorem.

Abstract: The dynamics of a Nicholson's blowflies equation with a finite delay are investigated. We prove that a sequence of Hopf bifurcations occur at the positive equilibrium as the delay increases. Explicit algorithm for determining the direction of the Hopf bifurcations and the stability of the bifurcating periodic solutions are derived, using the theory of normal form and center manifold. Global existence of periodic solutions are established using a global Hopf bifurcation result of Wu (Trans. Amer. Math. Soc. 350 (1998) 4799), and a Bendixson criterion for higher dimensional ordinary differential equations due to Li and Muldowney (J. Differential Equations 106 (1994) 27).

TL;DR: In this article, a detailed Hopf bifurcation analysis of the CIMA reaction was performed for both ODE and PDE models, and conditions for determining the bifurlcation direction and the stability of the bifting periodic solution were derived.

TL;DR: In this article, the authors considered a planar system with two delays and derived existence conditions for non-constant periodic solutions using degree theory methods, where linearized stability and local Hopf bifurcations were studied.