关于Semigroups of Linear Operators and Applications to Partial Differential Equations的两个注解

Differential-Difference Equations. By Richard Bellman and Kenneth L. Cooke. Pp. xvi, 465. 1963. (Academic Press)

Nonlinear Oscillations: Exact Solutions and their Approximations

In this paper, we first establish a basic theorem on the zeros of general transcendental functions. Based on the basic theorem, we develop a decomposition technique to investigate the stability of some exponential polynomials, that is, to find conditions under which all zeros of the exponential polynomials have negative real parts. The technique combines the D-decomposition and τ -decomposition methods so that it can be used to study differential equations with multiple delays. As an application, we study the stability and bifurcation of a scalar equation with two delays modeling compound optical resonators.

On the zeros of transcendental functions with applications to stability of delay differential equations with two delays

In what case do you like reading so much? What about the type of the complex population dynamics a theoretical empirical synthesis book? The needs to read? Well, everybody has their own reason why should read some books. Mostly, it will relate to their necessity to get knowledge from the book and want to read just to get entertainment. Novels, story book, and other entertaining books become so popular this day. Besides, the scientific books will also be the best reason to choose, especially for the students, teachers, doctors, businessman, and other professions who are fond of reading.

Complex Population Dynamics: A Theoretical/Empirical Synthesis

We investigate Hopf bifurcations in a delayed Nicholson’s blowflies equation of neutral type, derived from the Gurtin–MacCamy model. A key parameter that determines the direction of the Hopf bifurcation and the stability of the bifurcating periodic solutions is derived. Global extension of local Hopf branches is established by combining a global Hopf bifurcation theorem with a Bendixson criterion for higher dimensional ordinary differential equations. We show that a branch of slowly varying periodic solutions and a branch of fast oscillating periodic solutions coexist for all large delays.

Global Hopf Bifurcation Analysis of a Nicholson’s Blowflies Equation of Neutral Type

In this paper, we consider the dynamics of a delayed reaction–diffusion mussel-algae system subject to Neumann boundary conditions. When the delay is zero, we show the existence of positive solutio...

Bifurcation Analysis in a Diffusive Mussel-Algae Model with Delay

A diffusive logistic population model with multiple delays and Dirichlet boundary condition is considered in this paper. The stability/instability of the positive equilibrium and delay induced Hopf bifurcation are investigated. Moreover, we show which kind of delay could actually affect the dynamics.

Stability and Bifurcation in a Diffusive Logistic Population Model with Multiple Delays

We
consider a family of partial functional differential equations
which has a homoclinic orbit asymptotic to an isolated equilibrium
point at a critical value of the parameter. Under some technical
assumptions, we show that a unique stable periodic orbit
bifurcates from the homoclinic orbit. Our approach follows the
ideas of Sil'nikov for ordinary differential equations and of
Chow and Deng for semilinear parabolic equations and retarded
functional differential equations.

/pdf/bifurcation-from-a-homoclinic-orbit-in-partial-functional-3wl7muyc2v.pdf

Bifurcation from a homoclinic orbit in partial functional differential equations

In this paper, we show the existence of a Hopf bifurcation in a delayed single population model with patch structure. The effect of the dispersal rate on the Hopf bifurcation is considered. Especially, if each patch is favorable for the species, we show that when the dispersal rate tends to zero, the limit of the Hopf bifurcation value is the minimum of the “local” Hopf bifurcation values over all patches. On the other hand, when the dispersal rate tends to infinity, the Hopf bifurcation value tends to that of the “average” model.

Junjie Wei

Papers

Global Hopf Bifurcation Analysis of a Nicholson’s Blowflies Equation of Neutral Type

Bifurcation Analysis in a Diffusive Mussel-Algae Model with Delay

Stability and Bifurcation in a Diffusive Logistic Population Model with Multiple Delays

Bifurcation from a homoclinic orbit in partial functional differential equations

Hopf Bifurcation of a Delayed Single Population Model with Patch Structure