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

http://jxshix.people.wm.edu/shi/09-Yi-Wei-Shi-JDE.pdf

Bifurcation and spatiotemporal patterns in a homogeneous diffusive predator–prey system

/pdf/stability-and-bifurcation-in-a-neural-network-model-with-two-pupxglej9g.pdf

Stability and bifurcation in a neural network model with two delays

Global bifurcation analysis of a class of general predator–prey models with a strong Allee effect in prey population is given in details. We show the existence of a point-to-point heteroclinic orbit loop, consider the Hopf bifurcation, and prove the existence/uniqueness and the nonexistence of limit cycle for appropriate range of parameters. For a unique parameter value, a threshold curve separates the overexploitation and coexistence (successful invasion of predator) regions of initial conditions. Our rigorous results justify some recent ecological observations, and practical ecological examples are used to demonstrate our theoretical work.

/pdf/predator-prey-system-with-strong-allee-effect-in-prey-5gqon3d54k.pdf

Predator–prey system with strong Allee effect in prey

In this paper, we first study the distribution of the zeros of a third degree exponential polynomial. Then we apply the obtained results to a delay model for the control of testosterone secretion. It is shown that under certain assumptions on the coefficients the steady state of the delay model is asymptotically stable for all delay values. Under another set of conditions, there is a critical delay value, the steady state is stable when the delay is less than the critical value and unstable when the delay is greater than the critical value. Thus, oscillations via Hopf bifurcation occur at the steady state when the delay passes through the critical value. Numerical simulations are presented to illustrate the results.

/pdf/on-the-zeros-of-a-third-degree-exponential-polynomial-with-2bg33oms7t.pdf

Junjie Wei

Papers

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

Bifurcation and spatiotemporal patterns in a homogeneous diffusive predator–prey system

Stability and bifurcation in a neural network model with two delays

Predator–prey system with strong Allee effect in prey

On the zeros of a third degree exponential polynomial with applications to a delayed model for the control of testosterone secretion.