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

2015 ◽  
Vol 25 (08) ◽  
pp. 1550107 ◽  
Author(s):  
Shanshan Chen ◽  
Junjie Wei
Keyword(s):  
Boundary Condition ◽  
Hopf Bifurcation ◽  
Dirichlet Boundary Condition ◽  
Population Model ◽  
Dirichlet Boundary ◽  
Positive Equilibrium ◽  
Multiple Delays ◽  
Stability And Bifurcation ◽  
The Stability

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.

scholarly journals Global Attractivity of a Diffusive Nicholson's Blowflies Equation with Multiple Delays

2013 ◽  
Vol 2013 ◽  
pp. 1-6
Author(s):  
Xiongwei Liu ◽  
Xiao Wang
Keyword(s):  
Boundary Condition ◽  
Neumann Boundary Condition ◽  
Global Attractivity ◽  
Neumann Boundary ◽  
Positive Equilibrium ◽  
Multiple Delays ◽  
Open Problems ◽  
Nicholson’S Blowflies Equation ◽  
Trivial Equilibrium ◽  
The Stability

The present paper considers a diffusive Nicholson's blowflies model with multiple delays under a Neumann boundary condition. Delay independent conditions are derived for the global attractivity of the trivial equilibrium and the positive equilibrium, respectively. Two open problems concerning the stability of positive equilibrium and the occurrence of Hopf bifurcation are proposed.

scholarly journals On some classes of generalized Schrödinger equations

2020 ◽  
Vol 10 (1) ◽  
pp. 522-533
Author(s):  
Amanda S. S. Correa Leão ◽  
Joelma Morbach ◽  
Andrelino V. Santos ◽  
João R. Santos Júnior
Keyword(s):  
Boundary Condition ◽  
Dirichlet Boundary Condition ◽  
Dirichlet Boundary ◽  
Laplacian Operator ◽  
Schrodinger Equations ◽  
Schrödinger Equations ◽  
Nontrivial Solutions ◽  
Homogeneous Dirichlet Boundary Condition ◽  
Stationary Problems

Abstract Some classes of generalized Schrödinger stationary problems are studied. Under appropriated conditions is proved the existence of at least 1 + $\begin{array}{} \sum_{i=2}^{m} \end{array}$ dim Vλi pairs of nontrivial solutions if a parameter involved in the equation is large enough, where Vλi denotes the eigenspace associated to the i-th eigenvalue λi of laplacian operator with homogeneous Dirichlet boundary condition.

scholarly journals Stability and Hopf Bifurcation in a Delayed SEIRS Worm Model in Computer Network

2013 ◽  
Vol 2013 ◽  
pp. 1-9 ◽  
Author(s):  
Zizhen Zhang ◽  
Huizhong Yang
Keyword(s):  
Hopf Bifurcation ◽  
Computer Network ◽  
Sufficient Conditions ◽  
Positive Equilibrium ◽  
Normal Form Theory ◽  
Center Manifold Theorem ◽  
Local Hopf Bifurcation ◽  
Form Theory ◽  
Worm Model ◽  
The Stability

A delayed SEIRS epidemic model with vertical transmission in computer network is considered. Sufficient conditions for local stability of the positive equilibrium and existence of local Hopf bifurcation are obtained by analyzing distribution of the roots of the associated characteristic equation. Furthermore, the direction of the local Hopf bifurcation and the stability of the bifurcating periodic solutions are determined by using the normal form theory and center manifold theorem. Finally, a numerical example is presented to verify the theoretical analysis.

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