Critical values of stability and Hopf bifurcations for a delayed population model with delay-dependent parameters

2010 ◽  
Vol 11 (1) ◽  
pp. 341-355 ◽  
Author(s):  
Li Fan ◽  
Zhongke Shi ◽  
Sanyi Tang
Keyword(s):  
Population Model ◽  
Critical Values ◽  
Hopf Bifurcations ◽  
Delay Dependent ◽  
Delayed Population Model

Stability switches and Hopf bifurcations of an isolated population model with delay-dependent parameters

2015 ◽  
Vol 264 ◽  
pp. 99-115
Author(s):  
Min Xiao ◽  
Guoping Jiang ◽  
Lindu Zhao ◽  
Wenying Xu ◽  
Youhong Wan ◽  
...  
Keyword(s):  
Population Model ◽  
Hopf Bifurcations ◽  
Isolated Population ◽  
Stability Switches ◽  
Delay Dependent

Traveling Waves Connecting Equilibrium and Periodic Orbit for a Delayed Population Model on a Two-Dimensional Spatial Lattice

2016 ◽  
Vol 26 (03) ◽  
pp. 1650049 ◽  
Author(s):  
Cui-Ping Cheng ◽  
Wan-Tong Li ◽  
Zhi-Cheng Wang ◽  
Shenzhou Zheng
Keyword(s):  
Periodic Orbit ◽  
Traveling Waves ◽  
Population Model ◽  
Traveling Wave Solution ◽  
Heteroclinic Orbits ◽  
Two Dimensional ◽  
Regular Perturbation ◽  
Perturbation Problem ◽  
Spatial Lattice ◽  
Delayed Population Model

This paper is concerned with the existence of fast traveling waves connecting an equilibrium and a periodic orbit in a delayed population model with stage structure on a two-dimensional spatial lattice, under the assumption that the corresponding ODEs have heteroclinic orbits connecting an equilibrium point and a periodic solution. In this work, we rewrite the mixed functional differential equation as an integral equation in a Banach space and analyze the corresponding linear operator. Our approach eventually reduces a singular perturbation problem to a regular perturbation problem. The existence of traveling wave solution therefore is obtained by using the Liapunov–Schmidt method and implicit function theorem.

scholarly journals Dynamic Properties of the Solow Model with Increasing or Decreasing Population and Time-to-Build Technology

2013 ◽  
Vol 2013 ◽  
pp. 1-7 ◽  
Author(s):  
Luca Guerrini ◽  
Mauro Sodini
Keyword(s):  
Population Dynamics ◽  
Dynamic Properties ◽  
Hopf Bifurcations ◽  
Solow Model ◽  
Dynamic Features ◽  
Stability Switches ◽  
Time To Build ◽  
Delayed Differential Equations ◽  
Delay Dependent ◽  
Equations With Delay

We introduce a time-to-build technology in a Solow model with nonconstant population. Our analysis shows that the population dynamics may be a source of stability switches and Hopf bifurcations. The analytical results are obtained using the recent technique introduced by Beretta and Kuang (2002) in the studying of delayed differential equations with delay-dependent coefficients in characteristic equation. Numerical simulations are performed in order to illustrate the main dynamic features of the model.

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