Multiparametric Bifurcation Analysis of a Basic Two-Stage Population Model

2006 ◽  
Vol 66 (4) ◽  
pp. 1339-1365 ◽  
Author(s):  
S. M. Baer ◽  
B. W. Kooi ◽  
Yu. A. Kuznetsov ◽  
H. R. Thieme
Keyword(s):  
Bifurcation Analysis ◽  
Population Model ◽  
Two Stage

Global Bifurcation Analysis of a Population Model with Stage Structure and Beverton–Holt Saturation Function

2015 ◽  
Vol 25 (12) ◽  
pp. 1550170 ◽  
Author(s):  
Li Fan ◽  
Sanyi Tang
Keyword(s):  
Bifurcation Analysis ◽  
Population Model ◽  
Birth Rate ◽  
Global Bifurcation ◽  
Stage Structure ◽  
Phase Portraits ◽  
Approximation Techniques ◽  
Codimension Two ◽  
Codimension One ◽  
Stage Transition

In the present paper, we perform a complete bifurcation analysis of a two-stage population model, in which the per capita birth rate and stage transition rate from juveniles to adults are density dependent and take the general Beverton–Holt functions. Our study reveals a rich bifurcation structure including codimension-one bifurcations such as saddle-node, Hopf, homoclinic bifurcations, and codimension-two bifurcations such as Bogdanov–Takens (BT), Bautin bifurcations, etc. Moreover, by employing the polynomial analysis and approximation techniques, the existences of equilibria, Hopf and BT bifurcations as well as the formulas for calculating their bifurcation sets have been provided. Finally, the complete bifurcation diagrams and associate phase portraits are obtained not only analytically but also confirmed and extended numerically.

scholarly journals Dynamics of Spruce budworms and single species competition models with bifurcation analysis

2020 ◽  
Vol 9 (6) ◽  
pp. 217-222
Author(s):  
Farah Tasnim ◽  
Md. Kamrujjaman
Keyword(s):  
North America ◽  
Mathematical Models ◽  
Bifurcation Analysis ◽  
Population Model ◽  
Choristoneura Fumiferana ◽  
Single Species ◽  
Species Competition ◽  
Numerical Examples ◽  
Competition Models ◽  
Forest Lands

Choristoneura Fumiferana is perilous defoliators of forest lands in North America and many countries in Europe. In this study, we consider mathematical models in ecology, epidemiology and bifurcation studies; the spruce budworm model and the population model with harvesting. The study is designed based on bifurcation analysis. In particular, the results support population thresholds necessary for survival in certain cases. In a series of numerical examples, the outcomes are presented graphically to compare with bifurcation results.

A two-stage population model

1970 ◽  
Vol 8 (3-4) ◽  
pp. 371-378 ◽  
Author(s):  
Keith P. Tognetti ◽  
A. Mazanov
Keyword(s):  
Population Model ◽  
Two Stage

Stability and Neimark—Sacker bifurcation analysis of a food-limited population model with a time delay

2013 ◽  
Vol 22 (3) ◽  
pp. 030204 ◽  
Author(s):  
Xiao-Wei Jiang ◽  
Zhi-Hong Guan ◽  
Xian-He Zhang ◽  
Ding-Xue Zhang ◽  
Feng Liu
Keyword(s):  
Time Delay ◽  
Bifurcation Analysis ◽  
Population Model
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