scholarly journals Asymptotic stability of traveling wavefronts in a delayed population model with stage structure on a two-dimensional spatial lattice

2010 ◽  
Vol 13 (3) ◽  
pp. 559-575 ◽  
Author(s):  
Cui-Ping Cheng ◽  
◽  
Wan-Tong Li ◽  
Zhi-Cheng Wang ◽  
Keyword(s):  
Asymptotic Stability ◽  
Population Model ◽  
Stage Structure ◽  
Two Dimensional ◽  
Spatial Lattice ◽  
Delayed Population Model

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.

PERMANENCE AND THE EXISTENCE OF THE PERIODIC SOLUTION OF THE NON-AUTONOMOUS TWO-SPECIES COMPETITIVE MODEL WITH STAGE STRUCTURE

2004 ◽  
Vol 07 (03n04) ◽  
pp. 385-393 ◽  
Author(s):  
GUANGZHAO ZENG ◽  
LANSUN CHEN ◽  
LIHUA SUN ◽  
YING LIU
Keyword(s):  
Periodic Solution ◽  
Asymptotic Stability ◽  
Periodic System ◽  
Stage Structure ◽  
Competitive Model

This paper considers a non-autonomous competitive two-species model with stage structure in one species. The conditions of permanence obtained. Furthermore, the existence and asymptotic stability of the periodic solution are proved under some assumptions if this model turns out to be a periodic system.

Parameter-dependent robust H∞ filtering for uncertain two-dimensional discrete systems in the FM second model

2020 ◽  
Vol 37 (4) ◽  
pp. 1114-1132
Author(s):  
Khalid Badie ◽  
Mohammed Alfidi ◽  
Mohamed Oubaidi ◽  
Zakaria Chalh
Keyword(s):  
Asymptotic Stability ◽  
Lyapunov Function ◽  
Discrete Systems ◽  
Performance Criterion ◽  
Linear Matrix ◽  
Two Dimensional ◽  
Matrix Inequalities ◽  
Parameter Uncertainties ◽  
Error System ◽  
Parameter Dependent

Abstract This paper deals with the problem of robust $H_{\infty }$ filtering for uncertain two-dimensional discrete systems in the Fornasini–Marchesini second model with polytopic parameter uncertainties. Firstly, a new $H_{\infty }$ performance criterion is derived by exploiting a new structure of the parameter-dependent Lyapunov function. Secondly, based on the criterion obtained, a new condition for the existence of a robust $H_{\infty }$ filter that ensures asymptotic stability, and a prescribed $H_{\infty }$ performance level of the filtering error system, for all admissible uncertainties is established in terms of linear matrix inequalities. Finally, two examples are given to illustrate the effectiveness and advantage of the proposed method.

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.

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