Positive steady-state solutions of the Noyes–Field model for Belousov–Zhabotinskii reaction

2004 ◽  
Vol 56 (3) ◽  
pp. 451-464 ◽  
Author(s):  
Rui Peng ◽  
Mingxin Wang
Keyword(s):  
Steady State ◽  
Field Model ◽  
Positive Steady State ◽  
Belousov Zhabotinskii Reaction ◽  
Steady State Solutions

Positive Solutions of a Strongly Coupled Prey-Predator System

2013 ◽  
Vol 748 ◽  
pp. 432-436
Author(s):  
Xiao Zhou Feng ◽  
Mei Hua Wei ◽  
Yan Ling Li
Keyword(s):  
Steady State ◽  
Fixed Point Index ◽  
Equation System ◽  
Point Index ◽  
Differential Equation System ◽  
Strongly Coupled ◽  
Positive Steady State ◽  
Holling Ii Functional Response ◽  
Steady State Solutions ◽  
Predator System

In this paper, the positive steady-state solutions of a strongly coupled partial differential equation system with Holling II functional response is studied. The existence for positive steady-state solutions of system is established by calculating the fixed point index in cone.

scholarly journals Stability of the positive steady-state solutions of systems of nonlinear Volterra difference equations of population models with diffusion and infinite delay

2000 ◽  
Vol 23 (4) ◽  
pp. 261-270 ◽  
Author(s):  
B. Shi
Keyword(s):  
Steady State ◽  
Difference Equations ◽  
Infinite Delay ◽  
Steady State Solution ◽  
Population Models ◽  
Monotone Iterative ◽  
Positive Steady State ◽  
Infinite Delays ◽  
Steady State Solutions ◽  
Volterra Difference Equations

An open problem given by Kocic and Ladas in 1993 is generalized and considered. A sufficient condition is obtained for each solution to tend to the positive steady-state solution of the systems of nonlinear Volterra difference equations of population models with diffusion and infinite delays by using the method of lower and upper solutions and monotone iterative techniques.

A mean-field model of superconducting vortices

1996 ◽  
Vol 7 (2) ◽  
pp. 97-111 ◽  
Author(s):  
S. J. Chapman ◽  
J. Rubinstein ◽  
M. Schatzman
Keyword(s):  
Steady State ◽  
Field Model ◽  
Local Existence ◽  
Mean Field ◽  
State Problem ◽  
Mean Field Model ◽  
Type Ii Superconductor ◽  
Superconducting Vortices ◽  
Steady State Problem ◽  
Steady State Solutions

A mean-field model for the motion of rectilinear vortices in the mixed state of a type-II superconductor is formulated. Steady-state solutions for some simple geometries are examined, and a local existence result is proved for an arbitrary smooth geometry. Finally, a variational formulation of the steady-state problem is given which shows the solution to be unique.

scholarly journals Global Bifurcation Structure of a Predator-Prey System with a Spatial Degeneracy and B-D Functional Response

Complexity ◽  
2021 ◽  
Vol 2021 ◽  
pp. 1-10
Author(s):  
Xiaozhou Feng ◽  
Changtong Li ◽  
Hao Sun ◽  
Yuzhen Wang
Keyword(s):  
Steady State ◽  
Functional Response ◽  
Bifurcation Theory ◽  
A Priori Estimates ◽  
Global Bifurcation ◽  
Local Bifurcation ◽  
Predator Prey ◽  
Positive Steady State ◽  
Prey System ◽  
Steady State Solutions

In this paper, we investigate a predator-prey system with Beddington–DeAngelis (B-D) functional response in a spatially degenerate heterogeneous environment. First, for the case of the weak growth rate on the prey ( λ 1 Ω < a < λ 1 Ω 0 ), a priori estimates on any positive steady-state solutions are established by the comparison principle; two local bifurcation solution branches depending on the bifurcation parameter are obtained by local bifurcation theory. Moreover, the demonstrated two local bifurcation solution branches can be extended to a bounded global bifurcation curve by the global bifurcation theory. Second, for the case of the strong growth rate on the prey ( a > λ 1 Ω 0 ), a priori estimates on any positive steady-state solutions are obtained by applying reduction to absurdity and the set of positive steady-state solutions forms an unbounded global bifurcation curve by the global bifurcation theory. In the end, discussions on the difference of the solution properties between the traditional predator-prey system and the predator-prey system with a spatial degeneracy and B-D functional response are addressed.

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