scholarly journals Global bifurcation structure of stationary solutions for a Lotka-Volterra competition model

2002 ◽  
Vol 8 (1) ◽  
pp. 147-162 ◽  
Author(s):  
Yukio Kan-On ◽  
Keyword(s):  
Global Bifurcation ◽  
Stationary Solutions ◽  
Competition Model ◽  
Bifurcation Structure

Bifurcation structure of coexistence states for a prey–predator model with large population flux by attractive transition

2021 ◽  
pp. 1-24
Author(s):  
Kousuke Kuto ◽  
Kazuhiro Oeda
Keyword(s):  
Positive Solutions ◽  
Large Population ◽  
Global Bifurcation ◽  
Competition Model ◽  
The Other ◽  
Bifurcation Structure ◽  
Nonlinear Anal ◽  
Connected Set ◽  
Coexistence States ◽  
Predator Model

This paper is concerned with a prey–predator model with population flux by attractive transition. Our previous paper (Oeda and Kuto, 2018, Nonlinear Anal. RWA, 44, 589–615) obtained a bifurcation branch (connected set) of coexistence steady states which connects two semitrivial solutions. In Oeda and Kuto (2018, Nonlinear Anal. RWA, 44, 589–615), we also showed that any positive steady-state approaches a positive solution of either of two limiting systems, and moreover, one of the limiting systems is an equal diffusive competition model. This paper obtains the bifurcation structure of positive solutions to the other limiting system. Moreover, this paper implies that the global bifurcation branch of coexistence states consists of two parts, one of which is a simple curve running in a tubular domain near the set of positive solutions to the equal diffusive competition model, the other of which is a connected set characterized by positive solutions to the other limiting system.

Global bifurcation structure of a Bonhoeffer-van der Pol oscillator driven by periodic pulse trains

1994 ◽  
Vol 72 (1) ◽  
pp. 55-67 ◽  
Author(s):  
Taishin Nomura ◽  
Shunsuke Sato ◽  
Shinji Doi ◽  
Jose P. Segundo ◽  
Michael D. Stiber
Keyword(s):  
Global Bifurcation ◽  
Van Der Pol Oscillator ◽  
Bifurcation Structure ◽  
Van Der Pol ◽  
Pulse Trains ◽  
Periodic Pulse

Global Bifurcation of Stationary Solutions for a Volume-Filling Chemotaxis Model with Logistic Growth

2020 ◽  
Vol 30 (13) ◽  
pp. 2050182
Author(s):  
Yaying Dong ◽  
Shanbing Li
Keyword(s):  
Bifurcation Theory ◽  
Global Bifurcation ◽  
Neumann Boundary ◽  
Stationary Solutions ◽  
Logistic Growth ◽  
Fredholm Operators ◽  
Chemotaxis Model ◽  
Volume Filling ◽  
Constant Solution ◽  
Global Bifurcation Theory

In this paper, we show how the global bifurcation theory for nonlinear Fredholm operators (Theorem 4.3 of [Shi & Wang, 2009]) and for compact operators (Theorem 1.3 of [Rabinowitz, 1971]) can be used in the study of the nonconstant stationary solutions for a volume-filling chemotaxis model with logistic growth under Neumann boundary conditions. Our results show that infinitely many local branches of nonconstant solutions bifurcate from the positive constant solution [Formula: see text] at [Formula: see text]. Moreover, for each [Formula: see text], we prove that each [Formula: see text] can be extended into a global curve, and the projection of the bifurcation curve [Formula: see text] onto the [Formula: see text]-axis contains [Formula: see text].

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