American Institute of Mathematical Sciences

Advanced
January  2002, 8(1): 147-162. doi: 10.3934/dcds.2002.8.147

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

Yukio Kan-On 1,

1. 

Department of Mathematics, Faculty of Education, Ehime University, Matsuyama, 790-8577, Japan

Received  March 2001 Revised  May 2001 Published  October 2001

In this paper, we establish the global bifurcation structure of positive stationary solutions for a certain Lotka-Volterra competition model with diffusion. To do this, the comparison principle and the bifurcation theory are employed.
Keywords: comparison principle., Competition model, global bifurcation.
Mathematics Subject Classification: 35B3.
Citation: Yukio Kan-On. Global bifurcation structure of stationary solutions for a Lotka-Volterra competition model. Discrete & Continuous Dynamical Systems, 2002, 8 (1) : 147-162. doi: 10.3934/dcds.2002.8.147
[1]

Yukio Kan-On. Bifurcation structures of positive stationary solutions for a Lotka-Volterra competition model with diffusion II: Global structure. Discrete & Continuous Dynamical Systems, 2006, 14 (1) : 135-148. doi: 10.3934/dcds.2006.14.135
[2]

Mohamed Dellal, Bachir Bar. Global analysis of a model of competition in the chemostat with internal inhibitor. Discrete & Continuous Dynamical Systems - B, 2021, 26 (2) : 1129-1148. doi: 10.3934/dcdsb.2020156
[3]

Timothy Blass, Rafael De La Llave, Enrico Valdinoci. A comparison principle for a Sobolev gradient semi-flow. Communications on Pure & Applied Analysis, 2011, 10 (1) : 69-91. doi: 10.3934/cpaa.2011.10.69
[4]

E. Cabral Balreira, Saber Elaydi, Rafael Luís. Local stability implies global stability for the planar Ricker competition model. Discrete & Continuous Dynamical Systems - B, 2014, 19 (2) : 323-351. doi: 10.3934/dcdsb.2014.19.323
[5]

Xiaomei Feng, Zhidong Teng, Kai Wang, Fengqin Zhang. Backward bifurcation and global stability in an epidemic model with treatment and vaccination. Discrete & Continuous Dynamical Systems - B, 2014, 19 (4) : 999-1025. doi: 10.3934/dcdsb.2014.19.999
[6]

Fabien Crauste. Global Asymptotic Stability and Hopf Bifurcation for a Blood Cell Production Model. Mathematical Biosciences & Engineering, 2006, 3 (2) : 325-346. doi: 10.3934/mbe.2006.3.325
[7]

Pengmiao Hao, Xuechen Wang, Junjie Wei. Global Hopf bifurcation of a population model with stage structure and strong Allee effect. Discrete & Continuous Dynamical Systems - S, 2017, 10 (5) : 973-993. doi: 10.3934/dcdss.2017051
[8]

Nicolas Forcadel, Mamdouh Zaydan. A comparison principle for Hamilton-Jacobi equation with moving in time boundary. Evolution Equations & Control Theory, 2019, 8 (3) : 543-565. doi: 10.3934/eect.2019026
[9]

Shigeaki Koike, Takahiro Kosugi. Remarks on the comparison principle for quasilinear PDE with no zeroth order terms. Communications on Pure & Applied Analysis, 2015, 14 (1) : 133-142. doi: 10.3934/cpaa.2015.14.133
[10]

Xiaowei Tang, Xilin Fu. New comparison principle with Razumikhin condition for impulsive infinite delay differential systems. Conference Publications, 2009, 2009 (Special) : 739-743. doi: 10.3934/proc.2009.2009.739
[11]

Thomas Leroy. Relativistic transfer equations: Comparison principle and convergence to the non-equilibrium regime. Kinetic & Related Models, 2015, 8 (4) : 725-763. doi: 10.3934/krm.2015.8.725
[12]

Maria Francesca Betta, Rosaria Di Nardo, Anna Mercaldo, Adamaria Perrotta. Gradient estimates and comparison principle for some nonlinear elliptic equations. Communications on Pure & Applied Analysis, 2015, 14 (3) : 897-922. doi: 10.3934/cpaa.2015.14.897
[13]

Yasuhito Miyamoto. Global bifurcation and stable two-phase separation for a phase field model in a disk. Discrete & Continuous Dynamical Systems, 2011, 30 (3) : 791-806. doi: 10.3934/dcds.2011.30.791
[14]

Hongying Shu, Lin Wang. Global stability and backward bifurcation of a general viral infection model with virus-driven proliferation of target cells. Discrete & Continuous Dynamical Systems - B, 2014, 19 (6) : 1749-1768. doi: 10.3934/dcdsb.2014.19.1749
[15]

Tatsuki Mori, Kousuke Kuto, Masaharu Nagayama, Tohru Tsujikawa, Shoji Yotsutani. Global bifurcation sheet and diagrams of wave-pinning in a reaction-diffusion model for cell polarization. Conference Publications, 2015, 2015 (special) : 861-877. doi: 10.3934/proc.2015.0861
[16]

Inmaculada Antón, Julián López-Gómez. Global bifurcation diagrams of steady-states for a parabolic model related to a nuclear engineering problem. Conference Publications, 2013, 2013 (special) : 21-30. doi: 10.3934/proc.2013.2013.21
[17]

Mingshang Hu. Stochastic global maximum principle for optimization with recursive utilities. Probability, Uncertainty and Quantitative Risk, 2017, 2 (0) : 1-. doi: 10.1186/s41546-017-0014-7
[18]

Bernd Kawohl, Vasilii Kurta. A Liouville comparison principle for solutions of singular quasilinear elliptic second-order partial differential inequalities. Communications on Pure & Applied Analysis, 2011, 10 (6) : 1747-1762. doi: 10.3934/cpaa.2011.10.1747
[19]

Shuxia Pan. Asymptotic spreading in a delayed dispersal predator-prey system without comparison principle. Electronic Research Archive, 2019, 27: 89-99. doi: 10.3934/era.2019011
[20]

Shanshan Chen, Jianshe Yu. Stability and bifurcation on predator-prey systems with nonlocal prey competition. Discrete & Continuous Dynamical Systems, 2018, 38 (1) : 43-62. doi: 10.3934/dcds.2018002

2020 Impact Factor: 1.392

Tools

Metrics

  • PDF downloads (67)
  • HTML views (0)
  • Cited by (2)

Other articles
by authors

[Back to Top]

Copyright © 2022 American Institute of Mathematical Sciences | Privacy Policy