December  2008, 22(4): 1091-1120. doi: 10.3934/dcds.2008.22.1091

Exponential attractors for competing species model with cross-diffusions

1. 

Department of Applied Physics, Osaka University, Suita, Osaka, 565-0871

Received  June 2007 Revised  November 2007 Published  September 2008

This paper is concerned with the competing species model presented by Shigesada-Kawasaki-Teramoto in 1979. Under a suitable condition on self-diffusions and cross-diffusions, we construct a dynamical system determined from the model. Furthermore, under the same condition we construct exponential attractors of the dynamical system.
Citation: Atsushi Yagi. Exponential attractors for competing species model with cross-diffusions. Discrete & Continuous Dynamical Systems - A, 2008, 22 (4) : 1091-1120. doi: 10.3934/dcds.2008.22.1091
[1]

Hongyong Zhao, Qianjin Zhang, Linhe Zhu. The spatial dynamics of a zebrafish model with cross-diffusions. Mathematical Biosciences & Engineering, 2017, 14 (4) : 1035-1054. doi: 10.3934/mbe.2017054

[2]

Kimun Ryu, Inkyung Ahn. Positive steady--states for two interacting species models with linear self-cross diffusions. Discrete & Continuous Dynamical Systems - A, 2003, 9 (4) : 1049-1061. doi: 10.3934/dcds.2003.9.1049

[3]

Roberto A. Saenz, Herbert W. Hethcote. Competing species models with an infectious disease. Mathematical Biosciences & Engineering, 2006, 3 (1) : 219-235. doi: 10.3934/mbe.2006.3.219

[4]

Kimun Ryu, Inkyung Ahn. On certain elliptic systems with nonlinear self-cross diffusions. Conference Publications, 2003, 2003 (Special) : 752-759. doi: 10.3934/proc.2003.2003.752

[5]

Linda J. S. Allen, Vrushali A. Bokil. Stochastic models for competing species with a shared pathogen. Mathematical Biosciences & Engineering, 2012, 9 (3) : 461-485. doi: 10.3934/mbe.2012.9.461

[6]

Frédéric Grognard, Frédéric Mazenc, Alain Rapaport. Polytopic Lyapunov functions for persistence analysis of competing species. Discrete & Continuous Dynamical Systems - B, 2007, 8 (1) : 73-93. doi: 10.3934/dcdsb.2007.8.73

[7]

Rafael Bravo De La Parra, Luis Sanz. A discrete model of competing species sharing a parasite. Discrete & Continuous Dynamical Systems - B, 2017, 22 (11) : 0-0. doi: 10.3934/dcdsb.2019204

[8]

Sze-Bi Hsu, Chiu-Ju Lin. Dynamics of two phytoplankton species competing for light and nutrient with internal storage. Discrete & Continuous Dynamical Systems - S, 2014, 7 (6) : 1259-1285. doi: 10.3934/dcdss.2014.7.1259

[9]

Julián López-Gómez. On the structure of the permanence region for competing species models with general diffusivities and transport effects. Discrete & Continuous Dynamical Systems - A, 1996, 2 (4) : 525-542. doi: 10.3934/dcds.1996.2.525

[10]

Shu Dai, Dong Li, Kun Zhao. Finite-time quenching of competing species with constrained boundary evaporation. Discrete & Continuous Dynamical Systems - B, 2013, 18 (5) : 1275-1290. doi: 10.3934/dcdsb.2013.18.1275

[11]

Xinfu Chen, King-Yeung Lam, Yuan Lou. Corrigendum: Dynamics of a reaction-diffusion-advection model for two competing species. Discrete & Continuous Dynamical Systems - A, 2014, 34 (11) : 4989-4995. doi: 10.3934/dcds.2014.34.4989

[12]

Xinfu Chen, King-Yeung Lam, Yuan Lou. Dynamics of a reaction-diffusion-advection model for two competing species. Discrete & Continuous Dynamical Systems - A, 2012, 32 (11) : 3841-3859. doi: 10.3934/dcds.2012.32.3841

[13]

Patrick J. Johnson, Mark E. Burke. An investigation of the global properties of a two-dimensional competing species model. Discrete & Continuous Dynamical Systems - B, 2008, 10 (1) : 109-128. doi: 10.3934/dcdsb.2008.10.109

[14]

Zhiguo Wang, Hua Nie, Jianhua Wu. Spatial propagation for a parabolic system with multiple species competing for single resource. Discrete & Continuous Dynamical Systems - B, 2019, 24 (4) : 1785-1814. doi: 10.3934/dcdsb.2018237

[15]

José A. Langa, Alain Miranville, José Real. Pullback exponential attractors. Discrete & Continuous Dynamical Systems - A, 2010, 26 (4) : 1329-1357. doi: 10.3934/dcds.2010.26.1329

[16]

Kei Matsuura, Mitsuharu Otani. Exponential attractors for a quasilinear parabolic equation. Conference Publications, 2007, 2007 (Special) : 713-720. doi: 10.3934/proc.2007.2007.713

[17]

Qi Wang, Lu Zhang, Jingyue Yang, Jia Hu. Global existence and steady states of a two competing species Keller--Segel chemotaxis model. Kinetic & Related Models, 2015, 8 (4) : 777-807. doi: 10.3934/krm.2015.8.777

[18]

Yunfeng Jia, Jianhua Wu, Hong-Kun Xu. On qualitative analysis for a two competing fish species model with a combined non-selective harvesting effort in the presence of toxicity. Communications on Pure & Applied Analysis, 2013, 12 (5) : 1927-1941. doi: 10.3934/cpaa.2013.12.1927

[19]

Chiun-Chuan Chen, Yin-Liang Huang, Li-Chang Hung, Chang-Hong Wu. Semi-exact solutions and pulsating fronts for Lotka-Volterra systems of two competing species in spatially periodic habitats. Communications on Pure & Applied Analysis, 2020, 19 (1) : 1-18. doi: 10.3934/cpaa.2020001

[20]

Atsushi Yagi, Koichi Osaki, Tatsunari Sakurai. Exponential attractors for Belousov-Zhabotinskii reaction model. Conference Publications, 2009, 2009 (Special) : 846-856. doi: 10.3934/proc.2009.2009.846

2018 Impact Factor: 1.143

Metrics

  • PDF downloads (12)
  • HTML views (0)
  • Cited by (2)

Other articles
by authors

[Back to Top]