American Institute of Mathematical Sciences

Advanced
April  2010, 26(2): 397-415. doi: 10.3934/dcds.2010.26.397

The dynamics of a class of cooperative systems

Pablo Álvarez-Caudevilla 1, and  Julián López-Gómez 2,

1. 

Centro de Ricerca Matematica Ennio De Giorgi, Scuola Normale Superiore, Piazza dei Cavalieri 3, 56100-Pisa, Italy
2. 

Departamento de Matemática Aplicada, Universidad Complutense de Madrid, Plaza de Ciencias 3, 28040-Madrid

Received  January 2009 Revised  June 2009 Published  October 2009

This paper characterizes the dynamics of the positive solutions of a class of sublinear parabolic cooperative systems whose analysis is imperative for ascertaining the dynamics of wider classes of sublinear cooperative and superlinear indefinite Reaction-Diffusion systems, like those introduced by López-Gómez and Molina-Meyer [15].
Keywords: Cooperative systems, Dynamics., Positive steady-states.
Mathematics Subject Classification: Primary: 35K40, 35K50; Secondary: 35K57, 35K6.
Citation: Pablo Álvarez-Caudevilla, Julián López-Gómez. The dynamics of a class of cooperative systems. Discrete & Continuous Dynamical Systems, 2010, 26 (2) : 397-415. doi: 10.3934/dcds.2010.26.397
[1]

Yunfeng Jia, Yi Li, Jianhua Wu. Qualitative analysis on positive steady-states for an autocatalytic reaction model in thermodynamics. Discrete & Continuous Dynamical Systems, 2017, 37 (9) : 4785-4813. doi: 10.3934/dcds.2017206
[2]

Kousuke Kuto, Tohru Tsujikawa. Bifurcation structure of steady-states for bistable equations with nonlocal constraint. Conference Publications, 2013, 2013 (special) : 467-476. doi: 10.3934/proc.2013.2013.467
[3]

Tian Xiang. A study on the positive nonconstant steady states of nonlocal chemotaxis systems. Discrete & Continuous Dynamical Systems - B, 2013, 18 (9) : 2457-2485. doi: 10.3934/dcdsb.2013.18.2457
[4]

Hisashi Okamoto, Takashi Sakajo, Marcus Wunsch. Steady-states and traveling-wave solutions of the generalized Constantin--Lax--Majda equation. Discrete & Continuous Dynamical Systems, 2014, 34 (8) : 3155-3170. doi: 10.3934/dcds.2014.34.3155
[5]

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
[6]

Kousuke Kuto. Stability and Hopf bifurcation of coexistence steady-states to an SKT model in spatially heterogeneous environment. Discrete & Continuous Dynamical Systems, 2009, 24 (2) : 489-509. doi: 10.3934/dcds.2009.24.489
[7]

Pablo Álvarez-Caudevilla, Julián López-Gómez. Characterizing the existence of coexistence states in a class of cooperative systems. Conference Publications, 2009, 2009 (Special) : 24-33. doi: 10.3934/proc.2009.2009.24
[8]

Shanshan Chen. Nonexistence of nonconstant positive steady states of a diffusive predator-prey model. Communications on Pure & Applied Analysis, 2018, 17 (2) : 477-485. doi: 10.3934/cpaa.2018026
[9]

Wenshu Zhou, Hongxing Zhao, Xiaodan Wei, Guokai Xu. Existence of positive steady states for a predator-prey model with diffusion. Communications on Pure & Applied Analysis, 2013, 12 (5) : 2189-2201. doi: 10.3934/cpaa.2013.12.2189
[10]

Yan'e Wang, Jianhua Wu. Stability of positive constant steady states and their bifurcation in a biological depletion model. Discrete & Continuous Dynamical Systems - B, 2011, 15 (3) : 849-865. doi: 10.3934/dcdsb.2011.15.849
[11]

Qian Xu. The stability of bifurcating steady states of several classes of chemotaxis systems. Discrete & Continuous Dynamical Systems - B, 2015, 20 (1) : 231-248. doi: 10.3934/dcdsb.2015.20.231
[12]

Miguel A. Herrero, Marianito R. Rodrigo. Remarks on accessible steady states for some coagulation-fragmentation systems. Discrete & Continuous Dynamical Systems, 2007, 17 (3) : 541-552. doi: 10.3934/dcds.2007.17.541
[13]

Soohyun Bae. Weighted $L^\infty$ stability of positive steady states of a semilinear heat equation in $\R^n$. Discrete & Continuous Dynamical Systems, 2010, 26 (3) : 823-837. doi: 10.3934/dcds.2010.26.823
[14]

Kaigang Huang, Yongli Cai, Feng Rao, Shengmao Fu, Weiming Wang. Positive steady states of a density-dependent predator-prey model with diffusion. Discrete & Continuous Dynamical Systems - B, 2018, 23 (8) : 3087-3107. doi: 10.3934/dcdsb.2017209
[15]

Kimun Ryu, Inkyung Ahn. Positive steady--states for two interacting species models with linear self-cross diffusions. Discrete & Continuous Dynamical Systems, 2003, 9 (4) : 1049-1061. doi: 10.3934/dcds.2003.9.1049
[16]

Kazuhiro Oeda. Positive steady states for a prey-predator cross-diffusion system with a protection zone and Holling type II functional response. Conference Publications, 2013, 2013 (special) : 597-603. doi: 10.3934/proc.2013.2013.597
[17]

Yaping Wu, Qian Xu. The existence and structure of large spiky steady states for S-K-T competition systems with cross-diffusion. Discrete & Continuous Dynamical Systems, 2011, 29 (1) : 367-385. doi: 10.3934/dcds.2011.29.367
[18]

Wei Wang, Wanbiao Ma. Global dynamics and travelling wave solutions for a class of non-cooperative reaction-diffusion systems with nonlocal infections. Discrete & Continuous Dynamical Systems - B, 2018, 23 (8) : 3213-3235. doi: 10.3934/dcdsb.2018242
[19]

Sébastien Guisset. Angular moments models for rarefied gas dynamics. Numerical comparisons with kinetic and Navier-Stokes equations. Kinetic & Related Models, 2020, 13 (4) : 739-758. doi: 10.3934/krm.2020025
[20]

Li Ma, Youquan Luo. Dynamics of positive steady-state solutions of a nonlocal dispersal logistic model with nonlocal terms. Discrete & Continuous Dynamical Systems - B, 2020, 25 (7) : 2555-2582. doi: 10.3934/dcdsb.2020022

2019 Impact Factor: 1.338

Tools

Metrics

  • PDF downloads (43)
  • HTML views (0)
  • Cited by (5)

Other articles
by authors

[Back to Top]

Copyright © 2021 American Institute of Mathematical Sciences