# American Institute of Mathematical Sciences

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

## The dynamics of a class of cooperative systems

 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].
Citation: Pablo Álvarez-Caudevilla, Julián López-Gómez. The dynamics of a class of cooperative systems. Discrete & Continuous Dynamical Systems - A, 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 - A, 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 - A, 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 - A, 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 - A, 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 - A, 2010, 26 (3) : 823-837. doi: 10.3934/dcds.2010.26.823 [14] 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 [15] 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 [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 - A, 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] József Z. Farkas, Peter Hinow. Steady states in hierarchical structured populations with distributed states at birth. Discrete & Continuous Dynamical Systems - B, 2012, 17 (8) : 2671-2689. doi: 10.3934/dcdsb.2012.17.2671 [20] Anne Nouri, Christian Schmeiser. Aggregated steady states of a kinetic model for chemotaxis. Kinetic & Related Models, 2017, 10 (1) : 313-327. doi: 10.3934/krm.2017013

2018 Impact Factor: 1.143