American Institute of Mathematical Sciences

Advanced
November  2010, 14(4): 1671-1688. doi: 10.3934/dcdsb.2010.14.1671

Dynamics of three-component reversible Gray-Scott model

Yuncheng You 1,

1. 

Department of Mathematics and Statistics, University of South Florida, Tampa, FL 33620-5700, United States

Received  August 2009 Revised  January 2010 Published  August 2010

The existence of a global attractor for the solution semiflow of a three-component reversible Gray-Scott system with Neumann boundary condition on a bounded domain of space dimension $n\le 3$ is proved. The methodology features the re-scaling and grouping estimation to overcome the difficulty of non-dissipative coupling of three variables and the coefficient barrier. It is also shown that the global attractor turns out to be an $(H, E)$ global attractor.
Keywords: asymptotic compactness., Reversible Gray-Scott system, global attractor, asymptotic dynamics, absorbing set.
Mathematics Subject Classification: Primary: 37L30; Secondary: 35B40, 35B41, 35K55, 35K57, 35Q80, 35Q9.
Citation: Yuncheng You. Dynamics of three-component reversible Gray-Scott model. Discrete & Continuous Dynamical Systems - B, 2010, 14 (4) : 1671-1688. doi: 10.3934/dcdsb.2010.14.1671
[1]

Yuncheng You. Global attractor of the Gray-Scott equations. Communications on Pure & Applied Analysis, 2008, 7 (4) : 947-970. doi: 10.3934/cpaa.2008.7.947
[2]

Gaocheng Yue, Chengkui Zhong. Global attractors for the Gray-Scott equations in locally uniform spaces. Discrete & Continuous Dynamical Systems - B, 2016, 21 (1) : 337-356. doi: 10.3934/dcdsb.2016.21.337
[3]

Junwei Feng, Hui Liu, Jie Xin. Uniform attractors of stochastic two-compartment Gray-Scott system with multiplicative noise. Discrete & Continuous Dynamical Systems - B, 2017, 22 (11) : 0-0. doi: 10.3934/dcdsb.2020116
[4]

Keisuke Matsuya, Mikio Murata. Spatial pattern of discrete and ultradiscrete Gray-Scott model. Discrete & Continuous Dynamical Systems - B, 2015, 20 (1) : 173-187. doi: 10.3934/dcdsb.2015.20.173
[5]

Yuncheng You. Asymptotic dynamics of reversible cubic autocatalytic reaction-diffusion systems. Communications on Pure & Applied Analysis, 2011, 10 (5) : 1415-1445. doi: 10.3934/cpaa.2011.10.1415
[6]

Chunyou Sun, Daomin Cao, Jinqiao Duan. Non-autonomous wave dynamics with memory --- asymptotic regularity and uniform attractor. Discrete & Continuous Dynamical Systems - B, 2008, 9 (3&4, May) : 743-761. doi: 10.3934/dcdsb.2008.9.743
[7]

Mohammad A. Safi, Abba B. Gumel. Global asymptotic dynamics of a model for quarantine and isolation. Discrete & Continuous Dynamical Systems - B, 2010, 14 (1) : 209-231. doi: 10.3934/dcdsb.2010.14.209
[8]

Jui-Pin Tseng. Global asymptotic dynamics of a class of nonlinearly coupled neural networks with delays. Discrete & Continuous Dynamical Systems - A, 2013, 33 (10) : 4693-4729. doi: 10.3934/dcds.2013.33.4693
[9]

Seung-Yeal Ha, Jinyeong Park, Xiongtao Zhang. A global well-posedness and asymptotic dynamics of the kinetic Winfree equation. Discrete & Continuous Dynamical Systems - B, 2020, 25 (4) : 1317-1344. doi: 10.3934/dcdsb.2019229
[10]

Jack Schaeffer. Global existence for the Vlasov-Poisson system with steady spatial asymptotic behavior. Kinetic & Related Models, 2012, 5 (1) : 129-153. doi: 10.3934/krm.2012.5.129
[11]

Ivan Gentil, Bogusław Zegarlinski. Asymptotic behaviour of reversible chemical reaction-diffusion equations. Kinetic & Related Models, 2010, 3 (3) : 427-444. doi: 10.3934/krm.2010.3.427
[12]

Michel Chipot, Karen Yeressian. On the asymptotic behavior of variational inequalities set in cylinders. Discrete & Continuous Dynamical Systems - A, 2013, 33 (11&12) : 4875-4890. doi: 10.3934/dcds.2013.33.4875
[13]

Tibor Krisztin. The unstable set of zero and the global attractor for delayed monotone positive feedback. Conference Publications, 2001, 2001 (Special) : 229-240. doi: 10.3934/proc.2001.2001.229
[14]

Sergio Grillo, Jerrold E. Marsden, Sujit Nair. Lyapunov constraints and global asymptotic stabilization. Journal of Geometric Mechanics, 2011, 3 (2) : 145-196. doi: 10.3934/jgm.2011.3.145
[15]

Tomás Caraballo, Francisco Morillas, José Valero. Asymptotic behaviour of a logistic lattice system. Discrete & Continuous Dynamical Systems - A, 2014, 34 (10) : 4019-4037. doi: 10.3934/dcds.2014.34.4019
[16]

Rong Yang, Li Chen. Mean-field limit for a collision-avoiding flocking system and the time-asymptotic flocking dynamics for the kinetic equation. Kinetic & Related Models, 2014, 7 (2) : 381-400. doi: 10.3934/krm.2014.7.381
[17]

Tobias Black. Global existence and asymptotic stability in a competitive two-species chemotaxis system with two signals. Discrete & Continuous Dynamical Systems - B, 2017, 22 (4) : 1253-1272. doi: 10.3934/dcdsb.2017061
[18]

Fengqi Yi, Hua Zhang, Alhaji Cherif, Wenying Zhang. Spatiotemporal patterns of a homogeneous diffusive system modeling hair growth: Global asymptotic behavior and multiple bifurcation analysis. Communications on Pure & Applied Analysis, 2014, 13 (1) : 347-369. doi: 10.3934/cpaa.2014.13.347
[19]

Mihaela Negreanu. Global existence and asymptotic behavior of solutions to a chemotaxis system with chemicals and prey-predator terms. Discrete & Continuous Dynamical Systems - B, 2017, 22 (11) : 0-0. doi: 10.3934/dcdsb.2020064
[20]

Toru Sasaki, Takashi Suzuki. Asymptotic behaviour of the solutions to a virus dynamics model with diffusion. Discrete & Continuous Dynamical Systems - B, 2018, 23 (2) : 525-541. doi: 10.3934/dcdsb.2017206

2018 Impact Factor: 1.008

Tools

Metrics

  • PDF downloads (33)
  • HTML views (0)
  • Cited by (15)

Other articles
by authors

[Back to Top]

Copyright © 2020 American Institute of Mathematical Sciences