Citation: Chunting Ji, Hui Liu, Jie Xin. Random attractors of the stochastic extended Brusselator system with a multiplicative noise[J]. AIMS Mathematics, 2020, 5(4): 3584-3611. doi: 10.3934/math.2020233
[1] | I. Prigogine, R. Lefever, Symmetry-breaking instabilities in dissipative systems, J. Chem. Phys., 48 (1968), 1695-1700. doi: 10.1063/1.1668896 |
[2] | K. Brown, F. Davidson, Global bifurcation in the Brusselator system, Nonlinear Anal., 24 (1995), 1713-1725. doi: 10.1016/0362-546X(94)00218-7 |
[3] | J. Pearson, Complex patterns in a simple system, Science, 261 (1993), 189-192. doi: 10.1126/science.261.5118.189 |
[4] | K. J. Lee, W. D. Mccormick, Q. Ouyang, et al. Pattern formation by interacting chemical fronts, Science, 261 (1993), 192-194. doi: 10.1126/science.261.5118.192 |
[5] | P. Gray, S. K. Scott, Autocatalytic reactions in the isothermal, continuous stirred tank reactor: Isolas and other forms of multistability, Chem. Eng. Sci., 38 (1983), 29-43. doi: 10.1016/0009-2509(83)80132-8 |
[6] | P. Gray, S. K. Scott, Autocatalytic reactions in the isothermal, continuous stirred tank reactor: Oscillations and instabilities in the system A + 2B → 3B; B → C, Chem. Eng. Sci., 39 (1984), 1087-1097. doi: 10.1016/0009-2509(84)87017-7 |
[7] | B. Guo, Y. Han, Attractor and spatial chaos for the Brusselator in RN, Nonlinear Anal. Theor., 70 (2009), 3917-3931. doi: 10.1016/j.na.2008.08.002 |
[8] | Y. You, Global dynamics of the Brusselator equations, Dynam. Part. Differ. Eq., 4 (2007), 167-196. doi: 10.4310/DPDE.2007.v4.n2.a4 |
[9] | Y. You, Global attractor of a coupled two-cell Brusselator model, In: Infinite Dimensional Dynamical Systems, Springer, New York, 2013, 319-352. |
[10] | Q. Bie, Pattern formation in a general two-cell Brusselator model, J. Math. Anal. Appl., 376 (2011), 551-564. doi: 10.1016/j.jmaa.2010.10.066 |
[11] | R. D. Parshad, S. Kouachi, N. Kumari, et al. Global existence and long time dynamics of a four compartment Brusselator type system, Dyn. Contin. Discrete Impuls. Syst. Ser. A Math. Anal., 24 (2017), 79-120. |
[12] | C. Florinda, D. L. Roberta, T. Isabella, Influence of diffusion on the stability of a full Brusselator model, Atti Accad. Naz. Lincei Rend. Lincei Mat. Appl., 29 (2018), 661-679. doi: 10.4171/RLM/827 |
[13] | H. Kitano, Systems biology: A brief overview, Science, 295 (2002), 1662-1664. doi: 10.1126/science.1069492 |
[14] | P. Gormley, K. Li, G. W. Irwin, Modeling molecular interaction pathways using a two-stage identification algorithm, Syst. Synth. Biol., 1 (2007), 145-160. doi: 10.1007/s11693-008-9012-5 |
[15] | Y. You, S. Zhou, Global dissipative dynamics of the extended Brusselator system, Nonlinear Anal. Real, 13 (2012), 2767-2789. doi: 10.1016/j.nonrwa.2012.04.005 |
[16] | J. Tu, Y. You, Random attractor of stochastic Brusselator system with multiplicative noise, Discrete Contin. Dyn. Syst., 36 (2016), 2757-2779. doi: 10.3934/dcds.2016.36.2757 |
[17] | H. Crauel, F. Flandoli, Attractors for random dynamical systems, Probab. Theory. Rel., 100 (1994), 365-393. doi: 10.1007/BF01193705 |
[18] | H. Crauel, A. Debussche, F. Flandoli, Random attractors, J. Dyn. Differ. Equ., 9 (1997), 307-341. doi: 10.1007/BF02219225 |
[19] | L. Arnold, Random Dynamical Systems, Springer-Verlag, Berlin, 1998. |
[20] | P. W. Bates, K. Lu, B. Wang, Random attractors for stochastic reaction-diffusion equation on unbounded domains, J. Differ. Equations, 246 (2009), 845-869. doi: 10.1016/j.jde.2008.05.017 |
[21] | B. Wang, Random attractors for non-autonomous stochastic wave equations with multiplicative noise, Discrete Contin. Dyn. Syst., 34 (2014), 269-300. doi: 10.3934/dcds.2014.34.269 |
[22] | X. Jia, J. Gao, X. Ding, Random attractors for stochastic two-compartment Gray-Scott equations with a multiplicative noise, Open Math., 14 (2016), 586-602. doi: 10.1515/math-2016-0052 |
[23] | N. Liu, J. Xin, Existence of random attractor for stochastic fractional long-short wave equations with periodic boundary condition, Discrete Dyn. Nat. Soc., 2017 (2017), 1-11. |
[24] | X. J. Li, X. L. Li, K. Lu, Random attractors for stochastic parabolic equations with additive noise in weighted spaces, Commun. Pure Appl. Anal., 17 (2018), 729-749. doi: 10.3934/cpaa.2018038 |
[25] | F. Wang, J. Li, Y. Li, Random attractors for Ginzburg-Landau equations driven by difference noise of a Wiener-like process, Adv. Differ. Equ., 2019 (2019), 1-18. doi: 10.1186/s13662-018-1939-6 |
[26] | R. Sell, Y. You, Dynamics of Evolutionary Equations, Springer-Verlag, New York, 2002. |
[27] | V. V. Chepyzhov, M. I. Vishik, Attractors for Equations of Mathematical Physics, American Mathematical Society, Providence, Rhode Island, 2002. |
[28] | I. Chueshov, Monotone Random Systems Theory and Applications, Springer, Berlin, Heidelberg, 2002. |