Bates, Peter W.; Lu, Kening; Wang, Bixiang Attractors for lattice dynamical systems. (English) Zbl 1091.37515 Int. J. Bifurcation Chaos Appl. Sci. Eng. 11, No. 1, 143-153 (2001). Summary: We study the asymptotic behavior of solutions for lattice dynamical systems. We first prove asymptotic compactness and then establish the existence of global attractors. The upper semicontinuity of the global attractor is also obtained when the lattice differential equations are approached by finite-dimensional systems. Cited in 2 ReviewsCited in 178 Documents MSC: 37L60 Lattice dynamics and infinite-dimensional dissipative dynamical systems 37L30 Attractors and their dimensions, Lyapunov exponents for infinite-dimensional dissipative dynamical systems PDFBibTeX XMLCite \textit{P. W. Bates} et al., Int. J. Bifurcation Chaos Appl. Sci. Eng. 11, No. 1, 143--153 (2001; Zbl 1091.37515) Full Text: DOI References: [1] DOI: 10.1142/S0218127494000459 · Zbl 0870.58049 [2] DOI: 10.1017/S0308210500031498 · Zbl 0721.35029 [3] DOI: 10.1007/s003329900037 · Zbl 0903.58020 [4] DOI: 10.1007/s002050050189 · Zbl 0956.74037 [5] DOI: 10.1016/0025-5564(81)90085-7 · Zbl 0454.92009 [6] Bell J., Quart. Appl. Math. 42 pp 1– (1984) [7] DOI: 10.1109/81.473583 [8] DOI: 10.1137/S0036139994261757 · Zbl 0840.34012 [9] Chow S., Rand. Comput. Dyn. 4 pp 109– (1996) [10] DOI: 10.1006/jdeq.1998.3478 · Zbl 0911.34050 [11] DOI: 10.1109/31.7600 · Zbl 0663.94022 [12] DOI: 10.1109/31.7601 [13] DOI: 10.1109/81.222795 · Zbl 0800.92041 [14] DOI: 10.1142/S0218127498000152 · Zbl 0933.37042 [15] Erneux T., Physica 67 pp 237– (1993) [16] Feireisl E., C. R. Acad. Sci. Paris Ser. pp 147– (1994) [17] DOI: 10.1006/jdeq.1996.0117 · Zbl 0862.35058 [18] DOI: 10.1007/BF01192578 [19] DOI: 10.1137/0147038 · Zbl 0649.34019 [20] DOI: 10.1016/S0022-5193(05)80465-5 [21] DOI: 10.1021/j100191a038 [22] DOI: 10.1109/81.473584 [23] DOI: 10.1006/jdeq.1996.0172 · Zbl 0867.35045 [24] DOI: 10.1109/81.251828 · Zbl 0844.93056 [25] DOI: 10.1007/BF02479046 [26] DOI: 10.1137/S0036139995282670 · Zbl 0868.58059 [27] Wang B., Physica 128 pp 41– (1999) [28] DOI: 10.1016/0022-0396(92)90142-A · Zbl 0752.34007 This reference list is based on information provided by the publisher or from digital mathematics libraries. Its items are heuristically matched to zbMATH identifiers and may contain data conversion errors. In some cases that data have been complemented/enhanced by data from zbMATH Open. This attempts to reflect the references listed in the original paper as accurately as possible without claiming completeness or a perfect matching.