Xie, Lingli; Teo, Kok-Lay; Zhao, Yi Invariant manifold with complete foliations and chaotification analysis for a kind of PDEs with boundary coupling. (English) Zbl 1185.37160 Int. J. Bifurcation Chaos Appl. Sci. Eng. 17, No. 9, 3183-3198 (2007). Summary: We are concerned with the existence of invariant manifolds and complete foliations for a class of PDEs with boundary coupling. Some new form of gap relative coupling and inequality conditions are obtained. Further, we prove the topological equivalence of the flows in the respective attractors between the system and its spatial discretization system (an ODE system). Finally, the chaotification of the system is discussed through an example and simulation is generated to illustrate the theoretical results. MSC: 37L25 Inertial manifolds and other invariant attracting sets of infinite-dimensional dissipative dynamical systems 37D45 Strange attractors, chaotic dynamics of systems with hyperbolic behavior 35Q53 KdV equations (Korteweg-de Vries equations) PDFBibTeX XMLCite \textit{L. Xie} et al., Int. J. Bifurcation Chaos Appl. Sci. Eng. 17, No. 9, 3183--3198 (2007; Zbl 1185.37160) Full Text: DOI References: [1] Bruschi S. M., J. DE 168 pp 67– [2] Capasso V., SIAM. J. Appl. Math. 57 pp 327– [3] DOI: 10.1006/jmaa.1997.5774 · Zbl 0907.34039 · doi:10.1006/jmaa.1997.5774 [4] Chen X. Y., J. DE 139 pp 283– [5] Chow S. N., J. DE 74 pp 285– [6] DOI: 10.1017/S0308210500027748 · Zbl 0692.58019 · doi:10.1017/S0308210500027748 [7] DOI: 10.1051/cocv:2004028 · Zbl 1088.93008 · doi:10.1051/cocv:2004028 [8] DOI: 10.1016/j.na.2004.11.007 · Zbl 1072.93013 · doi:10.1016/j.na.2004.11.007 [9] Le D., Com. in PDE 22 pp 413– [10] Olaf H., Discr. Contin. Dyn. Syst. 3 pp 541– [11] DOI: 10.1007/978-1-4612-5561-1 · Zbl 0516.47023 · doi:10.1007/978-1-4612-5561-1 [12] DOI: 10.1080/002071798222848 · Zbl 0943.93051 · doi:10.1080/002071798222848 [13] DOI: 10.1007/978-1-4612-0645-3 · doi:10.1007/978-1-4612-0645-3 [14] Zhao Y., Contr. Th. Appl. 2 pp 11– [15] DOI: 10.1007/978-3-540-40018-9_7 · doi:10.1007/978-3-540-40018-9_7 [16] DOI: 10.1142/S021812740501234X · Zbl 1082.37032 · doi:10.1142/S021812740501234X 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.