Abstract
The following notes are based on my lectures given at CIME Session on ”Dynamical Systems” from June 19 to June 26, 2000 in Cetraro (Cosenza). In Section 1, we study spatially discrete nonlinear diffusion equations and discuss various phenomenon; in Section 2, we introduce the idea of spatial chaos by studying Nagumo equation; in Section 3, 4 and 5, we present a general theory for pattern formation and spatial chaos in lattice dynamics systems; finally in Section 6 and 7, we study the special case of synchronisation phenomena of lattice systems.
I would like to express my thanks to Professors P. Zecca and J. Macki and the host of the conference for inviting me to participate in this conference and making the publication of this note possible. I would also like to express my gratitude to Ms G. M. Wu, without whose help these notes would not have been completed. Mimmie, thank you for your patience and hard work.
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© 2003 Springer-Verlag Berlin Heidelberg
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Chow, SN. (2003). Lattice Dynamical Systems. In: Macki, J.W., Zecca, P. (eds) Dynamical Systems. Lecture Notes in Mathematics, vol 1822. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-540-45204-1_1
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DOI: https://doi.org/10.1007/978-3-540-45204-1_1
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