2024-03-28T22:59:42Zhttps://eprints.lib.hokudai.ac.jp/dspace-oai/requestoai:eprints.lib.hokudai.ac.jp:2115/697392022-11-17T02:08:08Zhdl_2115_45007hdl_2115_116SPATIO-TEMPORAL CHAOS IN A DISCRETE TURING MODELKANG, HUNSEOKTuring ModelCoupled Map LatticesTraveling WaveHyperbolic setSmale-horseshoeSpatio-Temporal Chaos410In this paper, a discrete version of a reaction-diffusion equation, lso known as coupled map lattice (CML), which corresponds to the Tur- ng model of morphogenesis is studied. It is shown that CML possesses a yperbolic property displaying a type of spatio-temporal chaos. Through- ut a mathematical background of hyperbolic properties in lattice dynamical ystems which are related to spatio-temporal chaos, a mathematical proof is iven that the CML obtained from the Turing model possesses such hyperbolic roperties. Finally, numerical studies of this finding in varying parameters to resent a variety of chaotic behaviors of this system is performed.Department of Mathematics, Hokkaido UniversityDepartmental Bulletin Paperapplication/pdfhttp://hdl.handle.net/2115/69739info:doi/10.14943/84079https://eprints.lib.hokudai.ac.jp/dspace/bitstream/2115/69739/1/pre931.pdfHokkaido University Preprint Series in Mathematics9311202008-12-08engpublisher