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New theory of spatio‐temporal chaos in nonlinear systems of partial differential equations
Author(s) -
A.Magnitskii Nikolai
Publication year - 2007
Publication title -
pamm
Language(s) - English
Resource type - Journals
ISSN - 1617-7061
DOI - 10.1002/pamm.200700512
Subject(s) - nonlinear system , mathematics , torus , partial differential equation , mathematical analysis , cascade , differential equation , type (biology) , chaos (operating system) , subharmonic , dynamical systems theory , physics , computer science , quantum mechanics , geometry , ecology , chemistry , computer security , chromatography , biology
It is shown that there exists one universal scenario of transition to chaos in three considered systems of nonlinear partial differential equations of diffusion type. It is the subharmonic cascade of bifurcations of two‐dimensional tori along one or both frequencies. So, it is shown that the new universal Feigenbaum‐Sharkovskii‐Magnitskii theory of dynamical chaos in nonlinear differential equations is applicable also for nonlinear partial differential equations of diffusion type. (© 2008 WILEY‐VCH Verlag GmbH & Co. KGaA, Weinheim)