Stability And Persistence Of Two-Dimensional Patterns

    Authors

    S. R. Choudhury

    Comments

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    Abbreviated Journal Title

    Nonlinear Anal.-Theory Methods Appl.

    Keywords

    stability conditions for two-dimensional dissipative patterns; nonlinear; persistence, disruption, and decay of structures; numerical results, ; comparisons with simulations; Mathematics, Applied; Mathematics

    Abstract

    The canonical equations for evolution of the amplitude order parameters describing the nonlinear development and persistence of two-dimensional three-mode spatial patterns generated by Turing instability in dissipative systems are considered, The stability conditions for persistent hexagonal patterns are generalized, and the conditions under which patterns are either disrupted, exhibit bounded quasiperiodic or chaotic behavior, or decay under nonlinear evolution are derived. These conditions are applied to the specific three-mode amplitude evolution equations derived for the Schnackenberg model and a delay predator-prey system in Chapter 3. Numerical results are presented for the persistence, disruption and decay of patterns in these systems, including fairly detailed comparisons with simulation results for the Schnackenberg model.

    Journal Title

    Nonlinear Analysis-Theory Methods & Applications

    Volume

    30

    Issue/Number

    8

    Publication Date

    1-1-1997

    Document Type

    Article; Proceedings Paper

    Language

    English

    First Page

    5491

    Last Page

    5498

    WOS Identifier

    WOS:000072052900096

    ISSN

    0362-546X

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