Global-in-time behavior of lotka-volterra system with diffusion: Skew-symmetric case

Takashi Suzuki, Yoshio Yamada

    Research output: Contribution to journalArticle

    6 Citations (Scopus)

    Abstract

    We study the global-in-time behavior of the Lotka- Volterra system with diffusion. In the first category, the interaction matrix is skew-symmetric and the linear terms are non-increasing. There, the solution exists globally in time with compact orbit, provided that n ≥ 2, where n denotes the space dimension. Under the presence of entropy, its Ö-limit set is composed of a spatially homogeneous orbit. Furthermore, any spatially homogeneous solution is periodic in time, provided with constant entropy. In the second category, the interaction matrix exhibits a dissipative profile. There, the solution exists globally in time with compact orbit if n ≥ 3. Its ω-limit set, furthermore, is contained in spatially homogeneous stationary states. In particular, no periodic-in-time solution is admitted.

    Original languageEnglish
    Pages (from-to)181-216
    Number of pages36
    JournalIndiana University Mathematics Journal
    Volume64
    Issue number1
    DOIs
    Publication statusPublished - 2015

    Keywords

    • Blowup analysis
    • Lotka-Volterra system
    • Periodic-in-time solution
    • Thermodynamic
    • Ω-limit set

    ASJC Scopus subject areas

    • Mathematics(all)

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