Transient and asymptotic dynamics of a prey-predator system with diffusion

Evangelos Latos*, Takashi Suzuki, Yoshio Yamada

*この研究の対応する著者

    研究成果: Article査読

    14 被引用数 (Scopus)

    抄録

    In this paper, we study a prey-predator system associated with the classical Lotka-Volterra nonlinearity. We show that the dynamics of the system are controlled by the ODE part. First, we show that the solution becomes spatially homogeneous and is subject to the ODE part as t → ∞. Next, we take the shadow system to approximate the original system as D → ∞. The asymptotics of the shadow system are also controlled by those of the ODE. The transient dynamics of the original system approaches to the dynamics of its ODE part with the initial mean as D → ∞. Although the asymptotic dynamics of the original system are also controlled by the ODE, the time periods of these ODE solutions may be different. Concerning this property, we have that any δ > 0 admits D 0 > 0 such that if TÌ, the time period of the ODE, satisfies TÌ>δ, then the solution to the original system with D ≥ D 0 cannot approach the stationary state.

    本文言語English
    ページ(範囲)1101-1109
    ページ数9
    ジャーナルMathematical Methods in the Applied Sciences
    35
    9
    DOI
    出版ステータスPublished - 2012 6

    ASJC Scopus subject areas

    • 数学 (全般)
    • 工学(全般)

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