Unique Existence of Globally Asymptotical Input-to-State Stability of Positive Stationary Solution for Impulsive Gilpin-Ayala Competition Model with Diffusion and Delayed Feedback under Dirichlet Zero Boundary Value

Ruofeng Rao

doi:10.20944/preprints202009.0052.v1

Preprint Article Version 1 Preserved in Portico This version is not peer-reviewed

Version 1 : Received: 2 September 2020 / Approved: 3 September 2020 / Online: 3 September 2020 (04:26:14 CEST)

By partly generalizing the Lipschitz condition of existing results to the generalized Lipschitz one, the author utilizes a fixed point theorem, variational method and Lyapunov function method to derive the unique existence of globally asymptotical input-to-state stability of positive stationary solution for Gilpin-Ayala competition model with diffusion and delayed feedback under Dirichlet zero boundary value. Remarkably, it is the first paper to derive the unique existence of the stationary solution of reaction-diffusion Gilpin-Ayala competition model, which is globally asymptotical input-to-state stability. And numerical examples illuminate the effectiveness and feasibility of the proposed methods.

Gilpin-Ayala competition model; globally asymptotical stability; Lyapunov function; Markovian jumping

Computer Science and Mathematics, Applied Mathematics

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Unique Existence of Globally Asymptotical Input-to-State Stability of Positive Stationary Solution for Impulsive Gilpin-Ayala Competition Model with Diffusion and Delayed Feedback under Dirichlet Zero Boundary Value

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