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Stability results for a nonlinear two-species competition model with size-structure

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Abstract

We formulate a system of integro-differential equations to model the dynamics of competition in a two-species community, in which the mortality, fertility and growth are size-dependent. Existence and uniqueness of nonnegative solutions to the system are analyzed. The existence of the stationary size distributions is discussed, and the linear stability is investigated by means of the semigroup theory of operators and the characteristic equation technique. Some sufficient conditions for asymptotical stability / instability of steady states are obtained. The resulting conclusion extends some existing results involving age-independent and age-dependent population models.

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Authors and Affiliations

  1. Department of Mathematics, China Jiliang University, Hangzhou, 310018, China

    Yan Liu

  2. Institute of Operational Research and Cybernetics, Hangzhou Dianzi University, Hangzhou, 310018, China

    Ze-rong He

Authors
  1. Yan Liu
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  2. Ze-rong He
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Corresponding authors

Correspondence to Yan Liu or Ze-rong He.

Additional information

Supported by the National Natural Science Foundation of China (11871185, 11401549) and Zhejiang Provincial Natural Science Foundation of China (LY18A010010).

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Liu, Y., He, Zr. Stability results for a nonlinear two-species competition model with size-structure. Appl. Math. J. Chin. Univ. 36, 1–15 (2021). https://doi.org/10.1007/s11766-021-3322-8

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  • DOI: https://doi.org/10.1007/s11766-021-3322-8

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