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AMJCUB
Applied Mathematics-A Journal of Chinese Universities  2021, Vol. 36 Issue (1): 1-15    DOI:
    
Stability results for a nonlinear two-species competition model with size-structure
LIU Yan,  HE Ze-rong
1 Department of Mathematics, China Jiliang University, Hangzhou 310018, China.
2 Institute of Operational Research and Cybernetics, Hangzhou Dianzi University, Hangzhou 310018,China.
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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 sizedependent. 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.

Key words： competition      size-structure      existence and uniqueness      semigroup      stability     
Published: 15 March 2021
CLC:  92D05  
  47D06  
  35B35  
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LIU Yan
HE Ze-rong
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LIU Yan, HE Ze-rong. Stability results for a nonlinear two-species competition model with size-structure. Applied Mathematics-A Journal of Chinese Universities, 2021, 36(1): 1-15.

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http://www.zjujournals.com/amjcub/     OR     http://www.zjujournals.com/amjcub/Y2021/V36/I1/1


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

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 sizedependent. 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.

关键词： competition,  size-structure,  existence and uniqueness,  semigroup,  stability 
[1] FEI Chen, FEI Wei-yin, YAN Li-tan. Existence and Stability of Solutions to Highly Nonlinear Stochastic Differential Delay Equations Driven by G-Brownian Motion[J]. Applied Mathematics-A Journal of Chinese Universities, 2019, 34(2): 184-.
[2] P Indhumathi, A Leelamani. Existence and uniqueness results for mild solutions of random impulsive abstract neutral partial differential equation over real axis[J]. Applied Mathematics-A Journal of Chinese Universities, 2018, 33(1): 71-87.