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Positive periodic solutions of periodic neutral Lotka–Volterra system with distributed delays

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  • Li, Yongkun

Abstract

By using a fixed point theorem of strict-set-contraction, some criteria are established for the existence of positive periodic solutions of the following periodic neutral Lotka–Volterra system with distributed delaysdxi(t)dt=xi(t)ai(t)-∑j=1nbij(t)∫-Tij0Kij(θ)xj(t+θ)dθ-∑j=1ncij(t)∫-Tˆij0Kˆij(θ)xj′(t+θ)dθ,i=1,2,…,n,where ai,bij,cij∈C(R,R+) (i, j=1,2,…,n) are ω-periodic functions, Tij,Tˆij∈(0,∞) (i, j=1,2,…,n) and Kij,Kˆij∈(R,R+) satisfying ∫-Tij0Kij(θ)dθ=1,∫-Tˆij0Kˆij(θ)dθ=1, i, j=1,2,…,n.

Suggested Citation

  • Li, Yongkun, 2008. "Positive periodic solutions of periodic neutral Lotka–Volterra system with distributed delays," Chaos, Solitons & Fractals, Elsevier, vol. 37(1), pages 288-298.
    • Handle: RePEc:eee:chsofr:v:37:y:2008:i:1:p:288-298
    DOI: 10.1016/j.chaos.2006.09.025
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    1. Zhao, Hongyong & Ding, Nan, 2006. "Existence and global attractivity of positive periodic solution for competition-predator system with variable delays," Chaos, Solitons & Fractals, Elsevier, vol. 29(1), pages 162-170.
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