periodicity in a nonlinear predator-prey system with state dependent delays
Author(s): FENG Dechen, JIN Linshischoolofmathematicsandcomputer, FUZHOU University, FUZHOU 350002, china
Pages: 49-60
Year: 2005 Issue: 1
Journal: Acta Mathematicae Applicatae Sinica
Keyword: periodic solutions; nonlinear; delay; predator-prey; coincidence degree;
Abstract: <正> With the help of a continuation theorem based on Gaines and Mawhin\'s coincidence degree, easily verifiable criteria are established for the global existence of positive periodic solutions of the following nonlinear state dependent delays predator-prey system where a_i(t),c_j(t),d_i(t) are continuous positive periodic functions with periodic ω>0, b_1(t),b_2(t) are continuous periodic functions with periodic ωand ∫_0~ωbi(t)dt>0. T_i,σ_j, p_i (i=1,2,…,n, j=1, 2,…,m) are continuous and ω-periodic with respect to their first arguments, respectively, α_i, β_j,γ_i(i=1,2,…,n, j=1,2, …, m) are positive constants.
Pages: 49-60
Year: 2005 Issue: 1
Journal: Acta Mathematicae Applicatae Sinica
Keyword: periodic solutions; nonlinear; delay; predator-prey; coincidence degree;
Abstract: <正> With the help of a continuation theorem based on Gaines and Mawhin\'s coincidence degree, easily verifiable criteria are established for the global existence of positive periodic solutions of the following nonlinear state dependent delays predator-prey system where a_i(t),c_j(t),d_i(t) are continuous positive periodic functions with periodic ω>0, b_1(t),b_2(t) are continuous periodic functions with periodic ωand ∫_0~ωbi(t)dt>0. T_i,σ_j, p_i (i=1,2,…,n, j=1, 2,…,m) are continuous and ω-periodic with respect to their first arguments, respectively, α_i, β_j,γ_i(i=1,2,…,n, j=1,2, …, m) are positive constants.
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