摘要
With the help of a continuation theorem based on Gaines and Mawhinscoincidence degree, easily verifiable criteria are established for the global existence of positiveperiodic solutions of the following nonlinear state dependent delays predator-prey system{dN_1(t)/dt = N_1(t)[b_1(t) - ∑ from i=1 to n of ai(t)(N_1(t-τ_i(t,N_1(t), N_2(t))))^(α_i) - ∑from j=1 to m of c_j(t)(N_2(t - σ_j(t,N1(t),N_2(t))))^(β_j)] dN_2(t)/dt = N_2(t)[-b_2(t) + ∑ fromi=1 to n of d_i(5)(N_1(t - ρ_i(t,N_1(t),N_2(t))))^(γ_i)], where a_i(t), c_j(t), d_i(t) arecontinuous positive periodic functions with periodic 】 0, b_1(t), b_2(t) are continuous periodicfunctions with periodic ω and ∫_0~ωb_i(t)dt 】 0. τ_i, σ_j, ρ_i (i = 1,2,…,m) are continuousand 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.
With the help of a continuation theorem based on Gaines and Mawhinscoincidence degree, easily verifiable criteria are established for the global existence of positiveperiodic solutions of the following nonlinear state dependent delays predator-prey system{dN_1(t)/dt = N_1(t)[b_1(t) - ∑ from i=1 to n of ai(t)(N_1(t-τ_i(t,N_1(t), N_2(t))))^(α_i) - ∑from j=1 to m of c_j(t)(N_2(t - σ_j(t,N1(t),N_2(t))))^(β_j)] dN_2(t)/dt = N_2(t)[-b_2(t) + ∑ fromi=1 to n of d_i(5)(N_1(t - ρ_i(t,N_1(t),N_2(t))))^(γ_i)], where a_i(t), c_j(t), d_i(t) arecontinuous positive periodic functions with periodic > 0, b_1(t), b_2(t) are continuous periodicfunctions with periodic ω and ∫_0~ωb_i(t)dt > 0. τ_i, σ_j, ρ_i (i = 1,2,…,m) are continuousand 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.
基金
Supported by the National Natural Science Foundation of China (Tian Yuan Foundation) (No.10426010)
the Foundation of Science and Technology of Fujian Province for Young Scholars (2004J0002)
the Foundation of Fujian Education Bureau (JA04156, JA0301
