Periodic solutions of delayed ratio-dependent predator–prey models with monotonic or nonmonotonic functional responses
By Yong-Hong Fan, Wan-Tong Li, Linlin Wang. 2004
66 citations recorded by the source corpus.
Abstract In this paper, by using the continuation theorem of coincidence degree theory, we establish several existence results of positive periodic solutions for the delayed ratio-dependent predator–prey model x′(t)=x(t) a(t)−b(t) ∫ −∞ t K(t−s)x(s) d s −c(t)g x(t) y(t) y(t), y′(t)=y(t) e(t)g x(t−τ(t)) y(t−τ(t)) −d(t) , when functional response function g is a monotonic or nonmonotonic, where a ( t ), b ( t ), e ( t ), τ ( t ) and d ( t ) are all positive periodic continuous functions with period ω >0, K is a dense function. As corollaries, some applications are listed. In particular, our results extend some known criteria.
Subfields: Applied Mathematics, Geometry and Topology, Public Health, Environmental and Occupational Health
View Paper: https://www.semanticscholar.org/paper/0f45ac20fafbcbf4f831db0675102bf4d2692063
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Citations in the corpus
- Global asymptotic stability of a ratio-dependent predator-prey system with diffusion (2006, background): “2) with periodic coefficients, in [5] we explored the existence of periodic solutions with delays.”