Periodicity in a food-limited population model with toxicants and state dependent delays☆

By Fengde Chen, D. Sun, Jinlin Shi. 2003

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Abstract 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 a food-limited population model with toxicant and state dependent delays, that is du(t) dt =u(t) r(t)−a(t)u(t)−∑ j=1 m b j (t)u(t−τ j (t,u(t))) k(t)+c(t)u(t)+∑ j=1 m d j (t)u(t−η j (t,u(t))) , where r(t),k(t),a(t),bj(t),dj(t), j=1,2,…,m, are continuous, real-valued periodic functions with period ω>0 and r(t),k(t),a(t)>0; bj(t),dj(t)⩾0, j=1,2,…,m, are periodic continuous functions with period ω>0, τj,ηj are ω-periodic with respect to their first arguments. Some new results are obtained.

Subfields: Applied Mathematics, Mathematical Physics, Public Health, Environmental and Occupational Health

View Paper: https://www.semanticscholar.org/paper/870542a4a0c1f5f0de04632e8e54be7d71372ea7