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By using the continuation theorem base on Gaines and Mawhin''s coincidence degree, sufficient and realistic conditions are obtained for the global existence of positive periodic solutions for a discrete time nonautonomous food chain model, and sufficient conditions for the global stability of positive periodic solutions are also obtained. Some known results are extended. [Copyright &y& Elsevier]

By using the continuation theorem base on Gaines and Mawhin''s coincidence degree, sufficient and realistic conditions are obtained for the global existence of positive periodic solution for a delayed predator–prey system without dominating instantaneous negative feedback. Indeed, our result are applicable to statedependent delays. [Copyright &y& Elsevier]

With the help of continuation theorem base on Gaines and Mawhin''s coincidence degree, sufficient and realistic conditions are obtained for the global existence of positive periodic solutions for both the first and the second Leslie–Gower predator–prey models with distributed or state dependent delays. [Copyright &y& Elsevier]

With the help of continuation theorem in coincidence degree theory and Lyapunov functions, we derive sufficient and realistic conditions that guarantee the existence of a positive periodic solution for a delayed discrete predator–prey system, and also obtain sufficient conditions for the global stability of positive periodic solutions. [Copyright &y& Elsevier]

With the help of continuation theorem based on Gaines and Mawhin’s coincidence degree, sufficient and realistic conditions are obtained for the global existence of positive periodic solutions for the delay differential system with feedback control. When these results are applied to some special delay population models, some new results are obtained, and some known results are generalized. [Copyright &y& Elsevier]

This paper studies the existence, global stability and uniform persistence of positive periodic solutions of a periodic predator–prey system with Holling type III functional response. By using the continuation theorem of coincidence degree theory and Liapunov functional, some sufficient conditions are obtained. [Copyright &y& Elsevier]