Periodicity in a Nonlinear Predator-prey System with State Dependent Delays |
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| Authors: | Feng-de Chen Jin-lin Shi |
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| Affiliation: | (1) School of Mathematics and Computer, Fuzhou University, Fuzhou 350002, China |
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| Abstract: | 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 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 ω and  are positive constants. 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, JA03014) and the Foundation of Developing Science and Technical of Fuzhou University (2003-QX-21). |
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| Keywords: | periodic solutions nonlinear delay predator-prey coincidence degree |
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{{dt}} = N_{1} {left( t right)}left[ {b_{1} {left( t right)} - {sumlimits_{i = 1}^n {a_{i} {left( t right)}{left( {N_{1} {left( {t - tau _{i} {left( {t,N_{1} {left( t right)},N_{2} {left( t right)}} right)}} right)}} right)}^{{alpha _{i} }} } }} right.}
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{frac{{dN_{2} {left( t right)}}}
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