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Analysis for a Food Chain Model with Crowley–Martin Functional Response and Time Delay

Authors: Kejun Zhuang, Zhaohui Wen


This paper is concerned with a nonautonomous three species food chain model with Crowley–Martin type functional response and time delay. Using the Mawhin-s continuation theorem in theory of degree, sufficient conditions for existence of periodic solutions are obtained.

Keywords: Periodic solutions, food chain model, coincidence degree, Crowley–Martin functional response

Digital Object Identifier (DOI):

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[1] B. Mukhopadhyay, R. Bhattacharyya. Bifurcation analysis of an ecological food-chain model with switching predator. Applied Mathematics and Computation, 201(2008) 260-271.
[2] R.K. Naji, R.K. Upadhyay, V. Rai. Dynamical consequences of predator interference in a tri-trophic model food chain. Nonlinear Analysis: RWA, 11(2010) 809-818.
[3] A. Maiti, A.K. Pal, G.P. Samanta. Effect of time-delay on a food chain model. Applied Mathematics and Computation, 200(2008) 189-203.
[4] S. Pathak, A. Maiti, G.P. Samanta. Rich dynamics of a food chain model with Hassell-Varley type functional responses. Applied Mathematics and Computation, 208(2009) 303-317.
[5] K. Zhuang, Z. Wen. Dynamics of a discrete three species food chain system. International Journal of Computational and Mathematical Sciences, 5(2011) 13-15.
[6] C. Shen. Permanence and global attractivity of the food-chain system with Holling IV type functional response. Applied Mathematics and Computation, 194(2007) 179-185.
[7] R.K. Upadhyay, R. K. Naji. Dynamics of a three species food chain model with Crowley-Martin type functional response. Chaos, Solitons and Fractals, 42(2009) 1337-1346.
[8] R.K. Upadhyay, S.N. Raw, V. Rai. Dynamical complexities in a tri- trophic hybrid food chain model with Holling type II and Crowley- Martin functional responses. Nonlinear Analysis: Modelling and Control, 15(2010) 361-375.
[9] X. Shi, X. Zhou, X. Song. Analysis of a stage-structured predator- prey model with Crowley-Martin function. J. Appl. Math. Comput., DOI 10.1007/s12190-010-0413-8.
[10] G.T. Skalski, J.F. Gilliam. Functional responses with predator interference: viable alternatives to the Holling type II model. Ecology, 82(2001) 3083-3092.
[11] B. Zhang and M. Fan, A remark on the application of coincidence degree to periodicity of dynamic equations on time scales, J. Northeast Normal University (Natural Science Edition), 39(2007) 1-3. (in Chinese)
[12] R. Gaines and J. Mawhin, Coincidence degree and nonlinear differential equations, Springer Verlag, Berlin, 1977.