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, Journal of Theoretical Biology   79 (3): 303-315. Xu, R., Chaplain, M. A. J. and Davidson F. A. (2004). Periodic solutions for a delayed predator-prey model of prey dispersal in two-patch environments, Nonlinear Analysis: Real World Applications   5 (1): 183-206. Xu, R. and Ma, Z. E. (2008). Stability and Hopf bifurcation in a ratio-dependent predator-prey system with stage structure, Chaos, Solitons & Fractals   38 (3): 669-684. Yan, X. P. and Li, W. T. (2006). Hopf bifurcation and global periodic solutions in a delayed predator-prey system, Applied Mathematics and

References [1] AUGER, P.-PARRA, R. B-MORAND, S.-SÁNCHEZ, E.: A predator-prey model with predators using hawk and dove tactics, Mathematical Biosciences 177&178 (2002), 185-200. [2] KUZNETSOV, Y. A.: Elements of Applied Bifurcation Theory. Springer-Verlag, Berlin, New York, Inc. 1998.

density and its role in mimicry and population regulation, Memoirs of the Entomological Society of Canada 97 (45): 1-60. Hsu, S.B. (1978). The application of the Poincare-transform to the Lotka-Volterra model, Journal of Mathematical Biology 6 (1): 67-73. Hu, Z., Teng, Z. and Zhang, L. (2011). Stability and bifurcation analysis of a discrete predator-prey model with nonmonotonic functional response, Nonlinear Analysis: Real World Applications 12 (4): 2356-2377. Huang, J. and Xiao, D. (2004). Analyses of bifurcations and stability in a predator-prey system with

References [1] BOLKER, M. B.: Ecological Models and Data in R. Princeton Univ. Press, Princeton, NJ, 2008. [2] BRITTON, N. F.: Essential Mathematical Biology. Springer-Verlag, London, 2003. [3] CARPENTER, S. R.-COTTINGHAM,K. L.-STOW, C. A.: Fitting predator-prey models to time series with observation errors, Ecology 75 (1994), 1254-1264. [4] GAUSE, G. F.: The Struggle for Existence. Williams&Wilkins, Baltimore, 1934. [5] HLUCHÝ, M.-POSPÍŠIL, Z.: Use of the predatory mite Typhlodromus pyri Scheuten (Acari: Phytoseiidae) for biological protection of grape

. 10 (2005), 681-691. [9] N. Kasarinoff and P. van der Deiesch, A model of predator-prey system with functional response, Math. Biosci. 39 (1978), 124-134. [10] J. M. McNair, The effects of refuges on predator-prey interactions: a reconsideration, Theor. Popul. Biol. 29 (1986), 38-63. [11] S. Ruan and D. Xiao, Global analysis in a predator-prey system with nonmonotonic functional response, SIAM J. Appl. Math. 61 (2001), 1445-1472. [12] G. D. Ruxton, Short term refuge use and stability of predator-prey models, Theor. Popul. Biol. 47(1) (1995), 1-17. [13] A

applications to predator-prey models, Journal of Computational and Applied Mathematics 189 (1): 98-108. Dimitrov, D. and Kojouharov, H. (2007). Stability-preserving finite-difference methods for general multi-dimensional autonomous dynamical systems, International Journal of Numerical Analysis Modeling 4 (2): 280-290. Karcz-Dul˛eba, I. (2004). Asymptotic behaviour of a discrete dynamical system generated by a simple evolutionary process, International Journal of AppliedMathematics and Computer Science 14 (1): 79-90. Gumel, A., McCluskey, C. and van den Driessche, P

(2): 280-290. Dimitrov, D. and Kojouharov, H. (2008). Nonstandard finite difference methods for predator-prey models with general functional response, Mathematics and Computers in Simulation 78(1): 1-11. Ding, D., Ma, Q. and Ding, X. (2013). A non-standard finite difference scheme for an epidemic model with vaccination, Journal of Difference Equations and Applications 19(2): 179-190. Dumont, Y. and Lubuma, J.M.-S. (2005). Non-standard finite-difference methods for vibro-impact problems, Proceedings of the Royal Society, A: Mathematical, Physical and Engineering Sciences

and application of a mathematical cholera model, Mathematical Biosciences and Engineering 8(3):733-752. Liu, X. and Wang, C. (2010). Bifurcation of a predator-prey model with disease in the prey, Nonlinear Dynamics 62(4):841-850. Marino, S., Hogue, I., Ray, C.J. and Kirschner, D.E.(2008). A methodology for performing global uncertainty and sensitivity analysis in system biology, Journal of Theoretical Biology 254(1): 178-196. Moghadas, S.M. and Gumel, A.B. (2002). Global stability of a two-stage epidemic model with generalized non-linear incidence, Mathematics and

explains the interaction between cancer and the human body. Furthermore, in [ 2 ], Ö. Akın and Ö. Oruç have studied a predator-prey model with fuzzy initial values. Then, by considering a second-order initial values Ö. Akın, T. Khaniyev, Ö. Oruç and I. B. Turksen [ 3 ] have generalized the model. Works about the prey-predator model of fuzzy numbers can be seen in [ 1 , 26 , 28 ]. Lastly, Benli and Keskin [ 8 ] considered a model which has a predator-prey structure between the monoclonal tumor and the macrophages. In this study, a new model upon the work of F. Bozkurt

-Volterra predator-prey model with two delays, International Journal of Applied Mathematics and Computer Science 21 (1): 97-107, DOI: 10.2478/v10006-011-0007-0. Zahnle, K., Schaefer, L. and Fegley, B. (2010). Earth’s earliest atmospheres, Cold Spring Harbor Perspectives in Biology 2 (10): 1-17.