An Optimal Control Policy for A Discrete Model with Holling-Tanner Functional Response
R.P. Agarwal, Difference Equations and Inequalities, Marcel Dekker, Inc., New York (2000).
J.R. Beddington, Mutual interference between parasites or predators and its effect on searching efficiency, J. Animal Ecol. 44 (1975), 331–340.
G. Calio, Z.J. Jing aand P. Sy, Qualitative analysis of a mathematical model of a predator-prey system, in Proceedings of Functional and Global Analysis, University of the Philippines, Diliman, Quezon city (1997).
C.W. Clark, Mathematical Bioeconomics: The Optimal Management of Renewable Resources, Wiley, New York (1976).
D.L. De Angelis, R.A. Goldstein and R.V. O’Neill, A model for trophic interaction, Ecology 56 (1975), 881 – 892.
M. Danca, S. Codreanu and B. Bako, Detailed analysis of a nonlinear prey-predator model, J. Biol. Phys. 23 (1997), 11 – 20.
S. Eladyi, An Introduction to Difference Equations, Springer (2000).
C.S. Holling, The functional response of predator to prey density and its role in mimicry and population regulation, Mem. Ent. Soc. Canada 45 (1965), 1 – 60.
A. Hastings, Population Biology, Concepts and Models, Springer, New York (1998).
Z.J. Jing and J. Yang, Bifurcation and chaos discrete-time predator-prey system, Chaos Solitons Fractals 27 (2006), 259 – 277.
M.R.S. Kulenovie and M. Nurkanovic, Global asymptotic behavior of a two dimensional system of difference equations modeling cooperation, J. Differ. Equat. Appl. 9 (2003), 149 – 59.
Y. Lamontagne, C. Coutu and C. Rousseau, Bifurcation analysis of a predator-prey system with generalized Holling type III functional response, Journal of Dynamics and Differential Equations 20 (3) (2008), 535 – 571.
S. Lenhart and J.T. Workman, Optimal control applied to biological models, in Mathematical and Computational Biology Series, Chapman Hall/CRC, London, UK (2007).
J.D. Murray, Mathematical Biology, 3rd edition, Springer-Verlag, Berlin—Heidelberg—New York (2002).
V. Rai, V. Kumar and L.K. Pandey, A new prey-pradator model, IEEE Trans. Systems Man Cybernet. 21 (1) (1991), 261 – 263.
X. Song and H. Guo, Global stability of a stage-structured predator-prey system, Int. J. Biomath. 1 (3) (2008), 313 – 326.
S.P. Sethi and G.L. Thomson, Optimal Control Theory: Applications to Management Science and Economics, Kluwer, Boston (2000).
J.T. Tanner, The stability and the intrinsic growth rates of prey-and predator populations, Ecology 56 (1975), 855 – 867.
P. Turchin, Complex Population Dynamics, Princeton Univ. Press, Princeton, NJ (2003).
W.B. Zhang, Discrete Dynamical Systems, Bifurcations and Chaos in Economics, Elsevier (2006).
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