[1]
|
Berryman, A.A. (1992) The Origins and Evolution of Predator-Prey Theory. Ecology, 5, 1530-1535.
https://doi.org/10.2307/1940005
|
[2]
|
May, R.M. (2001) Stability and Complexity in Model Ecosystems. Princeton University Press, Princeton.
|
[3]
|
Murray, J.D. (2003) Mathematical Biology II: Spatial Models and Biomedical Applications. 3rd Edition, Springer, New York.
|
[4]
|
Arditi, R. and Ginzburg, L.R. (1989) Coupling in Predator-Prey Dynamics: Ratio-Dependence. Journal of Theoretical Biology, 139, 311-326. https://doi.org/10.1016/S0022-5193(89)80211-5
|
[5]
|
Collings, J.B. (1997) The Effects of the Functional Response on the Bifurcation Behavior of a Mite Predator-Prey Interaction System. Journal of Mathematical Biology, 36, 149-168. https://doi.org/10.1007/s002850050095
|
[6]
|
Ruan, S. and Xiao, D. (2001) Global Analysis in a Predator-Prey System with Non-Monotonic Functional Response. SIAM Journal on Applied Mathematics, 61, 1445-1472. https://doi.org/10.1137/S0036139999361896
|
[7]
|
Skalski, G.T. and Gilliam, J.F. (2001) Functional Responses with Predator Interference: Viable Alternatives to the Holling Type II Mode. Ecology, 82, 3083-3092. https://doi.org/10.1890/0012-9658(2001)082[3083:FRWPIV]2.0.CO;2
|
[8]
|
Hassell, M.P. and Varley, G.C. (1969) New Inductive Population Model for Insect Parasites and Its Bearing on Biological Control. Nature, 5211, 1133-1137. https://doi.org/10.1038/2231133a0
|
[9]
|
Cosner, C., Deangelis, D.L., Ault, J.S. and Olson, D.B. (1999) Effects of Spatial Grouping on the Functional Response of Predators. Theoretical Population Biology, 1, 65-75. https://doi.org/10.1006/tpbi.1999.1414
|
[10]
|
Abrams, P.A. and Ginzburg, L.R. (2008) The Nature of Predation: Prey Dependent, Ratio Dependent or Neither. Trends in Ecology and Evolution, 8, 337-341.
|
[11]
|
Sutherland, W.J. (1983) Aggregation and the “Ideal Free” Distribution. The Journal of Animal Ecology, 3, 821-828.
https://doi.org/10.2307/4456
|
[12]
|
Gakkhar, S. and Naji, R.K. (2003) Chaos in Seasonally Perturbed Ratio-Dependent Prey-Predator System. Chaos, Solitons & Fractals, 1, 107-118. https://doi.org/10.1016/S0960-0779(02)00114-5
|
[13]
|
Sabin, G.C.W. and Summers, D. (1993) Chaos in a Periodically Forced Predator-Prey Ecosystem Model. Mathematical Biosciences, 1, 91-113. https://doi.org/10.1016/0025-5564(93)90010-8
|
[14]
|
Upadhyay, R.K. and Lyengar, S.P.K. (2005) Effect of Seasonality on the Dynamics of 2 and 3 Species Prey-Predator System. Nonlinear Analysis: Real World Applications, 6, 509-530. https://doi.org/10.1016/j.nonrwa.2004.11.001
|
[15]
|
Ackland, G.J. and Gallagher, I.D. (2004) Stabilization of Large Generalized Lotka-Volterra Food Webs by Evolutionary Feedback. Physical Review Letters, 93, Article ID: 158701.
|
[16]
|
Jiang, G. and Lu, Q. (2006) The Dynamics of a Prey-Predator Model with Impulsive State Feedback Control. Discrete and Continuous Dynamical Systems. Series B, 6, 1301-1320. https://doi.org/10.3934/dcdsb.2006.6.1301
|
[17]
|
Liu, X. and Chen, L. (2003) Complex Dynamics of Holling Type II Lotka-Volterra Predator-Prey System with Impulsive Perturbations on the Predator. Chaos, Solitons & Fractals, 2, 311-320.
https://doi.org/10.1016/S0960-0779(02)00408-3
|
[18]
|
Liu, B., Zhang, Y. and Chen, L. (2005) Dynamic Complexities in a Lotka-Volterra Predator-Prey Model Concerning Impulsive Control Strategy. International Journal of Bifurcation and Chaos in Applied Sciences and Engineering, 2, 517-531. https://doi.org/10.1142/S0218127405012338
|
[19]
|
Samoilenko, A.M. and Perestyuk, N.A. (1995) Impulsive Differential Equations, World Scientific, Singapore.
https://doi.org/10.1142/2892
|
[20]
|
Zavalishchin, S.T. and Sesekin, A.N. (1997) Dynamic Impulse Systems Theory and Applications. Mathematics and Its Applications. Kluwer, Dordrecht, 394.
|
[21]
|
Lakshmikantham, V. and Liu, X. (1989) On Quasi-Stability for Impulsive Differential Systems. Nonlinear Analysis: Theory, Methods & Applications, 13, 819-828. https://doi.org/10.1016/0362-546X(89)90074-6
|
[22]
|
Liu, X. and Rolf, K. (1998) Impulsive Control of a Lotka-Volterra System. IMA Journal of Mathematical Control and Information, 15, 269-284. https://doi.org/10.1093/imamci/15.3.269
|
[23]
|
Akhmet, M.U. (2003) On the General Problem of Stability for Impulsive Differential Equations. Journal of Mathematical Analysis and Applications, 288, 182-196. https://doi.org/10.1016/j.jmaa.2003.08.001
|
[24]
|
Liu, X. and Chen, L. (2004) Global Dynamics of the Periodic Logistic System with Periodic Impulsive Perturbations. Journal of Mathematical Analysis and Applications, 289, 279-291. https://doi.org/10.1016/j.jmaa.2003.09.058
|
[25]
|
Negi, K. and Gakkhar, S. (2007) Dynamics in a Beddington-DeAngelis Prey-Predator System with Impulsive Harvesting. Ecological Modelling, 206, 421-430. https://doi.org/10.1016/j.ecolmodel.2007.04.007
|
[26]
|
Lakshmikantham, V., Bainov, D.D. and Simeonov, P.C. (1989) Theory of Impulsive Differential Equations. World Scientific, Singapore. https://doi.org/10.1142/0906
|
[27]
|
Benchohra, M., Henderson, J. and Ntouyas, S. (2006) Impulsive Differential Equations and Inclusions. Hindawi Publishing Corporation, New York. https://doi.org/10.1155/9789775945501
|
[28]
|
Zavalishchin, S.T. and Sesekin, A.N. (1997) Dynamic Impulsive Systems: Theory and Applications. Mathematics and Its Application. Kluwer Academic Publishers Group, Dordrecht. https://doi.org/10.1007/978-94-015-8893-5
|
[29]
|
Tan, Y., Tao, F. and Chen, L. (2008) Dynamics of a Non-Autonomous System with Impulsive Output. International Journal of Biomathematics, 1, 225-238. https://doi.org/10.1142/S1793524508000187
|
[30]
|
Bainov, D.D. and Simeonov, P.S. (1993) Impulsive Differential Equations: Periodic Solutions and Applications, Pitman Monographs and Surveys in Pure and Applied Mathematics. Longman Scientific and Technical, Essex.
|
[31]
|
Ang, T.Y. (2001) Impulsive Control Theory. World Scientific, Singapore.
|
[32]
|
Bainov, D.D. and Simeonov, P.C. (1989) System with Impulsive Effect: Stability, Theory and Applications. Ellis Horwood Limited, Chichester.
|
[33]
|
Bainov, D.D. and Simeonov, P.S. (1993) Impulsive Differential Equations: Asymptotic Properties of the Solutions. World Scientific, Singapore.
|