
Mathematical Biosciences and Engineering, 2020, 17(6): 69636992. doi: 10.3934/mbe.2020360
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Bifurcations and hybrid control in a 3×3 discretetime predatorprey model
1 Department of Mathematics, University of Azad Jammu and Kashmir, Muzaffarabad 13100, Pakistan
2 Department of Mathematics, Mirpur University of Science and Technology (MUST), Mirpur10250 (AJK), Pakistan
Received: , Accepted: , Published:
Special Issues: Numerical Linear Algebra for LargeScale Dynamical Systems
References
1. M. Braun, Differential Equations and Their Applications: An Introduction to Applied Mathematics, SpringerVerlage, New York, 1983.
2. F. Brauer, C. CastilloChavez, Mathematical Models in Population Biology and Epidemiology, Springer, New York, 2001.
3. T. Räz, The volterra principle generalized, Philos. Sci., 84 (2017), 737760.
4. S. Ahmad, On the nonautonomous LotkaVolterra competition equation, Proc. Am. Math. Soc., 117 (1993), 199204.
5. X. Liu, A note on the existence of periodic solution in discrete predatorprey models, Appl. Math. Model., 34 (2010), 24772483.
6. X. Tang, X. Zou, On positive periodic solutions of LotkaVoletrra competition systems with deviating arguments, Proc. Am. Math. Soc., 134 (2006), 29672974.
7. H. N. Agiza, E. M. ELabbasy, H. ELMetwally, A. A. Elsadany, Chaotic dynamics of a discrete preypredator model with Holling type II, Nonlinear Anal. Real World Appl., 10 (2009), 116129.
8. A. G. M. Selvam, R. Janagaraj, P. Rathinavel, A discrete model of three species preypredator system. Int. J. Innovative Res. Sci., 4 (2015), 1857618584.
9. A. M. Yousef, S. M. Salman, A. A. Elsadany, Stability and bifurcation analysis of a delayed discrete predatorprey model. Int. J. Bifurcat. Chaos, 28 (2018), 126.
10. M. R. Sagayaraj, A. G. M. Selvam, R. Janagaraj, D. Pushparajan, Dynamical behavior in a three species discrete model of preypredator interactions, Int. J. Comput. Sci. Math., 5 (2013), 1120.
11. E. A. Grove, G. Ladas, Periodicities in Nonlinear Difference Equations, Chapman and Hall/CRC, 2004.
12. J. Guckenheimer, P. Holmes, Nonlinear Oscillations, Dynamical Systems and Bifurcation of Vector Fields, SpringerVerlag, New York, 1983.
13. W. B. Zhang, Discrete Dynamical Systems, Bifurcations and Chaos in Economic, Elsevier, 2006.
14. A. Q. Khan, T. Khalique, Bifurcations and chaos control in a discretetime biological model. Int. J. Biomath., 13 (2020), 135.
15. A. Wikan, Discrete Dynamical Systems: With an Introduction to Discrete Optimization Problems, Bookboon, 2013.
16. D. Whitley, Discrete dynamical systems in dimensions one and two, Bull. London Math. Soc., 15 (1983), 177217.
17. M. G. Neubert, M. Kot, The subcritical collapse of predator populations in discretetime predatorprey models, Math. Biosci., 110 (1992), 4566.
18. M. Sen, M. Banerjee, A. Morozov, Bifurcation analysis of a ratiodependent preypredator model with the Allee effect, Ecol. Complex., 11 (2012), 1227.
19. Y. A. Kuznetsov, Elements of Applied Bifurcation Theorey, 3rd edition, SpringerVerlag, New York, 2004.
20. G. Wen, Criterion to identify hopf bifurcations in maps of arbitrary dimension, Phys. Rev. E, 72 (2005), 026201.
21. S. Yao, New bifurcation critical criterion of FlipNeimarkSacker bifurcations for twoparameterized family ofdimensional discrete systems, Discrete Dyn. Nat. Soc., 2012 (2012), 112.
22. G. Wen, S. Chen, Q. Jin, A new criterion of perioddoubling bifurcation in maps and its application to an inertial impact shaker, J. Sound Vib., 311 (2008), 212223.
23. C. Tunç, On the stability and boundedness of solutions to third order nonlinear differential equations with retarded argument, Nonlinear Dyn., 57 (2009), 97106.
24. C. Tunç, O. Tunç, A note on certain qualitative properties of a second order linear differential system, Appl. Math. Inf. Sci., 9 (2015), 953956.
25. C. Tunç, O. Tunç, On the boundedness and integration of nonoscillatory solutions of certain linear differential equations of second order, J. Adv. Res., 7 (2016), 165168.
26. L. G. Yuan, Q. G. Yang, Bifurcation, invariant curve and hybrid control in a discretetime predatorprey system, Appl. Math. Model., 39 (2015), 23452362.
27. E. M. Elabbasy, H. N. Agiza, H. ElMetwally, A. A. Elsadany, Bifurcation analysis, chaos and control in the Burgers mapping, Int. J. Nonlinear Sci., 4 (2007), 171185.
28. G. Chen, J. Q. Fang, Y. Hong, H. Qin, Controlling Hopf bifurcations: Discretetime systems, Discrete Dyn. Nat. Soc., 5 (2000), 2933.
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