Chaos Control in a Discrete Ecological System

Abstract

In research [1], the authors investigate the dynamic behaviors of a discrete ecological system. The period-double bifurcations and chaos are found in the system. But no strategy is proposed to control the chaos. It is well known that chaos control is the first step of utilizing chaos. In this paper, a controller is designed to stabilize the chaotic orbits and enable them to be an ideal target one. After that, numerical simulations are presented to show the correctness of theoretical analysis.

Share and Cite:

Zhang, L. and Zhang, C. (2012) Chaos Control in a Discrete Ecological System. International Journal of Modern Nonlinear Theory and Application, 1, 81-83. doi: 10.4236/ijmnta.2012.13011.

Conflicts of Interest

The authors declare no conflicts of interest.

References

[1] L. M. Zhang and L. Li, “Dynamic Complexities in a Discrete Predator-Prey System,” Journal of Wuhan University of Science and Engineering, Vol. 23, No. 3, 2010, pp. 36-40.
[2] L. M. Zhang, “Stability and Bifurcation in a Discrete Predator-Prey System with Leslie-Gower Type,” Sichuan University of Arts and Science Journal, Vol. 20, No. 2, 2010, pp. 13-15.
[3] C. Celik and O. Duman, “Allee Effect in a Discrete-Time Predator-Prey System,” Chaos, Solitons & Fractals, Vol. 40, No. 4, 2009, pp. 1956-1962. doi:10.1016/j.chaos.2007.09.077
[4] H. N. Agiza and E. M. Elabbssy, “Chaotic Dynamics of a Discrete Prey-Predator Model with Holling Type II,” Nonlinear Analysis: Real World Applications, Vol. 10, No. 1, 2009, pp. 116-129. doi:10.1016/j.nonrwa.2007.08.029
[5] X. L. Liu and D. M. Xiao, “Complex Dynamic Behaviors of a Discrete-Time Predator-Prey System,” Chaos, Solitons & Fractals, Vol. 32, No. 1, 2007, pp. 80-94. doi:10.1016/j.chaos.2005.10.081
[6] Z. J. Jing and J. P. Yang, “Bifurcation and Chaos in Discrete-Time Predator-Prey System,” Chaos, Solitons & Fractals, Vol. 27, No. 1, 2006, pp. 259-277. doi:10.1016/j.chaos.2005.03.040
[7] V. S. Ricard and G. P. G. Javier, “Controlling Chaos in Ecology: From Deterministic to Individual-Based Models,” Bulletin of Mathematical Biology, Vol. 61, No. 6, 1999, pp. 1187-1207. doi:10.1006/bulm.1999.0141
[8] Y. Zhang, Q. L. Zhang, L. C. Zhao and C. Y. Yang, “Dynamical Behaviors and Chaos Control in a Discrete Functional Response Model,” Chaos, Solitons and Fractals, Vol. 34, No. 4, 2007, pp. 1318-1327. doi:10.1016/j.chaos.2006.04.032
[9] A. A. Gomes, E. Manica, M. C. Varriale, “Applications of Chaos Control Techniques to a Three-Species Food Chain,” Chaos, Solitons & Fractals, Vol. 36, No. 4, pp. 1097-1107. doi:10.1016/j.chaos.2006.07.027
[10] S. Boccaletti, C. Grebogi, Y.-C. Lai, H. Mancin and D. Maza, “The Control of Chaos: Theory and Applications,” Physical Reports, Vol. 3, 2003, pp. 29-97.
[11] R. Thoresten, S. Alexander, U. Dressler, D. Robet, H. Bernd and M. Werner, “Chaos Control with Adjustable Control Times,” Chaos, Solitons & Fractals, Vol. 8, No. 9, 1997, pp. 1559-1576. doi:10.1016/S0960-0779(96)00155-5

Copyright © 2024 by authors and Scientific Research Publishing Inc.

Creative Commons License

This work and the related PDF file are licensed under a Creative Commons Attribution 4.0 International License.