- About this Journal ·
- Abstracting and Indexing ·
- Aims and Scope ·
- Annual Issues ·
- Article Processing Charges ·
- Author Guidelines ·
- Bibliographic Information ·
- Citations to this Journal ·
- Contact Information ·
- Editorial Board ·
- Editorial Workflow ·
- Free eTOC Alerts ·
- Publication Ethics ·
- Recently Accepted Articles ·
- Reviewers Acknowledgment ·
- Submit a Manuscript ·
- Subscription Information ·
- Table of Contents
Abstract and Applied Analysis
Volume 2013 (2013), Article ID 167065, 10 pages
Delayed Feedback Control and Bifurcation Analysis of an Autonomy System
1Institute of Information and System Computation Science, Beifang University of Nationalities, Yinchuan, Ningxia 750021, China
2Department of Mathematics and Information Science, Zhoukou Normal University, Zhoukou, Henan 466001, China
3Department of Applied Mathematics, Kunming University of Science and Technology, Kunming, Yunnan 650093, China
Received 28 February 2013; Accepted 26 March 2013
Academic Editor: Yisheng Song
Copyright © 2013 Zhen Wang et al. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.
- G. Corso and F. B. Rizzato, “Hamiltonian bifurcations leading to chaos in low-energy relativistic wave- particle system,” Physica D, vol. 80, pp. 296–306, 1995.
- M. Saleem and T. Agrawal, “Chaos in a tumor growth model with delayed responses of the immune system,” Journal of Applied Mathematics, vol. 2012, Article ID 891095, 16 pages, 2012.
- U. Kumar, “A retrospection of chaotic phenomene in electrical systems,” Active and Passive Electronic Components, vol. 21, pp. 1–15, 1998.
- Z. Chen, X. Zhang, and Q. Bi, “Bifurcations and chaos of coupled electrical circuits,” Nonlinear Analysis, vol. 9, no. 3, pp. 1158–1168, 2008.
- S. Hallegatte, M. Ghil, P. Dumas, and J. Hourcade, “Business cycles, bifurcations and chaos in a neo-classical model with investment dynamics,” Journal of Economic Behavior and Organization, vol. 67, pp. 57–77, 2008.
- D. Ghosh, A. R. Chowdhury, and P. Saha, “Bifurcation continuation, chaos and chaos control in nonlinear Bloch system,” Communications in Nonlinear Science and Numerical Simulation, vol. 13, no. 8, pp. 1461–1471, 2008.
- A. El-Gohary and A. S. Al-Ruzaiza, “Chaos and adaptive control in two prey, one predator system with nonlinear feedback,” Chaos, Solitons and Fractals, vol. 34, no. 2, pp. 443–453, 2007.
- H. Salarieh and A. Alasty, “Control of stochastic chaos using sliding mode method,” Journal of Computational and Applied Mathematics, vol. 225, no. 1, pp. 135–145, 2009.
- J. Guan, “Bifurcation analysis and chaos control in genesio system with delayed feedback,” ISRN Mathematical Physics, vol. 2012, Article ID 843962, 12 pages, 2012.
- H.-T. Yau and C.-S. Shieh, “Chaos synchronization using fuzzy logic controller,” Nonlinear Analysis, vol. 9, no. 4, pp. 1800–1810, 2008.
- N. Vasegh and A. Sedigh, “Delayed feedback control of time-delayed chaotic systems: analytical approach at Hopf bifurcation,” Physics Letters A, vol. 372, pp. 5110–5114, 2008.
- J. Lu, Z. Ma, and L. Li, “Double delayed feedback control for the stabilization of unstable steady states in chaotic systems,” Communications in Nonlinear Science and Numerical Simulation, vol. 14, no. 7, pp. 3037–3045, 2009.
- M. Bleich and J. Socolar, “Stability of periodic orbits controlled by time-delay feedback,” Physics Letters A, vol. 210, pp. 87–94, 1996.
- Y. Ding, W. Jiang, and H. Wang, “Delayed feedback control and bifurcation analysis of Rossler chaotic system,” Nonlinear Dynamics, vol. 61, no. 4, pp. 707–715, 2010.
- Y. Song and J. Wei, “Bifurcation analysis for Chen's system with delayed feedback and its application to control of chaos,” Chaos, Solitons and Fractals, vol. 22, no. 1, pp. 75–91, 2004.
- S. Ruan and J. Wei, “On the zeros of transcendental functions with applications to stability of delay differential equations with two delays,” Dynamics of Continuous, Discrete and Impulsive Systems A, vol. 10, no. 6, pp. 863–874, 2003.
- B. D. Hassard, N. D. Kazarinoff, and Y. H. Wan, Theory and Applications of Hopf Bifurcation, vol. 41, Cambridge University Press, Cambridge, UK, 1981.
- I. Fuente, L. Martinez, J. Veguillas, and J. Aguirregabiria, “Quasiperiodicity route to chaos in a biochemical system,” Biophysical Journal, vol. 71, pp. 2375–2379, 1998.