On the chaos control of the Qi system

详细信息    查看全文

• 作者：Changjin Xu (1)
  Qiming Zhang (2)
  
  1. Guizhou Key Laboratory of Economics System Simulation ; Guizhou University of Finance and Economics ; Guiyang ; 550004 ; People鈥檚 Republic of China
  2. College of Science ; Hunan University of Technology ; Zhuzhou ; 412007 ; People鈥檚 Republic of China
  
• 关键词：Chaos ; Hopf bifurcation ; Qi system ; Stability ; Time ; delayed feedback
• 刊名：Journal of Engineering Mathematics
• 出版年：2015
• 出版时间：February 2015
• 年：2015
• 卷：90
• 期：1
• 页码：67-81
• 全文大小：1,015 KB
• 参考文献：1. Chen GR (1999) Controlling chaos and bifurcations in engineering systems. CRC Press, Boca Raton
  2. Zhang XD, Shi F, Wang Z (2007) Construction and verification of a simple smooth chaotic system. Commun Theor Phys 48(2):267鈥?74 CrossRef
  3. Moon FC (1992) Chaotic and fractal dynamics. Wiley, New York CrossRef
  4. Chen GR, Dong X (1998) From chaos to order: methodologies, perspectives and applications. World Scientific, Singapore
  5. Kapitaniak T (1998) Chaos for engineers: theory, applications and control. Springer, Berlin CrossRef
  6. EI Naschie MS (1996) Introduction to chaos, information and diffusion in quantum physics. Chaos, Solitons Fractals 7(5):7鈥?0 CrossRef
  7. Kapitaniak T (1992) Controlling chaotic oscillations without feedback. Chaos, Solitons Fractals 2(5):519鈥?30 CrossRef
  8. Gakkhar S, Singh A (2012) Control of chaos due to additional predator in the Hastings鈥揚owell food chain model. J Math Anal Appl 385(1):423鈥?38 CrossRef
  9. Sadeghpour M, Khodabakhsh M, Salarieh H (2012) Intelligent control of chaos using linear feedback controller and neural network identifier. Commun Nonlinear Sci Numer Simul 17(12):4731鈥?739 CrossRef
  10. Bashkirtseva I, Chen GR, Ryashko L (2012) Stochastic equilibria control and chaos suppression for 3D systems via stochastic sensitivity synthesis. Commun Nonlinear Sci Numer Simul 17(8):3381鈥?389 CrossRef
  11. Ott E, Grebogi C, Yorke JA (1990) Controlling chaos. Phys Rev Lett 64(11):1196鈥?199 CrossRef
  12. Yassen MT (2003) Chaos control of Chen chaotic dynamical system. Chaos, Solitons Fractals 15(2):271鈥?83 CrossRef
  13. Wan M (2011) Convergence and chaos analysis of a blind decorrelation neural network. J Inf Comput Sci 8(5):791鈥?98
  14. Deng YW, Sun GX, E JQ (2010) Application of chaos optimization algorithm for robust controller design and simulation study. J Inf Comput Sci 7(13):2897鈥?905
  15. Yang XS, Chen GR (2002) Some observer-based criteria for discrete-time generalized chaos synchronization. Chaos, Solitons Fractals 13(6):1303鈥?308 CrossRef
  16. Chen GR, Dong X (1993) On feedback control of chaotic continuous time systems. IEEE Trans Circuits Syst 40(9):591鈥?01 CrossRef
  17. Yassen MT (2003) Chaos control of Chen chaotic dynamical system. Chaos, Solitons Fractals 15(2):271鈥?83 CrossRef
  18. Agiza HN (2002) Controlling chaos for the dynamical system of coupled dynamos. Chaos, Solitons Fractals 13(2):341鈥?52 CrossRef
  19. Bai EW, Lonngren KE (2000) Sequential synchronization of two Lorenz systems using active control. Chaos, Solitons Fractals 11(7):1041鈥?044 CrossRef
  20. Yassen MT (2001) Adaptive control and synchronization of a modified Chua鈥檚 circuit system. Appl Math Comput 135(1):113鈥?28 CrossRef
  21. Liao TL, Lin SH (1999) Adaptive control and synchronization of Lorenz system. J Franklin Inst 336(6):925鈥?37 CrossRef
  22. Sanchez EN, Martinez JP, Chen GR (2002) Chaos stabilization: an inverse optimal control approach. Lat Am Appl Res 32(1):111鈥?14
  23. Song YL, Wei JJ (2004) Bifurcation analysis for Chen鈥檚 system with delayed feedback and its application to control of chaos. Chaos, Solitons Fractals 22(1):75鈥?1 CrossRef
  24. Wang X, Chen GR (2012) A chaotic system with only one stable equilibrium. Commun Nonlinear Sci Numer Simul 17(3):1264鈥?272 CrossRef
  25. Sprott JC (1997) Simplest dissipative chaotic flow. Phys Lett A 228(3鈥?):271鈥?74 CrossRef
  26. Wang X, Chen GR (2013) Constructing a chaotic system with any number of equilibrium. Nonlinear Dyn 71(3):429鈥?36 CrossRef
  27. Song YL, Han MA, Wei JJ (2005) Stability and Hopf bifurcation analysis on a simplified BAM neural network with delays. Physica D 200:185鈥?04 CrossRef
  28. Qi GY, Du SZ, Chen GR, Chen ZQ, Yuan ZZ (2005) On a four-dimensional chaotic system. Chaos, Solitons Fractals 23(5):1671鈥?682 CrossRef
  29. Njah AN, Sunday OD (2009) Generalization on the chaos control of 4-D chaotic systems using recursive backstepping nonlinear controller. Chaos, Solitons Fractals 41(5):2371鈥?376 CrossRef
  30. Pyragas K (1992) Continuous control of chaos by self-controlling feedback. Phys Lett A 170(6):421鈥?28 CrossRef
  31. Ruan SG, Wei JJ (2001) On the zeros of a third degree exponential polynomial with applications to a delayed model for the control of testosterone secretion. IMA J Math Appl Med Biol 18(1):41鈥?2 CrossRef
  32. Kuang Y (1993) Delay differential equations with applications in population dynamics. Academic Press INC, Boston
  33. Hale J, Lunel S (1993) Introduction to functional differential equations. Spring, New York CrossRef
  
• 刊物类别：Physics and Astronomy
• 刊物主题：Physics
  Mechanics
  Applications of Mathematics
  Analysis
  Mathematical Modeling and IndustrialMathematics
  Numeric Computing
  
• 出版者：Springer Netherlands
• ISSN：1573-2703

文摘

This paper is devoted to the problem of controlling chaos in the Qi system. A time-delayed feedback control method is applied to suppress chaos to unstable equilibria or unstable periodic orbits. Using a local stability analysis, we theoretically prove that the Hopf bifurcation occurs. Some numerical simulations are carried out to support the theoretical predictions. Finally, main conclusions are drawn.