The gradient control of spatial-alternated Julia sets

详细信息    查看全文

• 作者：Pei Wang (1)
  Shutang Liu (1)
  
  1. College of Control Science and Engineering ; Shandong University ; Jinan ; 250061 ; China
  
• 关键词：Spatial ; alternated Julia sets ; Plane ; alternated Julia sets ; Gradient control ; Synchronization
• 刊名：Nonlinear Dynamics
• 出版年：2015
• 出版时间：May 2015
• 年：2015
• 卷：80
• 期：3
• 页码：1291-1302
• 全文大小：1,932 KB
• 参考文献：1. Danca, M-F, Romera, M, Pastor, G (2009) Alternated Julia sets and connectivity properties. Int. J. Bifurc. Chaos 19: pp. 2123-2129 CrossRef
  2. Zhang, YP, Liu, ST (2008) Gradient control and synchronization of Julia sets. Chin. Phys. B 17: pp. 543-549 CrossRef
  3. Zhang, Y.P.: The Control and Application of Fractal, Doctor鈥檚 thesis of Shandong University, pp. 27鈥?7 (2008) (in Chinese)
  4. Zhang, Y.P., Liu, S.T., Sun, W.H.: Feedback control in fractal mechanics. Choas Soliton Fract. 40, 337鈥?43 (2009)
  5. Liu, ST, Wu, S, Zhang, YP (2006) Uniformity and spatial chaos of spatial physics kinematic system. Int. J. Bifurc. Chaos 16: pp. 2697-2703 CrossRef
  6. Sui, S.G.: Spatial Fractal of Complex Dynamic Systems, Master鈥檚 thesis of Shandong University, pp. 64鈥?4 (2005) (in Chinese)
  7. Zhang, YP, Guo, XW (2012) Control of Julia sets of the complex Henon system. Nonlinear Dyn. 69: pp. 185-192 CrossRef
  8. Liu, P, Liu, CA (2011) Linear generalized synchronization of spatial Julia sets. Int. J. Bifurc. Chaos 21: pp. 1281-1291 CrossRef
  9. Liu, P, Liu, ST (2012) Control and coupling synchronization of Julia sets in coupled map lattice. Indian J. Phys. 86: pp. 455-462 CrossRef
  10. Liu, P, Liu, ST (2011) Control and synchronization of Julia sets in coupled map lattice. Commun. Nonlinear Sci. Number. Simul. 16: pp. 3344-3355 CrossRef
  11. Liu, ST, Chen, GR (2003) On spatial lyapunov exponent and spatial chaos. Int. J. Bifurc. Chaos 13: pp. 1163-1181 CrossRef
  12. Wang, P, Liu, ST (2014) Feedback control and linear generalized synchronization of spatial-alternated Julia sets. Acta Phys. Sin. 63: pp. 06050301-06050314
  13. Fradkov, AL, Pogromsky, AY (1999) Introduction to Control of Oscillations and Chaos. World Scientific, Singapore
  14. Brandt, ME, Chen, GR (1997) Bifurcation control of two nonlinear models of cardiac activity. IEEE Trans. Circuits Syst. I. 44: pp. 1301-1304 CrossRef
  
• 刊物类别：Engineering
• 刊物主题：Vibration, Dynamical Systems and Control
  Mechanics
  Mechanical Engineering
  Automotive and Aerospace Engineering and Traffic
  
• 出版者：Springer Netherlands
• ISSN：1573-269X

文摘

In this paper, we achieve the control of spatial-alternated Julia sets and plane-alternated Julia sets by using the gradient control. And we achieve the synchronization of two different plane-alternated Julia sets using the gradient control. The simulations illustrate the effectiveness of the control methods.