Stability Analysis for Mutually Delay-Coupled Semiconductor Lasers System

作者: Rina Su , Chunrui Zhang , Zuolin Shen

DOI: 10.1155/2013/248379

关键词: Equivariant mapStability (probability)Control theorySemiconductor laser theoryProperty (philosophy)Characteristic equationLinear stabilityMathematicsMathematical analysis

摘要: In this paper, the problem of stability for mutually delay-coupled semiconductor lasers system is investigated. By analyzing associated characteristic equation, linear investigated and Hopf bifurcations are demonstrated. The new phenomena such as switch found. equivariant property existence multiple periodic solutions also discussed. Numerical simulations presented to illustrate results in paper.

参考文章(11)
Jianhong Wu, SYMMETRIC FUNCTIONAL DIFFERENTIAL EQUATIONS AND NEURAL NETWORKS WITH MEMORY Transactions of the American Mathematical Society. ,vol. 350, pp. 4799- 4838 ,(1998) , 10.1090/S0002-9947-98-02083-2
Martin Golubitsky, Ian Stewart, David G. Schaeffer, Singularities and groups in bifurcation theory Springer Science+Business Media. ,(1985) , 10.1007/978-1-4612-4574-2
Shangjiang Guo, Lihong Huang, Hopf bifurcating periodic orbits in a ring of neurons with delays Physica D: Nonlinear Phenomena. ,vol. 183, pp. 19- 44 ,(2003) , 10.1016/S0167-2789(03)00159-3
Chunrui Zhang, Baodong Zheng, Liancheng Wang, Multiple Hopf bifurcations of three coupled van der Pol oscillators with delay Applied Mathematics and Computation. ,vol. 217, pp. 7155- 7166 ,(2011) , 10.1016/J.AMC.2011.01.110
Chunrui Zhang, Yazhuo Zhang, Baodong Zheng, A model in a coupled system of simple neural oscillators with delays Journal of Computational and Applied Mathematics. ,vol. 229, pp. 264- 273 ,(2009) , 10.1016/J.CAM.2008.10.048
Fátima Drubi, Santiago Ibáñez, J. Ángel Rodríguez, Coupling leads to chaos Journal of Differential Equations. ,vol. 239, pp. 371- 385 ,(2007) , 10.1016/J.JDE.2007.05.024
Lucas Illing, Greg Hoth, Lauren Shareshian, Christopher May, Scaling behavior of oscillations arising in delay-coupled optoelectronic oscillators. Physical Review E. ,vol. 83, pp. 026107- ,(2011) , 10.1103/PHYSREVE.83.026107
Ana Paula S. Dias, Jeroen S.W. Lamb, Local bifurcation in symmetric coupled cell networks: Linear theory Physica D: Nonlinear Phenomena. ,vol. 223, pp. 93- 108 ,(2006) , 10.1016/J.PHYSD.2006.08.014
Dejun Fan, Junjie Wei, Hopf bifurcation analysis in a tri-neuron network with time delay Nonlinear Analysis: Real World Applications. ,vol. 9, pp. 9- 25 ,(2008) , 10.1016/J.NONRWA.2006.08.008
Kenji Miyakawa, Kazuhiko Yamada, Entrainment in coupled salt-water oscillators Physica D: Nonlinear Phenomena. ,vol. 127, pp. 177- 186 ,(1999) , 10.1016/S0167-2789(98)00310-8