Symmetric periodic solutions of delay-coupled optoelectronic oscillators

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• 作者：Chunrui Zhang ; Hongpeng Li
• 关键词：optoelectronic oscillators ; symmetric bifurcation ; stability ; spatio ; temporal patterns ; delay
• 刊名：Advances in Difference Equations
• 出版年：2016
• 出版时间：December 2016
• 年：2016
• 卷：2016
• 期：1
• 全文大小：1,775 KB
• 刊物主题：Difference and Functional Equations; Mathematics, general; Analysis; Functional Analysis; Ordinary Differential Equations; Partial Differential Equations;
• 出版者：Springer International Publishing
• ISSN：1687-1847

文摘

Delay-coupled optoelectronic oscillators are considered. These structures are based on mutually coupled oscillators which oscillate at the same frequency. By taking the time delay as a bifurcation parameter, the stability of the zero equilibrium and the existence of Hopf bifurcations induced by delay are investigated, and then stability switches for the trivial solution are found. Conditions ensuring the stability and direction of the Hopf bifurcation are determined by applying the normal form theory and the center manifold theorem. Using the symmetric functional differential equation theories combined with the representation theory of Lie groups, the multiple Hopf bifurcations of the equilibrium are demonstrated. In particular, we find that the spatio-temporal patterns of bifurcating periodic oscillations will alternate according to the change of the propagation time delay in the coupling. The existence of multiple branches of bifurcating periodic solutions and their spatio-temporal patterns are obtained. Some numerical simulations are used to illustrate the effectiveness of the obtained results.