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Analysis of bifurcation in a system of n coupled oscillators with delays

机译:时滞n耦合振荡器系统的分岔分析。

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摘要

A n-coupled BVP oscillators system with delays is considered. By choosing the delays as the bifurcating parameters, some results of the Hopf bifurcations occurring at the zero equilibrium as the delays increase are exhibited. Using the symmetric functional differential equation theories of Wu [Jianhong Wu, Symmetric functional differential equations and neural networks with memory, Trans. Amer. Math. Soc. 350 (12) (1998) 4799-4838], the multiple Hopf bifurcations are obtained, and their spatio-temporal patterns: mirror-reflecting waves, standing waves, and discrete waves are demonstrated. Finally, computer simulations are performed to illustrate the analytical results found.
机译:考虑具有延迟的n耦合BVP振荡器系统。通过选择时延作为分叉参数,随着时延的增加,出现了在零平衡处发生的霍普夫分叉的一些结果。使用吴的对称泛函微分方程理论[吴建宏,对称泛函微分方程和具有记忆的神经网络,Trans。阿米尔。数学。 Soc。 [J.Am.Chem.Soc.Sci。,第350卷(12)(1998)4799-4838],获得了多个霍普夫分支,并展示了它们的时空模式:镜面反射波,驻波和离散波。最后,进行计算机模拟以说明发现的分析结果。

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