Abstract
The structure represented by one or several oscillators couple to a one-dimensional transmission environment (e.g. a vibrating string in the mechanical case or a lossless transmission line in the electrical case) turned to be attractive for the research in the field of complex structures and/or complex behavior. This is due to the fact that such a structure represents some generalization of various interconnection modes with lumped parameters for the oscillators.On the other hand the lossless and distortionless propagation along transmission lines has generated several research in electrical, thermal, hydro and control engineering leading to the association of some functional differential equations to the basic initial boundary value problems.The present research is performed at the crossroad of the aforementioned directions. We shall associate to the starting models some functional differential equations - in most cases of neutral type - and make use of the general theorems for existence and stability of forced oscillations for functional differential equations. The challenges introduced by the analyzed problems for the general theory are emphasized, together with the implication of the results for various applications.
Reference22 articles.
1. Y. I. Neymark, Dynamical Systems and Controlled Processes (in Russian). Moscow: Nauka Publishing House, 1978, pp. 11–14.
2. J. K. Hale, “Coupled Oscillators on a Circle,” Resenhas IME-USP, vol. 1, no. 4, pp. 441–457, 1994.
3. ——, “Diffusive coupling, dissipation and synchronization,” J. Dyn. Diff. Equ., vol. 9, no. 1, pp. 1–52, 1997.
4. M. Earl and S. Strogatz, “Synchronization in oscillator networks with delayed coupling: A stability criterion,” Physical Review E, vol. 67, 036204, pp. 1–4, 2003.
5. J. J. Fox, C. Jayaprakash, D. L. Wang, and S. R. Campbell, “Synchronization in Relaxation Oscillator Networks with Conduction Delays,” Neural Computation, vol. 13, pp. 1003–1021, 2001.
Cited by
1 articles.
订阅此论文施引文献
订阅此论文施引文献，注册后可以免费订阅5篇论文的施引文献，订阅后可以查看论文全部施引文献