Abstract
The dynamics of a physical system can change when exposed to an environment in which it interacts with other systems. In many situations, such interaction can lead to synchronization in the sense that the dynamics of all systems are essentially the same. Some results and references can be found in Hale (1997) for ode and certain types of pde. Other interesting classes of problems occur when the equations arise from the interaction of systems whose dynamics are defined by a pde on a given domain and the interaction of the systems is through the boundary. We give an illustration of how this can occur for lossless transmission lines which interact through resistive coupling at the end of the lines. The problem will be solved using the equivalent formulation in terms of a set of partial neutral functional differential equations.
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References
Hale, J.K. ([1994]) Coupled oscillators on a circle. Resenhas IME-USP 1, 441–457.
Hale, J.K. ([1997]) Diffusive coupling, dissipation, and synchronization. J. Dyn. Diff. Equ. 9, 1–52.
Hale, J.K. ([1988]) Asymptolic Behador of Dissipative Systems. Math. Surveys and Monographs, Vol. 25, American Math. Soc.
Hale, J.K. and J. Scheurle ([1985]) Smoothness of bounded solutions of nonlinear evolution equations. J. Differential Eqns. 56, 142–163.
Hale, J.K. and S.M. Verduyn Lunel ([1993]) Introduction to Functional Differential Equations. Springer-Verlag.
Hale, J.K. and M. Weedermann ([2002]) On penurootions of delay differential equations with periodic orbits. J. Differential Eqns.
Wu, J. ([1996]) Theory and Applications of Partial Newral Functional Differential Equations. Springer-Verlag.
Wu, J. and H. Xia ([1996]) Self-sustained oscillations in a ring array of transmission lines. J. Differential Eqns. 124, 247–248.
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© 2004 Springer-Verlag Berlin Heidelberg
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Hale, J.K. (2004). Synchronization Through Boundary Interaction. In: Niculescu, SI., Gu, K. (eds) Advances in Time-Delay Systems. Lecture Notes in Computational Science and Engineering, vol 38. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-18482-6_16
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DOI: https://doi.org/10.1007/978-3-642-18482-6_16
Publisher Name: Springer, Berlin, Heidelberg
Print ISBN: 978-3-540-20890-7
Online ISBN: 978-3-642-18482-6
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