Coupled Oscillators on a Circle
Palavras-chave:Transmission lines, Oscillators, Partial differential equations
ResumoWe consider a continuum of diffusively coupled oscillators on a circle. When each oscillator is of Lienard type, very little is known about the corresponding hyperbolic POE. When each oscillator is represented by a lossless transmission line, we obtain a partial neutral delay differential equation and give the beginnings of a qualitative theory for the dynamics. In particular, we discuss the properties of the solution map, the existence of the global attractor, behavior near an equilibrium point including the Hopf bifurcation, and some elementary properties near a periodic orbit.
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Hale, J. K. (2014). Coupled Oscillators on a Circle. Resenhas Do Instituto De Matemática E Estatística Da Universidade De São Paulo, 1(4), 441-457. https://doi.org/10.11606/resimeusp.v1i4.74670