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Global Analysis of Limit Cycles in Networks of Oscillators

Stan G.B. and Sepulchre R.

Proceedings of the 6th IFAC International Symposium on Nonlinear Control Systems (IFAC-NOLCOS 2004), Pages 1433--1438, September 2004

Abstract

This paper is concerned with the global stability of limit cycle oscillations fo r a particular class of systems and networks. In previous work, we defined a class of parameter-dependent nonlinear systems ex hibiting an almost globally asymptotically stable limit cycle. The results were proven for values of the parameter in the vicinity of a bifurcation value. In th e present paper we restrict ourselves to a piecewise linear version of this cla ss of systems and adapt numerical tools recently proposed in the literature to p rove global stability of the limit cycle for a fixed value of the parameter abov e the bifurcation value. Furthermore, we show how the global stability results f or one isolated oscillator are useful to prove the existence of a globally synch rone oscillation in particular networks of identical oscillators.

BibTex Entry

@InProceedings{,: author = {Stan G.B. and Sepulchre R.},; title = {Global Analysis of Limit Cycles in Networks of Oscillators},; address = {Stuttgart, Germany},; booktitle = {Proceedings of the 6th IFAC International Symposium on Nonlinear Control Systems (IFAC-NOLCOS 2004)},; month = {September},; pages = {1433--1438},; year = {2004}
}



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