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Breathing in a Class of Switched Linear Systems with Complex Eigenvalues

Ilse cervantes, Francisco J. Perez-Pinal, Daniel Cartas, Ricardo femat
This work describes qualitatively and quantitatively intermittent operation in a class of switched systems constituted by a time-varying linear system, which is subjected to both time and state dependent switching criteria. The continuous part of the system can be rewritten as invariant and linear but perturbed by a periodic orbit. It is shown that the intermittent operation is directly related to the perturbation term, but contrary to previous examples discussed in the literature, intermittent operation takes place when the system is perturbed with a periodic orbit of very low frequency. Bifurcation maps and other nonlinear tools allow us to show the conditions leading to intermittent operation of the system. Moreover, it is shown that although regular and chaotic intervals behave randomly, average variables behave surprisingly regular with respect to a critical parameter, following piece-wise power laws trends.
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