Predicting period-doubling bifurcations and multiple oscillations in nonlinear time-delayed feedback systems (original) (raw)
1998, IEEE Transactions on Circuits and Systems I: Fundamental Theory and Applications
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Bifurcations in Delay Differential Equations: An Algorithmic Approach in Frequency Domain
International Journal of Bifurcation and Chaos, 2016
In this work we study local oscillations in delay differential equations with a frequency domain methodology. The main result is a bifurcation equation from which the existence and expressions of local periodic solutions can be determined. We present an iterative method to obtain the bifurcation equation up to a fixed arbitrary order. It is shown how this method can be implemented in symbolic math programs.
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