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Analysis of nonlinear oscillatory network dynamics via time‐varying amplitude and phase variables
Author(s) -
Lanza Valentina,
Corinto Fernando,
Gilli Marco,
Civalleri Pier Paolo
Publication year - 2007
Publication title -
international journal of circuit theory and applications
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 0.364
H-Index - 52
eISSN - 1097-007X
pISSN - 0098-9886
DOI - 10.1002/cta.433
Subject(s) - harmonic balance , nonlinear system , ordinary differential equation , amplitude , control theory (sociology) , mathematics , phase (matter) , differential equation , mathematical analysis , computer science , physics , control (management) , quantum mechanics , artificial intelligence
The goal of this manuscript is to propose a method for investigating the global dynamics of nonlinear oscillatory networks, with arbitrary couplings. The procedure is mainly based on the assumption that the dynamics of each oscillator is accurately described by a couple of variables, that is, the oscillator periodic orbits are represented through time‐varying amplitude and phase variables. The proposed method allows one to derive a set of coupled nonlinear ordinary differential equations governing the time‐varying amplitude and phase variables. By exploiting these nonlinear ordinary differential equations, the prediction of the total number of periodic oscillations and their bifurcations is more accurate and simpler with respect to the one given by the latest available methodologies. Furthermore, it is proved that this technique also works for weakly connected oscillatory networks. Finally, the method is applied to a chain of third‐order oscillators (Chua's circuits) and the results are compared with those obtained via a numerical technique, based on the harmonic balance approach. Copyright © 2007 John Wiley & Sons, Ltd.