INTERNATIONAL JOURNAL OF CIRCUIT THEORY AND APPLICATIONS Int. J. Circ. Theor. Appl. 2007; 35:623–644 Published online in Wiley InterScience (www.interscience.wiley.com). DOI: 10.1002/cta.433 Analysis of nonlinear oscillatory network dynamics via time-varying amplitude and phase variables ‡ Valentina Lanza 1 , Fernando Corinto 2 , Marco Gilli 2, ∗, † and Pier Paolo Civalleri 2 1 Department of Mathematics, Politecnico di Torino, Turin, Italy 2 Department of Electronics, Politecnico di Torino, Turin, Italy SUMMARY 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. KEY WORDS: cellular nonlinear networks; nonlinear oscillatory networks; spectral techniques 1. INTRODUCTION Oscillatory networks have been one of the most used paradigms in order to mimic repetitive dy- namical processes taking place in complex systems. Large collections of coupled oscillators (cells), having several periodic attractors, have been studied in many fields of science and technology, including, for example, Biology, Physics and Engineering [1–7]. The leading feature of oscillatory networks is the emergence of synchronized oscillations among the cells, i.e. it is observed that quite ∗ Correspondence to: Marco Gilli, Department of Electronics, Politecnico di Torino, Turin, Italy. † E-mail: marco.gilli@polito.it ‡ Dedicated to Professor Se´ an Scanlan on the occasion of his 70th birthday. Contract/grant sponsor: Ministero dell’Istruzione, dell’Universit` a e della Ricerca; contract/grant number: RBAU01LRKJ Contract/grant sponsor: CRT Foundation Copyright 2007 John Wiley & Sons, Ltd.