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This paper presents a spectral approach, based on the harmonic-balance technique, for detecting limit-cycle bifurcations in complex nonlinear circuits. The key step of the proposed approach is a method for a simple and effective computation of the Floquet multipliers (FM's) that yield stability and bifurcation conditions. As a case-study, a quite complex system, Chua's circuit, is considered. It is shown that the spectral approach is able to accurately evaluate the most significant bifurcation curves.

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SUMMARY A topologically simple memristive‐based oscillatory network showing a wide plethora of dynamical behaviors may be a good candidate for the realization of innovative oscillatory associative and dynamic memories for the recognition of spatial–temporal synchronization states. The design of such pattern recognition systems may not leave aside a preliminary thorough investigation of the nonlinear dynamics of the network and its basic components. In a synchronization scenario with almost‐sinusoidal oscillations, each of the memristive elements used in the cells of the network under consideration features an unusual current–voltage behavior. This manuscript models the linear circuitry and the memristive element in each cell so as to capture the observed dynamics and then presents an analytical study explaining the quantitative dependence of memristive current–voltage behavior on excitation amplitude–angular frequency ratio and on initial condition on the system state. This work leads to the first rigorous classification of all possible current–voltage characteristics for a sine‐wave voltage‐driven memristive element. This analytical study shall pave way towards a better understanding of the complex and still unexplored dynamical properties of this nonlinear device, whose distinct features could improve the capabilities of future‐generation pattern recognition systems. Copyright © 2012 John Wiley & Sons, Ltd.