Periodic motions
Phase noise in oscillators: DAEs and colored noise sources
Proceedings of the 1998 IEEE/ACM international conference on Computer-aided design
Cellular Neural Networks
Computing phase noise eigenfunctions directly from steady-state Jacobian matrices
Proceedings of the 2000 IEEE/ACM international conference on Computer-aided design
Proceedings of the 2004 IEEE/ACM International conference on Computer-aided design
IEEE Transactions on Computer-Aided Design of Integrated Circuits and Systems
Comprehensive procedure for fast and accurate coupled oscillator network simulation
Proceedings of the 2008 IEEE/ACM International Conference on Computer-Aided Design
Evaluating pulling effects in oscillators due to small-signal injection
IEEE Transactions on Computer-Aided Design of Integrated Circuits and Systems
Simulation of mutually coupled oscillators using nonlinear phase macromodels
IEEE Transactions on Computer-Aided Design of Integrated Circuits and Systems
Synchronization analysis of two weakly coupled oscillators through a PPV macromodel
IEEE Transactions on Circuits and Systems Part I: Regular Papers
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We address the problem of fast and accurate computational analysis of large networks of coupled oscillators arising in nanotechnological and biochemical systems. Such systems are computationally and analytically challenging because of their very large sizes and the complex nonlinear dynamics they exhibit. We develop and apply a nonlinear oscillator macromodel that generalizes the wellknown Kuramoto model for interacting oscillators, and demonstrate that using our macromodel provides important qualitative and quantitive advantages, especially for predicting self-organization phenomena such as spontaneous pattern formation. Our approach extends and applies recently-developed computational methods for macromodelling electrical oscillators, and features both phase and amplitude components that are extracted automatically (using numerical algorithms) from more complex differential-equation oscillator models available in the literature. We apply our approach to networks of Tunneling Phase Logic (TPL) and Brusselator biochemical oscillators, predicting a variety of spontaneous pattern generation phenomena. Comparing our results with published measurements of spiral, circular and other pattern formation, we show that we can predict these phenomena correctly, and also demonstrate that prior models (like Kuramoto's) cannot do so. Our approach is more than 3 orders of magnitude faster than techniques that are comparable in accuracy.