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VLSI Design
Volume 13 (2001), Issue 1-4, Pages 257-264

The Deterministic Circuit Model for Noise Influence on the Averaged Transient Responses of Large-scale Nonlinear ICs Analyzed with Itô's Stochastic Differential Equations

Laboratory of Physical Electronics and Photonics, MC2, School of Physics and Engineering Physics, Chalmers University of Technology and Göteborg University, Giöteborg SE-412 96, Sweden

Copyright © 2001 Hindawi Publishing Corporation. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.


The second-order nonrandom ordinary differential equation (ODE) system derived as the noise-source-aware model for expectations of solutions of Itô's stochastic differential equation (ISDE) system is discussed in connection with large-scale integrated circuits (ICs). The work explains the reason why the new model consistently allows for the noise-induced phenomena in the expectations, namely, stochastic resonance, stochastic linearization, stochastic self-oscillations and stochastic chaos. The case of stochastic resonance is considered as an example. In spite of the fact that the above second-order model is more complex than the nonrandom first-order IC ODE system for the expectations commonly used in engineering, an efficient practical technique for its implementation is proposed. The corresponding predicted computing time is only in 2.5 times greater than in the case of the first-order model which does not include any noise-source influence upon the expectations of the modelled IC responses.