A universal concept based on cellular neural networks for ultrafast and flexible solving of differential equations

IEEE Transactions on Neural Networks and Learning Systems
Jean Chamberlain Chedjou, Kyandoghere Kyamakya

Abstract

This paper develops and validates a comprehensive and universally applicable computational concept for solving nonlinear differential equations (NDEs) through a neurocomputing concept based on cellular neural networks (CNNs). High-precision, stability, convergence, and lowest-possible memory requirements are ensured by the CNN processor architecture. A significant challenge solved in this paper is that all these cited computing features are ensured in all system-states (regular or chaotic ones) and in all bifurcation conditions that may be experienced by NDEs.One particular quintessence of this paper is to develop and demonstrate a solver concept that shows and ensures that CNN processors (realized either in hardware or in software) are universal solvers of NDE models. The solving logic or algorithm of given NDEs (possible examples are: Duffing, Mathieu, Van der Pol, Jerk, Chua, Rössler, Lorenz, Burgers, and the transport equations) through a CNN processor system is provided by a set of templates that are computed by our comprehensive templates calculation technique that we call nonlinear adaptive optimization. This paper is therefore a significant contribution and represents a cutting-edge real-time computational engineering a...Continue Reading

References

Feb 6, 2008·IEEE Transactions on Neural Networks·I E LagarisD G Papageorgiou
Feb 8, 2008·IEEE Transactions on Neural Networks·I E LagarisD I Fotiadis
Jun 6, 2009·IEEE Transactions on Neural Networks·Kevin Stanley McFall, James Robert Mahan

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Citations

Jan 24, 2017·Bioinspiration & Biomimetics·Zahra M BagheriDavid C O'Carroll

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