Approximate identity neural networks for analog synthesis of nonlinear dynamical systems

Analog computation seems to be not highly versatile when compared with its digital counterpart. This is mainly due to the fact that, with the exception of the linear case, no sufficiently general methods exist at present for the processing of electrical signals using analog systems, nonlinear dynamical systems of the kind described by ordinary differential equations are quite general since they embody a large class of problems. Thus, synthesis of such systems plays a central role in this context. The aim of this paper is to present an approach to the analog synthesis, based on the approximate identity neural networks (a class of neural networks recently proposed). The method is fairly general since it can be applied to a large category of nonlinear systems. Some examples of dynamical systems developed using conventional analog circuitry show the feasibility of the approach and the usefulness for the experimental evidence of many interesting effects such as subharmonic oscillations and chaotic behavior.<
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