Nonlinear Circuits and Neural Networks: Chip Implementation and Applications of the TeraOPS CNN Dynamic Array Supercomputer

GENERALIZING THE TWIST-AND-FLIP PARADIGM: II

International Journal of Bifurcation and Chaos ◽

10.1142/s0218127492000173 ◽

1992 ◽

Vol 02 (01) ◽

pp. 183-191 ◽

Cited By ~ 2

Author(s):

RAY BROWN ◽

LEON CHUA

Keyword(s):

Neural Networks ◽

Poincaré Map ◽

Nonlinear Circuits ◽

General Algorithm ◽

Nonlinear Phenomena ◽

Poincare Map

In this letter we introduce a new concept, the control manifold, which simultaneously points us toward a general algorithm relating the existence of horseshoes in a Poincare map to the parameters of an ODE, while also providing a mechanism for understanding how to control nonlinear phenomena and therefore utilize these phenomena in a disciplined and predictable manner in the design of nonlinear circuits, systems, and neural networks.

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AASERT Supplement to Nonlinear Circuits and Neural Networks.

10.21236/ada313484 ◽

1996 ◽

Author(s):

Leon O. Chua

Keyword(s):

Neural Networks ◽

Nonlinear Circuits

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A NEW APPROACH FOR THE ANALYSIS OF THE TRANSIENT AND STEADY STATE OF PIECEWISE-LINEAR CIRCUITS BY NEURAL NETWORKS

Journal of Circuits System and Computers ◽

10.1142/s021812660800485x ◽

2008 ◽

Vol 17 (06) ◽

pp. 1091-1109

Author(s):

REMZI TUNTAŞ ◽

YAKUP DEMIR ◽

MUHAMMET KÖKSAL

Keyword(s):

Neural Networks ◽

Steady State ◽

Piecewise Linear ◽

Nonlinear Circuits ◽

New Approach ◽

Matlab Simulink ◽

Switching Times ◽

Linear Circuits ◽

And Control ◽

Transient And Steady State

This paper presents a new approach based on Feed-Forward multilayered Neural Networks (FNNs) for the transient and steady-state analysis of piecewise-linear circuits. Nonlinear circuits are changed by linear circuits containing switches together with some state matrices and control inequalities by using piecewise linearization approach. One of the two problems arising in the analysis of these circuits is that control inequalities belonging to piecewise linearized components and control times for internally or externally controlled components is needed to determine switching times. Another is that the analysis time is very long. The proposed approach is considered as the solution to the problems. FNNs are used for modeling the piecewise linear circuits. By using the obtained model networks, the switching sequence and switching times from one state to another for transient and steady states are determined. The transient and steady-state solutions are fast accomplished through this knowledge. As an example, a nonlinear circuit is used for demonstrating the utility of the proposed approach, and the results are compared with that of the model constructed at Matlab/Simulink. Example circuit is analyzed in the time of 1 h 42 min by using the proposed approach but the time of 2 h 27 min by Matlab/Simulink. Moreover, simulation results demonstrate that the proposed approach yields more accurate approximation for the switched nonlinear circuits.

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