A Novel Fraction-Based Hopfield Neural Networks
In this paper, we propose a novel fractional-based Hopfield Neural Network (FHNN). The capacitors in the standard Hopfield Neural Network (HNN) with traditional integer order derivatives are replaced by fractance components with fractional order derivatives. From this, continues Hopfield net is extended to the fractional-based net in which fractional order equations describe its dynamical structure. We also prove the stability of FHNN through the Lyapunov energy function. In addition, we analyze the performance of FHNN by performing printed number recognition experiments. The simulation results in comparison with the standard HNN, showed some salient advantages in the fractional-based Hopfield Neural Network containing the higher capacity.
KeywordsFractional Calculus Hopfield Neural Networks Lyapunov Energy Function Number Recognition
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