Chaotic Synchronization of Neural Networks in FPGA

Abstract

The objective of this work is to obtain a complete synchronization of Hopfield Neural Networks (HNN) with a delay using a Field Programmable Gate Array (FPGA) simulating in real-time a Natural Neural Networks (NNN). This work is motivated by research in Neurosciences involving the implantation of chips between the skull and the brain to prevent or ameliorate diseases such as Parkinson’s, Epilepsy and Depression. Our contribution is the introduction of new synchronization techniques based on the Qualitative Theory of Differential Equations, Chaos Theory and Algebraic Topology substituting calculations using the Lyapunov Stability Criterion (LSC). The presented technique does not depend on the Neural Networks to be synchronized but also presents a lower computational cost in comparison with previous works. The results show that FPGAs are good platforms for such experiments.