Hopfield neural networks with diverse activation functions: impact of variable action gradients and electromagnetic radiation effects.

Abstract

Activation functions and their variable gradient action are pivotal in bridging artificial neural networks with the dynamic behavior of biological neurons. This study examines the dynamics of a Hopfield Neural Network (HNN) with heterogeneous activation functions, focusing on the interplay between variable action gradients and electromagnetic radiation in shaping its behavior. Using computational simulations and theoretical analyses, we investigate how these networks respond to distinct electromagnetic radiation regimes. The proposed model exhibits antimonotonicity, bursting oscillations, and multi-scroll attractors in the absence of external disturbances. Furthermore, our findings reveal a unique planar coexistence of total amplitude control and initial offset boosting under varying electromagnetic radiation conditions. To validate these results, we propose an experimental framework based on an FPGA design to complement numerical analysis. Pseudo-random numbers generated from these intricate dynamical behaviors successfully pass the NIST statistical tests, confirming cryptographic suitability. This research advances our understanding of how external perturbations (e.g. electromagnetic radiation) interact with internal network configurations (e.g. activation functions, gradients), offering insights for optimizing associative memory tasks. Additionally, the observed effects of electromagnetic radiation provide novel pathways to enhance diagnostic and therapeutic strategies for neurological disorders, bridging computational neuroscience with innovative medical applications grounded in dynamical systems theory.