A dual locally active memristive Hopfield neural network: hidden dynamics and multistability for medical image encryption.
Authors
Affiliations (2)
Affiliations (2)
- Applied Mathematics and Modeling Laboratory, Department of Mathematics, University Fréres Mentouri Constantine 1, 25000 Constantine, Algeria.
- Mathematical Modeling and Simulation Laboratory, Department of Mathematics, University Fréres Mentouri Constantine 1, 25000 Constantine, Algeria.
Abstract
The increasing demand for secure medical image transmission exposes limitations of conventional encryption. This work presents a two-memristor Hopfield neural network (2 M-HNN) incorporating two locally active memristors: a multi-equilibrium-state memristor with trigonometric-polynomial hybrid memductance and Gaussian-localized flux perturbation, emulating electromagnetic irradiation, and a Gaussian-envelope rational memristor with sech2 damping, replicating autaptic synaptic feedback. Both memristors follow nonlinear flux dynamics differing from prior polynomial and cubic models, while the host network employs a composite activation function combining hyperbolic tangent with sinusoidal modulation. The study characterizes nonlinear dynamics, revealing an infinite continuum of equilibrium points, hidden attractors, and pronounced multistability selected by initial conditions. Leveraging this complexity, a medical image encryption scheme combines 2 M-HNN chaotic sequences with DNA molecular computation. The algorithm operates in the spatial domain, employing bit-plane scrambling, central diffusion, and key-controlled DNA encoding via cubic DNA structures. Deployed within Picture Archiving and Communication System environments, it ensures secure diagnostic image transmission. Security evaluations validate resilience against statistical and differential cryptanalysis. The scheme achieves entropy of 7.9999 and effective key space of [Formula: see text]. Experimental results show that the software simulation achieves competitive efficiency with respect to recent schemes; real-time deployment inside a clinical PACS nevertheless requires hardware acceleration.