Novel compressive sensing image encryption using the dynamics of an adjustable gradient Hopfield neural network

Abstract In this contribution, the nonlinear dynamics of a non-autonomous model of two neurons based on the Hopfield neural network is considered. Using activation gradients as bifurcation control parameters, the properties of the model include dissipation with the existence of attractors and equilibrium points with their stability. Using traditional nonlinear analysis tools such as bifurcation diagrams, the graph of the maximum Lyapunov exponent, phase portraits, two-parameter diagrams, and attraction basins, the complex behaviour of the two-dimensional Hopfield neural network has been investigated and several windows of multistability involving the coexistence of up to four coexisting attractors have been found. Besides, the results of our numerical simulation of the multistability have been further supported using some Pspice simulation. The effect of the fractional-order derivative is also explored, and it is found that the route toward chaos is completely different when the order q of the HNN is varied between $$0<q<1$$ 0 < q < 1 . Finally, a compressive sensing approach is used to compress and encrypt color images based on the sequences of the above-mentioned system. The plain color image is decomposed into Red, Green, and Blue components. The Discrete Wavelet Transform (DWT) is applied to each component to obtain the corresponding sparse components. Confusion keys are obtained from the proposed chaotic system to scramble each sparse component. The measurement matrices obtained from the chaotic sequence are used to compress the confused sparse matrices corresponding to the Red, Green, and Blue components. Each component is quantified and a diffusion step is then applied to improve the randomness and, consequently, the information entropy. Experimental analysis of the proposed method yields a running time (t) of 6.85 ms, a maximum entropy value of 7.9996 for global and 7.9153 for local, an encryption throughput (ET) value of 114.80, and a number of cycles (NC) of 20.90. Analysis of these metrics indicates that the proposed scheme is competitive with some recent literature.