Neural networks have been widely and deeply studied in the field of computational neurodynamics. However, coupled neural networks and their brain-like chaotic dynamics have not been noticed yet. In this article, we focus on the coupled neural network-based brain-like initial boosting coexisting hyperchaos and its application in biomedical image encryption. We first construct a memristive-coupled neural network (MCNN) model based on two subneural networks and one multistable memristor synapse. Then we investigate its coupling strength-related dynamical behaviors, initial states-related dynamical behaviors, and initial-boosted coexisting hyperchaos using bifurcation diagrams, phase portraits, Lyapunov exponents, and attraction basins. The numerical results demonstrate that the proposed MCNN not only can generate hyperchaotic attractors with high complexity but also can boost the attractor positions by switching their initial states. This makes the MCNN more suitable for many chaos-based engineering applications. Moreover, we design a biomedical image encryption scheme to explore the application of the MCNN. Performance evaluations show that the designed cryptosystem has several advantages in the keyspace, information entropy, and key sensitivity. Finally, we develop a field-programmable gate array test platform to verify the practicability of the presented MCNN and the designed medical image cryptosystem.

Memristive Hopfield neural network (MHNN) has complex dynamic behavior, which is suitable for encryption applications. In order to ensure the information security of the medical data transmitted in Internet of Things (IoT), we propose three new MHNN models by using a non-ideal flux-controlled memristor model with multi-piecewise nonlinearity. In these models, there are complex dynamical behaviors such as coexisting attractors, multi-scroll attractors and grid multi-scroll attractors. In terms of hardware, the proposed model is implemented using field programmable gate array (FPGA). In addition, we provide a complete set of medical data sharing solution, which are helpful for the referral patients to receive timely medical treatment. The whole solution is successfully verified on Raspberry Pi, the encrypted Computed Tomography (CT) image is transmitted safely under Message Queuing Telemetry Transport (MQTT) protocol, and the CT image is subjected to basic security analysis. The results show that the ciphertext histogram is evenly distributed, the correlation between adjacent pixels is almost 0, the information entropy reaches 7.9977, and the values of number of pixels change rate (NPCR) and unified average change intensity (UACI) are 99.6078% and 33.4875%. The solution not only performs the exchange of medical data, but also protects the privacy of patients.

Memristors have recently demonstrated great promise in constructing memristive neural networks with complex dynamics. This article proposes a memristive Hopfield neural network with three memristive coupling synaptic weights. The complex dynamical behaviors of the triple-memristor Hopfield neural network (TM-HNN), which have never been observed in previous Hopfield-type neural networks, include space multistructure chaotic attractors and space initial-offset coexisting behaviors. Bifurcation diagrams, Lyapunov exponents, phase portraits, Poincaré maps, and basins of attraction are used to reveal and examine the specific dynamics. Theoretical analysis and numerical simulation show that the number of space multistructure attractors can be adjusted by changing the control parameters of the memristors, and the position of space coexisting attractors can be changed by switching the initial states of the memristors. Extreme multistability emerges as a result of the TM-HNN’s unique dynamical behaviors, making it more suitable for applications based on chaos. Moreover, a digital hardware platform is developed and the space multistructure attractors as well as the space coexisting attractors are experimentally demonstrated. Finally, we design a pseudorandom number generator to explore the potential application of the proposed TM-HNN.