In this paper, a novel kind of compound synchronization among four chaotic systems is investigated, where the drive systems have been conceptually divided into two categories: scaling drive systems and base drive systems. Firstly, a sufficient condition is obtained to ensure compound synchronization among four memristor chaotic oscillator systems based on the adaptive technique. Secondly, a secure communication scheme via adaptive compound synchronization of four memristor chaotic oscillator systems is presented. The corresponding theoretical proofs and numerical simulations are given to demonstrate the validity and feasibility of the proposed control technique. The unpredictability of scaling drive systems can additionally enhance the security of communication. The transmitted signals can be split into several parts loaded in the drive systems to improve the reliability of communication.

With the continuous development of computers, communication technology, and regional medical collaboration services, the security and confidentiality of information are becoming more and more important. In order to prevent the illegal leakage of sensitive patient information, it is of great significance to study medical image encryption. In this article, a flux-controlled hyperbolic memristor model with locally active characteristics is proposed, which has rich nonlinear characteristics. The memristor parameters affect the local activity of the memristor, which is explained by mathematical analysis. Based on the traditional hopfield neural network (HNN), a memristive fully connect neural network (MFNN) containing four neurons is constructed with more complex coupling relationships between individual neurons. The memristor can be used to characterize the effect of external electromagnetic radiation on neurons. The complex dynamical behaviors of MFNN are found by numerical simulations. An equivalent circuit for the neural network is constructed to verify the accuracy of the numerical simulation. In addition, a medical image encryption scheme based on MFNN is proposed. The encryption scheme performs a bit-level permutation of the original image using a chaotic sequence randomly generated by the chaotic system. Fibonacci $Q$ -matrix and central diffusion algorithm are used to diffuse the permutation image. Through numerical analysis, the maximum entropy of this encryption algorithm reaches 7.99, and the correlation is close to zero, which proves the resistance of the algorithm to statistical attacks. The algorithm takes only 3.9 s to encrypt an 8-bit medical image of 320 × 320 size on Windows 10 operating system. Experimental results show that the proposed encryption scheme is very secure and has good applications in medical image encryption.

Most memristor-based Pavlov associative memory neural networks strictly require that only simultaneous food and ring appear to generate associative memory. In this article, the time delay is considered, in order to form associative memory when the food stimulus lags behind the ring stimulus for a certain period of time. In addition, the rate of learning can be changed with the length of time between the ring stimulus and food stimulus. A memristive neural network circuit that can realize Pavlov associative memory with time delay is designed and verified by the simulation results. The designed circuit consists of a synapse module, a voltage control module, and a time-delay module. The functions, such as learning, forgetting, fast learning, slow forgetting, and time-delay learning, are implemented by the circuit. The Pavlov associative memory neural network with time-delay learning provides a reference for further development of the brain-like systems.

Most of the classical conditioning laws implemented by existing circuits are involved in learning and forgetting between only three neurons, and the problems between multiple neurons are not considered. In this article, a multimode generalization and differentiation circuit for the Pavlov associative memory is proposed based on memristors. The designed circuit is mainly composed of voltage control modules, synaptic neuron modules, and inhibition modules. The secondary differentiation is accomplished through the process of associative learning and forgetting among multiple neurons. The process of multiple generalization and differentiation is realized based on the nonvolatility and thresholding properties of memristors. The extinction inhibition and differentiation inhibition in forgetting is considered through the inhibition modules. The Pavlov associative memory neural network with multimodal generalization and differentiation may provide a reference for the further development of brain-like intelligence.