In this contribution, a novel memristor-based oscillator, obtained from Shinriki's circuit by substituting the nonlinear positive conductance with a first order memristive diode bridge, is introduced. The model is described by a continuous time four-dimensional autonomous system with smooth nonlinearities. The basic dynamical properties of the system are investigated including equilibria and stability, phase portraits, frequency spectra, bifurcation diagrams, and Lyapunov exponents' spectrum. It is found that in addition to the classical period-doubling and symmetry restoring crisis scenarios reported in the original circuit, the memristor-based oscillator experiences the unusual and striking feature of multiple attractors (i.e., coexistence of a pair of asymmetric periodic attractors with a pair of asymmetric chaotic ones) over a broad range of circuit parameters. Results of theoretical analyses are verified by laboratory experimental measurements.

In this contribution, the problem of multistability control in a simple model of 3D HNNs as well as its application to biomedical image encryption is addressed. The space magnetization is justified by the coexistence of up to six disconnected attractors including both chaotic and periodic. The linear augmentation method is successfully applied to control the multistable HNNs into a monostable network. The control of the coexisting four attractors including a pair of chaotic attractors and a pair of periodic attractors is made through three crises that enable the chaotic attractors to be metamorphosed in a monostable periodic attractor. Also, the control of six coexisting attractors (with two pairs of chaotic attractors and a pair of periodic one) is made through five crises enabling all the chaotic attractors to be metamorphosed in a monostable periodic attractor. Note that this controlled HNN is obtained for higher values of the coupling strength. These interesting results are obtained using nonlinear analysis tools such as the phase portraits, bifurcations diagrams, graph of maximum Lyapunov exponent, and basins of attraction. The obtained results have been perfectly supported using the PSPICE simulation environment. Finally, a simple encryption scheme is designed jointly using the sequences of the proposed HNNs and the sequences of real/imaginary values of the Julia fractals set. The obtained cryptosystem is validated using some well-known metrics. The proposed method achieved entropy of 7.9992, NPCR of 99.6299, and encryption time of 0.21 for the 256*256 sample 1 image.

The complex dynamics of a simple memristive tabu learning neuron (MTLN) are considered in this article. The analysis of the stability of its equilibria revealed that it displays self-excited dynamics. The investigation of the dynamics of the considered model highlighted that it is extremely sensitive to the initial conditions. That sensitivity to the initial conditions is supported by the coexistence of an infinite number of stable states for the same set of system parameters but using different initial states. Among the infinity of coexisting stable states, there are periodic, quasiperiodic, and chaotic ones. The coexistence of an infinite number of chaotic attractors found in this work and not yet reported in such a model represents the first important contribution of this work. The circuit of the coupled neuron is also realized in the PSPICE simulation environment to further support the obtained result in extreme multistability. Therefore, the revealed chaotic dynamics of the MTLN is applied to compress and encrypt digital medical images. The compressed sensing (CS) approach is combined with deoxyribonucleic acid (DNA) coding/decoding to achieve high compression/encryption performances, including very low computational cost (encryption time t = 0.162 ms, encryption throughput ET = 1618.1 MB/s, number of CPU cycles NC = 1.8) useful for real-time compression. The compression/encryption method developed in this work represents the second main contribution based on the results of the analysis metrics.