Constructing Multiscroll Memristive Neural Network With Local Activity Memristor and Application in Image Encryption.

Memristor possesses synapse-like properties that can mimic excitation and inhibition between neurons. This article introduces the Sigmoid functions to the memristor and constructs a new memristive Hopfield neural network (HNN). Its most distinctive feature is the simple topology, which contains only unidirectional connections in neurons. The equilibrium points analysis reveals the mechanism of its multiscroll attractors generation. Homogeneous and heterogeneous coexisting attractors are observed with the variation of the network parameters. Note that the state equation of memristor can affect the number of coexisting attractors. A hardware implementation is designed for it, and the multiscroll attractors are captured in the oscilloscope. Finally, it is also applied to developing an image encryption algorithm with excellent performance.

Coexisting Firing Patterns in an Improved Memristive Hindmarsh-Rose Neuron Model with Multi-Frequency Alternating Current Injection.

With the development of memristor theory, the application of memristor in the field of the nervous system has achieved remarkable results and has bright development prospects. Flux-controlled memristor can be used to describe the magnetic induction effect of the neuron. Based on the Hindmarsh-Rose (HR) neuron model, a new HR neuron model is proposed by introducing a flux-controlled memristor and a multi-frequency excitation with high-low frequency current superimposed. Various firing patterns under single and multiple stimuli are investigated. The model can exhibit different coexisting firing patterns. In addition, when the memristor coupling strength changes, the multiple stability of the model is eliminated, which is a rare phenomenon. Moreover, an analog circuit is built to verify the numerical simulation results.

Design and Application of Memristive Balanced Ternary Univariate Logic Circuit.

This paper proposes a unique memristor-based design scheme for a balanced ternary digital logic circuit. First, a design method of a single-variable logic function circuit is proposed. Then, by combining with a balanced ternary multiplexer, some common application-type combinational logic circuits are proposed, including a balanced ternary half adder, multiplier and numerical comparator. The above circuits are all simulated and verified in LTSpice, which demonstrate the feasibility of the proposed scheme.

Generation of Multi-Lobe Chua Corsage Memristor and Its Neural Oscillation.

The Chua corsage memristor (CCM) is considered as one of the candidates for the realization of biological neuron models due to its rich neuromorphic behaviors. In this paper, a universal model for m-lobe CCM memristor is proposed. Moreover, a novel small-signal equivalent circuit with one capacitor is derived based on the proposed model to determine the edge of chaos and obtain the zero-pole diagrams and analyze the frequency response and oscillation mechanism of the m-lobe CCM system, which are discussed in detail. In view of existence of the edge of chaos, the frequency response and the oscillation mechanism of the simplest oscillator is analysed using the proposed model. Finally, the proposed model has exhibited some essential neural oscillation, including the stable limit cycle, supercritical Hopf bifurcation, spiking and bursting oscillation. This study also reveals a previously undiscovered behavior of bursting oscillation in a CCM system.

A New Fault Diagnosis of Rolling Bearing Based on Markov Transition Field and CNN.

The rolling bearing is a crucial component of the rotating machine, and it is particularly vital to ensure its normal operation. In addition, the selection of different category features will add uncertainty and bias to the classification results. In order to decrease the interference of these factors to fault diagnosis, a new method that automatically learns the features of the data combined with Markov transition field (MTF) and convolutional neural network (CNN) is proposed in this paper, namely MTF-CNN. The MTF contributes to convert the original time series into corresponding figures, and the CNN is used to extract the deep feature information in the figure to complete the fault diagnosis. The effectiveness of the proposed method is verified by two public data sets. The experimental results show that MTF-CNN can classify different types of faults, and the highest accuracy rate can reach 100%. Likewise, the classification accuracy of this method is higher than some existing methods.

Locally active memristor based oscillators: The dynamic route from period to chaos and hyperchaos.

To explore the complexity of the locally active memristor and its application circuits, a tristable locally active memristor is proposed and applied in periodic, chaotic, and hyperchaotic circuits. The quantitative numerical analysis illustrated the steady-state switching mechanism of the memristor using the power-off plot and dynamic route map. For any pulse amplitude that can achieve a successful switching, there must be a minimum pulse width that enables the state variable to move beyond the attractive region of the equilibrium point. As local activity is the origin of complexity, the locally active memristor can oscillate periodically around a locally active operating point when connected in series with a linear inductor. A chaotic oscillation evolves from periodic oscillation by adding a capacitor in the periodic oscillation circuit, and a hyperchaotic oscillation occurs by further putting an extra inductor into the chaotic circuit. Finally, the dynamic behaviors and complexity mechanism are analyzed by utilizing coexisting attractors, dynamic route map, bifurcation diagram, Lyapunov exponent spectrum, and the basin of attraction.

A memcapacitor-based hyperchaotic conservative system.

To explore the applications of the memcapacitor in the conservative circuits, the nonlinear dynamics of a memcapacitor-based hyperchaotic conservative circuit are studied in detail. Specifically, the conservative condition of the system is obtained by combining divergence and Hamiltonian energy, and the perpetual points and equilibrium points of the memcapacitor-based system are also analyzed in detail. Subsequently, the influences of system parameters and initial conditions on the dynamics of the memcapacitor-based hyperchaotic conservative system are discussed through the dynamic map and the basin of attraction, where three dynamics phenomena can be observed, such as interior crisis, largest Lyapunov exponent jump, and coexisting conservative flows. Finally, the theoretical results are verified by the circuit experiment simulation through MULTISIM and digital signal processing; a pseudorandom number generator based on the hyperchaotic conservative system is also designed and compared with another system through an NIST test.

Coexisting hidden and self-excited attractors in a locally active memristor-based circuit.

This paper presents a chaotic circuit based on a nonvolatile locally active memristor model, with non-volatility and local activity verified by the power-off plot and the DC V-I plot, respectively. It is shown that the memristor-based circuit has no equilibrium with appropriate parameter values and can exhibit three hidden coexisting heterogeneous attractors including point attractors, periodic attractors, and chaotic attractors. As is well known, for a hidden attractor, its attraction basin does not intersect with any small neighborhood of any unstable equilibrium. However, it is found that some attractors of this circuit can be excited from an unstable equilibrium in the locally active region of the memristor, meaning that its basin of attraction intersects with neighborhoods of an unstable equilibrium of the locally active memristor. Furthermore, with another set of parameter values, the circuit possesses three equilibria and can generate self-excited chaotic attractors. Theoretical and simulated analyses both demonstrate that the local activity and an unstable equilibrium of the memristor are two reasons for generating hidden attractors by the circuit. This chaotic circuit is implemented in a digital signal processing circuit experiment to verify the theoretical analysis and numerical simulations.

Memcapacitor model and its application in chaotic oscillator with memristor.

Memristors and memcapacitors are two new nonlinear elements with memory. In this paper, we present a Hewlett-Packard memristor model and a charge-controlled memcapacitor model and design a new chaotic oscillator based on the two models for exploring the characteristics of memristors and memcapacitors in nonlinear circuits. Furthermore, many basic dynamical behaviors of the oscillator, including equilibrium sets, Lyapunov exponent spectrums, and bifurcations with various circuit parameters, are investigated theoretically and numerically. Our analysis results show that the proposed oscillator possesses complex dynamics such as an infinite number of equilibria, coexistence oscillation, and multi-stability. Finally, a discrete model of the chaotic oscillator is given and the main statistical properties of this oscillator are verified via Digital Signal Processing chip experiments and National Institute of Standards and Technology tests.

Design of Fuzzy Functional Observer-Controller via Higher Order Derivatives of Lyapunov Function for Nonlinear Systems.

In this paper, we investigate the stability of Takagi-Sugeno fuzzy-model-based (FMB) functional observer-control system. When system states are not measurable for state-feedback control, a fuzzy functional observer is designed to directly estimate the control input instead of the system states. Although the fuzzy functional observer can reduce the order of the observer, it leads to a number of observer gains to be determined. Therefore, a new form of fuzzy functional observer is proposed to facilitate the stability analysis such that the observer gains can be numerically obtained and the stability can be guaranteed simultaneously. The proposed form is also in favor of applying separation principle to separately design the fuzzy controller and the fuzzy functional observer. To design the fuzzy controller with the consideration of system stability, higher order derivatives of Lyapunov function (HODLF) are employed to reduce the conservativeness of stability conditions. The HODLF generalizes the commonly used first-order derivative. By exploiting the properties of membership functions and the dynamics of the FMB control system, convex and relaxed stability conditions can be derived. Simulation examples are provided to show the relaxation of the proposed stability conditions and the feasibility of designed fuzzy functional observer-controller.

Time lagged ordinal partition networks for capturing dynamics of continuous dynamical systems.

We investigate a generalised version of the recently proposed ordinal partition time series to network transformation algorithm. First, we introduce a fixed time lag for the elements of each partition that is selected using techniques from traditional time delay embedding. The resulting partitions define regions in the embedding phase space that are mapped to nodes in the network space. Edges are allocated between nodes based on temporal succession thus creating a Markov chain representation of the time series. We then apply this new transformation algorithm to time series generated by the Rössler system and find that periodic dynamics translate to ring structures whereas chaotic time series translate to band or tube-like structures-thereby indicating that our algorithm generates networks whose structure is sensitive to system dynamics. Furthermore, we demonstrate that simple network measures including the mean out degree and variance of out degrees can track changes in the dynamical behaviour in a manner comparable to the largest Lyapunov exponent. We also apply the same analysis to experimental time series generated by a diode resonator circuit and show that the network size, mean shortest path length, and network diameter are highly sensitive to the interior crisis captured in this particular data set.

Invariant set of weight of perceptron trained by perceptron training algorithm.

In this paper, an invariant set of the weight of the perceptron trained by the perceptron training algorithm is defined and characterized. The dynamic range of the steady-state values of the weight of the perceptron can be evaluated by finding the dynamic range of the weight of the perceptron inside the largest invariant set. In addition, the necessary and sufficient condition for the forward dynamics of the weight of the perceptron to be injective, as well as the condition for the invariant set of the weight of the perceptron to be attractive, is derived.