Multistability analysis,circuit implementations and application in image encryption of a novel memristive chaotic circuit

A novel memristive chaotic circuit is proposed by replacing the Chua’s diode in modified Chua’s circuit with a smooth active memristor, and the corresponding memristive model is analyzed and validated. The equilibrium point set, dissipativity and stability of this new chaotic circuit are developed theoretically. The dynamic characteristics for the new system are presented by means of phase diagrams, Lyapunov exponents, bifurcation diagrams and Poincaré maps. The coexistence of the memristive system is carried out from the perspective of asymmetric coexistence and symmetry coexistence. In addition, the coexistence of multiple states is studied by a more direct method with initial value as the system variable to gain a more intuitive observation. The circuit model of the memristive chaotic system is designed through Multisim simulation software. Finally, the memristive chaotic sequence is used to encrypt the image, and the influence of multistability on the encryption is investigated by the histogram, correlation and key sensitivity. The results show that the proposed new memristive chaotic system has high security.     

Chimera states and synchronization behavior in multilayer memristive neural networks

To study the effect of electromagnetic induction on the spatiotemporal dynamic behavior of neural networks, in this paper, we have mainly studied both the synchronization behavior and the evolution of chimera states (CS) in coupled neural networks. To do this, a multilayer memristive neural network was constructed by selecting the Hindmarsh–Rose neurons as the network nodes, and the effect of electromagnetic induction is introduced by using the cubic flux-controlled memristive model as synapse. For simplicity, the following coupling scheme is adopted: only the coupling connections for the neurons between different layers are considered with memristive synapses, while those neurons in each layer are still bidirectional coupled with the classical electrical synapses. It is found that, by adjusting the coupled strength of electrical synapses and the parameters of memristive synapses, the coexistence behavior of coherent and incoherent states, i.e., the CS, could appear in each layer. It is interesting that the CS are also found in inter-layer memristive synapse network. Furthermore, we have discussed the synchronization behavior in this multilayer memristive neural network, one can find when the whole multilayer network is in a synchronization state, not only the spatiotemporal consistency of the CS in each layer neural networks is observed, but also the memductance of all memristive synapses is completely synchronized. Our results suggest that the electromagnetic induction may play an important role in regulating the dynamic behavior of neural networks, and the introduction of memristive synapse into the biological neural network will provide useful clues for revealing the memory behavior of the neural system in human brain.     

A coupling method of double memristors and analysis of extreme transient behavior

Nonlinear Dynamics - By coupling a variable of the memristor in one memristive chaotic circuit with another memristor, an approach to construct a high-dimensional memristive chaotic system is...     

Memristive magnetic coupling feedback induces wave-pattern transition

Nonlinear Dynamics - In this paper, we design a memristive system involving magnetic coupling with time-delayed feedback. In a way of autaptic connection, the memristive magnetic coupling feedback...     

Observer-based synchronization of memristive systems with multiple networked input and output delays

This paper investigates the synchronization problem of memristive systems with multiple networked input and output delays via observer-based control. A memristive system is set up, and the fuzzy method has been employed to linearize the dynamical system of the memristive system; the networked input and output delays are considered in the synchronization problem of this system. A truncated predictor feedback approach is employed to design the observers. Under certain restrictions, a class of finite-dimensional observer-based output feedback controllers is designed. A numerical example is carried out to demonstrate the effectiveness of the proposed methods.     

Reproduce the biophysical function of chemical synapse by using a memristive synapse

Dynamical modeling of nervous systems is of fundamental importance in many scientific fields containing the topics relative to computational neuroscience and biophysics. Many feasible mathematical models have been suggested in the explanation and prediction of some features of neural activities. Considering the special experimental findings and the computational efficiency, it is necessary to find a perfect balance between estimating biophysical functions with complete dynamics and reducing complexity when a tractable model is built. In this paper, a chemical synaptic model is reproduced by using a memristive synapse because it not only remains synaptic characteristic but also exhibits a pinched hysteresis loop and active feature locally. That is, a neuron activated by chemical synapse can produce similar firing modes as the neuron coupled by a memristive synapse, and both the chemical synapse and memristive synapse have similar field effect and biophysical properties. By calculating the one-parameter and two-parameter bifurcation as well as the Lyapunov exponent spectrum, it is confirmed that a neuron can be excited by the chemical synapse or the memristive synapse for generating chaotic firing patterns. Oscillation of the circuit composed of neuron and functional synapse is analyzed, suggesting that there exists a relation between the local activity and the edge of chaos via Hopf bifurcation. A modular circuit is designed to construct large-scale neural network. These results in this paper provide new evidences for application of memristive components and guide us to know the biophysical function of chemical synapse from physical viewpoint, in which the chemical synapse could be a kind of memristive synapse because of the same biophysical function.

     

Dynamics analysis of Wien-bridge hyperchaotic memristive circuit system

In this paper, a hyperchaotic memristive circuit based on Wien-bridge chaotic circuit was designed. The mathematical model of the new circuit is established by using the method of normalized parameter. The equilibrium point and the stability point of the system are calculated. Meanwhile, the stable interval of corresponding parameter is determined. Using the conventional dynamic analysis method, the dynamical characteristics of the system are analyzed. During the analysis, some special phenomenon such as coexisting attractor is observed. Finally, the circuit simulation of system is designed and the practical circuit is realized. The results of theoretical analysis and numerical simulation show that the Wien-bridge hyperchaotic memristive circuit has very rich and complicated dynamical characteristics. It provides a theoretical guidance and a data support for the practical application of memristive chaotic system.     

Implementation and study of the nonlinear dynamics of a memristor-based Duffing oscillator

An electronic model of Duffing oscillator with a characteristic memristive nonlinear element is proposed instead of the classical cubic nonlinearity. The memristive Duffing oscillator circuit system is mathematically modeled, and the stability analysis presents the evolution of the proposed system. The dynamical behavior of this circuit is investigated through numerical simulations, statistical analysis, and real-time hardware experiments, which have been carried out under the external periodic force. The chaotic dynamics of the circuit is studied by means of phase diagram. It is found that the proposed circuit system shows complex behaviors, like bifurcations and chaos, three tori, transient chaos, and intermittency for a certain range of circuit parameters. The observed phenomena and scenario are illustrated in detail through experimental and numerical studies of memristive Duffing oscillator circuit. The existence of regular and chaotic behaviors is also verified by using 0–1 test measurements. In addition, the robustness of the signal strength is confirmed through signal-to-noise ratio. The numerically observed results are confirmed from the laboratory experiment.     

On hyperchaos in a small memristive neural network

This paper studies a small Hopfield neural network with a memristive synaptic weight. We show that the previous stable network after one weight replaced by a memristor can exhibit rich complex dynamics, such as quasi-periodic orbits, chaos, and hyperchaos, which suggests that the memristor is crucial to the behaviors of neural networks and may play a significant role. We also prove the existence of a saddle periodic orbit, and then present computer-assisted verification of hyperchaos through a homoclinic intersection of the stable and unstable manifolds, which gives a positive answer to an interesting question that whether a 4D memristive system with a line of equilibria can demonstrate hyperchaos.     

Global stability and stabilization for inertial memristive neural networks with unbounded distributed delays

Nonlinear Dynamics - This paper investigates the stability and stabilization of inertial memristive neural networks (IMNNs) with discrete and unbounded distributed delays. The considered IMNNs are...     

Impulsive method to reliable sampled-data control for uncertain fractional-order memristive neural networks with stochastic sensor faults and its applications

Nonlinear Dynamics - This paper is devoted to investigate the issue of fault-tolerant sampled-data control for a class of uncertain fractional-order memristive neural networks with random switching...     

Complex dynamical behavior in memristor–capacitor systems

Nonlinear Dynamics - The parallel and series circuits of a Hewlett–Packard memristor and a capacitor are foundational building blocks for realistic memristive circuits. Due to the...     

A new chaotic circuit with multiple memristors and its application in image encryption

Nonlinear Dynamics - In this paper, a new seventh-order mixed memristive chaotic circuit was designed, and the new mathematical model of the system was established. The origin as the only...     

Experimental verification of a memristive neural network

This paper presents an electronic circuit able to emulate the behavior of a neural network based on memristive synapses. The latter is built with two flux-controlled floating memristor emulator circuits operating at high frequency and two passive resistors. Synapses are connected in a way that a bridge circuit is obtained, and its dynamical behavioral model is derived from characterizing memristive synapses. Analysis of the memristor characteristics for obtaining a suitable synaptic response is also described. A neural network of one neuron and two inputs is connected using the proposed topology, where synaptic positive and negative weights can easily be reconfigured. The behavior of the proposed artificial neural network based on memristors is verified through MATLAB, HSPICE simulations and experimental results. Synaptic multiplication is performed with positive and negative weights, and its behavior is also demonstrated through experimental results getting 6% of error.     

Structural damage detection using convolutional neural networks combining strain energy and dynamic response

Meccanica - Based on the classification ability of a convolutional neural network (CNN), this paper proposes a structural damage detection method in which a CNN is used to classify the location and...     

基于并行卷积神经网络的地磁方向适配性分析

针对地磁方向适配性分析时人工特征提取主观性较强、所取特征难以表达深层的结构性特征的问题,并为了进一步提高方向适配性分析的准确率,提出了一种基于并行卷积神经网络的地磁方向适配性分析方法。首先,从不同角度建立了地磁场在6个代表方向上的适配性分析图;然后,从同一磁场的不同角度出发,利用卷积神经网络自动完成了特征学习,得到了更为全面的方向适配性特征描述;最后,在并行卷积神经网络所得特征的基础上,利用BP网络建立了地磁方向适配性的分析模型。仿真结果证明,该方法可以有效避免人工特征提取和计算等复杂步骤,实现了地磁方向适配性分析的自动化,而且可以获得优于传统网络和单路卷积神经网络的准确率。     

基于卷积神经网络的无网格形函数影响域优化研究

在无网格法中,离散节点之间的相互联系由节点形函数影响域的大小确定,因此形函数影响域的大小对无网格法的计算精度有着直接和重要的影响。但由于无网格形函数的形式较为复杂,目前形函数影响域大小的选择仍然缺乏系统的理论依据,通常在实际计算中仍凭借经验进行选取,难以保证计算精度。卷积神经网络是一类机器学习方法,其感受野与无网格形函数的影响域具有内在相似性,因此在形函数影响域选择方面有很好的适用性。基于该特性,本文通过引入卷积神经网络对无网格形函数的影响域进行了优化选择。首先,针对感受野和影响域的匹配关系,分析了卷积神经网络的结构设计和超参数选择,提出了一种无网格法内禀卷积神经网络结构的设计方法;然后依托该网络结构设计方法,建立了对无网格形函数影响域和数值解分别优化或同时优化的卷积神经网络。文中通过算例系统验证了所提无网格法内禀卷积神经网络对形函数影响域选择和计算结果的优化效应。     

Contrast Enhancement with a Nonlinear Oscillators Network

In this paper, we propose a contrast enhancement realized with a lattice of uncoupled nonlinear oscillators. We show theoretically and numerically that the contrast of a gray scale image is strongly enhanced even if it is initially very weak. An image inversion can also be obtained in real time without needing a reconfiguration of this Cellular Nonlinear Network (CNN). Finally, an electronic implementation of this (CNN) is discussed.     

Innovation Systems by Nonlinear Networks

Cellular Neural Networks (CNNs) constitute a powerful paradigm for modeling complex systems. Innovation systems are complex systems in which small and medium enterprises play the role of simple units interacting with each other. In this paper, innovation systems based on CNN are investigated. It is shown how a model based on CNN can reproduce the main features of innovation systems and how this model can be generalized to include different aspects of the actors of the financial market.     

Memristive oscillator based on Chua’s circuit: stability analysis and hidden dynamics

This paper presents a theoretical stability analysis of a memristive oscillator derived from Chua’s circuit in order to identify its different dynamics, which are mapped in parameter spaces. Since this oscillator can be represented as a nonlinear feedback system, its stability is analyzed using the method based on describing functions, which allows to predict fixed points, periodic orbits, hidden dynamics, routes to chaos, and unstable states. Bifurcation diagrams and attractors obtained from numerical simulations corroborate theoretical predictions, confirming the coexistence of multiple dynamics in the operation of this oscillator.