Synchronization behavior of coupled neuron circuits composed of memristors

The fluctuation of intracellular and extracellular ion concentration induces the variation of membrane potential, and also complex distribution of electromagnetic field is generated. Furthermore, the membrane potential can be modulated by time-varying electromagnetic field. Therefore, magnetic flux is proposed to model the effect of electromagnetic induction in case of complex electrical activities of cell, and memristor is used to connect the coupling between membrane potential and magnetic flux. Based on the improved neuron model with electromagnetic induction being considered, the bidirectional coupling-induced synchronization behaviors between two coupled neurons are investigated on Spice tool and also printed circuit board. It is found that electromagnetic induction is helpful for discharge of neurons under positive feedback coupling, while electromagnetic induction is necessary to enhance synchronization behaviors of coupled neurons under negative feedback coupling. The frequency analysis on isolate neuron confirms that the frequency spectrum is enlarged under electromagnetic induction, and self-induction effect is detected. These experimental results can be helpful for further dynamical analysis on synchronization of neuronal network subjected to electromagnetic radiation.     

A time-varying hyperchaotic system and its realization in circuit

A hyperchaotic system is often used to generate secure keys or carrier wave for secure communication and the realistic hyperchaotic circuit often is made of capacitor, nonlinear resistor unit and induction coil. Parameters are often fixed in these hyperchaotic circuits and the hyperchaotic property of the system can be estimated by using a scheme of synchronization and time series analysis. In this paper, a time-varying hyperchaotic system is proposed by introducing changeable electric power source into the circuit; the changeable electric power source is combined with induction coil or capacitor in series to generate changeable output signals to excite the system. The diagrams of improved circuit are illustrated and critical parameters in experimental circuits are presented; the Lyapunov exponent spectrum vs. external applied electric power source is calculated. It is confirmed that the improved circuit always holds two positive Lyapunov exponents when the external electric power source works, and the chaotic attractors are much too different from the original one; thus, a more changeable hyperchaotic system is constructed in experiment.     

基于电磁感应的扭转振动测量方法

设计了一种基于电磁感应效应的转子扭转振动测量方法.该方法的思路是使线圈与永磁体做相对运动,根据线圈切割磁感应线的速度与感应电动势正相关的原理,由线圈两端的电压变化量计算各点的瞬时速度变化量,进而积分求出扭振信息.算法上采用半周期插值以及与标准信号进行对应点比较,保证了瞬时速度变化量的精确度.装置设计方面通过适当的空间布局,在一定程度上消除了轴向振动和部分横振的影响.实测验证表明,该方法得出了与输入载荷一致的扭振信息,具有精确性良好,安装简易,操作方便的特点.     

Active coupling and its circuitry designs of chaotic systems against deteriorated and delayed networks

This paper is concerned with the problem of asymptotic synchronization of a class of chaotic systems in the presence of network deterioration and time-varying delays. Based on adaptive adjustment technique and circuitry principle, a new version of the active coupling as well as its circuit realization is proposed. Then, an approach that is based on application of Lyapunov stability theory for the synchronization error system is introduced to prove the asymptotic synchronization result of the overall chaotic system. Moreover, a condition which denotes that at least one coupling will not be deteriorated for synchronization of the network is provided in the paper. It is shown that, without control inputs, the result can also be established for the deteriorated coupling networks and any time-varying bounded delay under the topological structure satisfying the condition. Finally, the proposed active couplings are physically implemented by circuits and tested by simulation on a Chua??s circuit network.     

周期激励下广义蔡氏电路混沌运动中的概周期行为

由于广义蔡氏电路存在2个对称的稳定平衡点,周期激励可能导致系统出现相应于不同初值的2种共存的分岔模式. 概周期解由环面破裂进入混沌,混沌吸引子从相位不同步逐渐演化为同步,并进一步随着参数的变化,产生分裂现象. 分裂后的2个相互对称的混沌吸引子仍存在相位同步效应,这2个混沌吸引子再次相互作用后形成扩大了的混沌吸引子,并交替围绕2个子混沌结构来回振荡. 同时,在混沌过程中,其轨迹在相当长的一段时间内严格按照概周期行为振荡,即混沌结构中存在局部概周期行为,这种局部概周期行为随参数的变化会逐步减弱,直至消失.      

Cascade Magnetic Cumulation Generator on the Basis of Inductively Coupled Circuits with A Variable Coupling Coefficient

A scheme of a multicascade magnetic cumulation generator based on a dynamic variation of the coupling coefficient of inductively coupled circuits is proposed. Each cascade contains two circuits including two pairs of inductively coupled coils. One pair of coils is subjected to simultaneous deformation, and one of the coils in the other pair is arranged with the opposite connection. It is shown that the energy in the load can be gradually increased (from one cascade to another) by using additional cascades. By an example of a two-cascade system, the proposed circuit is compared to the known circuits of the cascade system design based on the magnetic cumulation principle (generator with a step-up transformer and dynamic transformer). Within the framework of the model that ignores the ohmic resistance of conductors, it is demonstrated that the proposed scheme allows one to obtain a greater energy in the high-inductance load than the schemes with a step-up or dynamic transformer owing to a change in the sign of the magnetic flux in the secondary circuit. It is found that the increase in energy in the new scheme is independent of the coupling coefficient (at high values of this coefficient) and becomes greater as the number of cascades is increased.     

FPGA implementation of novel fractional-order chaotic systems with two equilibriums and no equilibrium and its adaptive sliding mode synchronization

This paper introduces two novel fractional-order chaotic systems with cubic nonlinear resistor and investigates its adaptive sliding mode synchronization. Firstly the novel two equilibrium chaotic system with cubic nonlinear resistor (NCCNR) is derived and its dynamic properties are investigated. The fractional-order cubic nonlinear resistor system (FONCCNR) is then derived from the integer-order model and its stability and fractional-order bifurcation are discussed. Next a novel no-equilibrium chaotic cubic nonlinear resistor system (NECNR) is derived from NCCNR system. Dynamic properties of NECNR system are investigated. The fractional-order no equilibrium cubic nonlinear resistor system (FONECNR) is derived from NECNR. Stability and fractional-order bifurcation are investigated for the FONECNR system. The non-identical adaptive sliding mode synchronization of FONCCNR and FONECNR systems are achieved. Finally the proposed systems, adaptive control laws, sliding surfaces and adaptive controllers are implemented in FPGA.     

磁场中轴向运动条形板强非线性超谐共振及混沌运动

针对磁场环境中周期外载作用下轴向运动导电条形板的非线性振动及混沌运动问题进行研究。应用改进多尺度法对横向磁场中条形板的强非线性振动问题进行求解,得到超谐波共振下系统的分岔响应方程。根据奇异性理论对非线性动力学系统的普适开折进行分析,求得含两个开折参数的转迁集及对应区域的拓扑结构分岔图。通过数值算例,分别得到以磁感应强度、轴向拉力、激励力幅值和激励频率为分岔控制参数的分岔图和最大李雅普诺夫指数图,以及反映不同运动行为区域的动力学响应图形,讨论分岔参数对系统呈现的倍周期和混沌运动的影响。结果表明,可通过相应参数的改变实现对系统复杂动力学行为的控制。     

Coupled Chaotic Colpitts Oscillators: Identical and Mismatched Cases

A system consisting of two linearly coupled chaotic Colpitts oscillators is considered. Two different coupling configurations, namely coupled collector nodes (C–C) and coupled emitter nodes (E–E) have been investigated. In addition to identical oscillators the case of mismatched circuits has been studied. Specifically the influence of the transistor parameter mismatch has been analyzed. The relative synchronization error has been estimated for different mismatch levels provided the coupling coefficient is twice larger than the synchronization threshold. Illustrative experimental results, including phase portraits and synchronization error are presented.     

Analytic calculation of magnetic force between two current-carrying coils

Current-carrying coils are basic elements in electromagnetic equipments, for example, in high field magnets from high temperature superconducting wires or tapes. In the assembly of these systems and their current-carrying operation, unavoidable mis-alignment and shift from the original position can be induced by disturbances such as the imbalance of magnetic force due to safety problems. For two current-carrying coils with non-coplanar axes, the analytic expression of the magnetic force between the two coils is presented according to the rule of Ampere circulation and the Biot-Savart law. Based on the expression, the dependence of the magnetic force on the size and the relative position of each other is further investigated, and the variation of the magnetic force is obtained with the above parameters.     

Parameter-dependent synchronization of coupled neurons in cold receptor model

In this paper, synchronization in two coupled neurons with spiking, bursting and chaos firings is investigated as the coupling strength gets increased. Synchronization state can be identified by means of the bifurcation diagram, the correlation coefficient and ISI-distance. It is illustrated that the coupled neurons can exhibit different types of synchronization state when the coupling strength increases. The different synchronization processes appear similar, but their detailed processes are different depending on the parameter values. The synchronization of neuronal network with two different network connectivity patterns is also studied. It is shown that chaotic and high period pattern are more difficult to get complete synchronization than the situation in single spike and low period pattern. It is also demonstrated that the synchronization status of multiple neurons is dependent on the network connectivity patterns. These results may be instructive to understand synchronization in neuronal systems.     

Synchronization of two different chaotic systems with discontinuous coupling

This paper is concerned with the problem of synchronization between two different chaotic systems with discontinuous coupling. Based on the stability theory and the comparison theorem of differential equations, we derive less restrictive synchronization conditions than those resulting from the Lyapunov theory. The theoretical results show that generalized synchronization between two different chaotic systems can be achieved if the time-average coupling strength is large enough. Finally, the corresponding numerical simulations are presented to demonstrate the effectiveness of proposed schemes.     

Effect of coupling,synchronization of chaos and stick-slip motion in two mutually coupled dynamical systems

In this work, we study the synchronization of two coupled chaotic oscillators. The uncoupled system corresponds to a mass attached to a nonlinear spring and driven by a rolling carpet. For identical oscillators, complete synchronization is analyzed using Lyapunov stability theory. This first analysis reveals that stability area of synchronization increases with the values of the coupling coefficient. Numerical simulations are shown to illustrate and validate stick-slip and chaos synchronization. Some cases of anti-synchronization are detected. Curiously, amplification of fixed point either regular or chaotic is observed in the area of anti-synchronization. Furthermore, phase synchronization is studied for nonidentical oscillators. It appears that for certain values of the coupling coefficient, coincidence of the phases is obtained, while the amplitudes remain uncorrelated. Contrarily to the case of complete synchronization, it does not exist a threshold of the coupling from which phase synchronization could appear. Besides, when we add the modified tuned mass damper on the structure, the behavior of the system can change including the appearance of synchronization, particularly in the region of fixed point. More precisely, complete synchronization is improved in the region of fixed point, while the damage of synchronization is observed when the velocity of the carpets is less than \(0.30\) .     

Justification of equivalent substitution circuits used to optimize the dissipative properties of electroelastic bodies with external electric circuits

We consider elastoplastic systems which are piecewise homogeneous bodies composed of piezoelectric elements some of which have piezoelectrical properties. Electric series circuits consisting of resistors, capacitors, and inductance coils are applied to piezoelectric elements through the electrode coating on the body surface. The goal of the study is to develop efficient methods of mathematical modelling for determining the parameters of elements of the external electric circuit, which ensure, at prescribed resonance frequencies, the maximum damping properties of electroelastic bodies with external electric circuits. To choose effective circuits for solving the problem posed above, we suggest to pose the problem of natural vibrations of elastic bodies whose elements exhibit piezoeffect and have external electric circuits.As the most efficient approaches for calculating the electric circuit parameters necessary for the maximal damping, we propose some versions of equivalent circuits, which can be used to substitute elastic systems with piezoelectric elements. The most reliable equivalent substitution circuits are justified on the basis of the proposed problem of natural vibrations. Numerical results are obtained for a cantilever plate with a piezoelement connected through the electrode coated surface with a series electric circuit consisting of resistors, capacitors and inductance coils.     

A feasible neuron for estimating the magnetic field effect

Biological neurons are capable of encoding a variety of stimuli, and the synaptic plasticity can be enhanced for activating appropriate firing modes in the neural activities. Artificial neural circuits are effective to reproduce the main biophysical properties of neurons when the nonlinear circuits composed of reliable electronic components with distinct physical properties are tamed to generate similar firing patterns as biological neurons. In this paper, a simple neural circuit is proposed to estimate the effect of magnetic field on the neural activities by incorporating two physical electronic components. A magnetic flux-controlled memristor and an ideal Josephson junction in parallel connection are used to percept the induction currents induced by the magnetic field. The circuit equations are obtained according to the Kirchhoff’s theorem and an equivalent neuron model is acquired by applying scale transformation on the physical variables and parameters in the neural circuit. Standard bifurcation analysis is calculated to predict possible mode transition and evolution of firing patterns. The Hamilton energy is also obtained to find its dependence on the mode selection in electronic activities. Furthermore, External magnetic field is applied to estimate the mode transition of neural activities because the phase error and the junction current across the Josephson junction can be adjusted to change the dynamics of the neural circuit. It is found that the biophysical functional neuron can present rapid and sensitive response to external magnetic field. Nonlinear resonance is obtained when stochastic phase error is induced by external time-varying magnetic field. The neural circuit can be suitable for further calculating the collective behaviors of neurons exposed to magnetic field.

     

Implementation of chaotic circuits with a digital time-delay block

In this paper, the implementation of time-delay chaotic circuits is investigated. To implement the time-delay block, a solution based on a digital circuitry has been adopted. This solution leads to a programmable hardware which can be realized by using available field programmable gate arrays. In this paper, issues raised from this implementation such as the behavior of the system with respect to the precision and the sampling rate of the conversion process have been investigated. The synchronization error is proposed as an indicator of the accuracy of the whole implementation.     

Projective synchronization between two different time-delayed chaotic systems using active control approach

In this paper, we investigate the projective synchronization between two different time-delayed chaotic systems. A suitable controller is chosen using the active control approach. We relax some limitations of previous work, where projective synchronization of different chaotic systems can be achieved only in finite dimensional chaotic systems, so we can achieve projective synchronization of different chaotic systems in infinite dimensional chaotic systems. Based on the Lyapunov stability theory, we suggest a generic method to achieve the projective synchronization between two different time-delayed chaotic systems. The validity of the proposed method is demonstrated and verified by observing the projective synchronization between two well-known time-delayed chaotic systems; the Ikeda system and Mackey–Glass system. Numerical simulations fully support the analytical approach.     

Adaptive coupling synchronization in complex network with uncertain boundary

It is difficult that all the boundaries of chaotic system were estimated precisely; this is why the coupling coefficient cannot be determined beforehand in the problem of synchronization of complex networks. Thus, an estimation of coupling coefficient should be given before designing some controllers. In addition, to realize the synchronization, the estimated coupling coefficient has to be large enough. However, it is not true that the larger the coupling coefficient the better the synchronization is. In fact, a coupling coefficient which is larger than what it needs to be means the energy waste. To overcome this difficulty, in this paper we propose an adaptive coupling method. And a new concept about asymptotic stability is presented. Numerical simulations are implemented on different complex networks. The results indicate that the synchronization can be achieved without a large estimated coefficient.     

The complete synchronization condition in a network of piezoelectric micro-beams

This work deals with the dynamics of a network of piezoelectric micro-beams (a stack of disks). The complete synchronization condition for this class of chaotic nonlinear electromechanical system with nearest-neighbor diffusive coupling is studied. The nonlinearities within the devices studied here are in both the electrical and mechanical components. The investigation is made for the case of a large number of coupled discrete piezoelectric disks. The problem of chaos synchronization is described and converted into the analysis of the stability of the system via its differential equations. We show that the complete synchronization of N identical coupled nonlinear chaotic systems having shift invariant coupling schemes can be calculated from the synchronization of two of them. According to analytical, semi-analytical predictions and numerical calculations, the transition boundaries for chaos synchronization state in the coupled system are determined as a function of the increasing number of oscillators.

     

Magnetic Field Influence on the Gas Detonation Induced by Spark Discharge

The present paper describes the influence of magnetic field on the spark discharge utilized for initialization of detonation. The method of schlieren time-based scanning shows the increase of shock wave velocity in the case when magnetic field was applied to the area of electrical discharge in the air. The critical energy values are obtained for a direct initialization of detonation in hydrogen–air and hexane–air mixtures. Magnetic field has a significant influence on the deflagration–combustion transition in both mixtures at the critical energy values. Pressure and velocity of the shock front were measured by ICP pressure transducers, flame front was recorded by photo-diodes. Two cases were studied experimentally: external magnetic field is produced by inductance coils connected to capacitor; own magnetic field is induced directly by discharge current in the cables positioned in special way.