Signal feature recognition based on lightwave neuromorphic signal processing

We developed a hybrid analog/digital lightwave neuromorphic processing device that effectively performs signal feature recognition. The approach, which mimics the neurons in a crayfish responsible for the escape response mechanism, provides a fast and accurate reaction to its inputs. The analog processing portion of the device uses the integration characteristic of an electro-absorption modulator, while the digital processing portion employ optical thresholding in a highly Ge-doped nonlinear loop mirror. The device can be configured to respond to different sets of input patterns by simply varying the weights and delays of the inputs. We experimentally demonstrated the use of the proposed lightwave neuromorphic signal processing device for recognizing specific input patterns.     

INVARIANT LINEARIZATION CRITERIA FOR SYSTEMS OF CUBICALLY NONLINEAR SECOND-ORDER ORDINARY DIFFERENTIAL EQUATIONS

Invariant linearization criteria for square systems of second-order quadratically nonlinear ordinary differential equations (ODEs) that can be represented as geodesic equations are extended to square systems of ODEs cubically nonlinear in the first derivatives. It is shown that there are two branches for the linearization problem via point transformations for an arbitrary system of second-order ODEs and its reduction to the simplest system. One is when the system is at most cubic in the first derivatives. One obtains the equivalent of the Lie conditions for such systems. We explicitly solve this branch of the linearization problem by point transformations in the case of a square system of two second-order ODEs. Necessary and sufficient conditions for linearization to the simplest system by means of point transformations are given in terms of coefficient functions of the system of two second-order ODEs cubically nonlinear in the first derivatives. A consequence of our geometric approach of projection is a rederivation of Lie's linearization conditions for a single second-order ODE and sheds light on more recent results for them. In particular we show here how one can construct point transformations for reduction to the simplest linear equation by going to the higher space and just utilizing the coefficients of the original ODE. We also obtain invariant criteria for the reduction of a linear square system to the simplest system. Moreover these results contain the quadratic case as a special case. Examples are given to illustrate our results.     

Properties of Optical Phase-Locked Loop Based on Four Wave Mixing in Semiconductor Laser Amplifiers

In this paper, the properties of the optical phase-locked loop(PLL) based on the four-wave mixing in the semiconductor laser amplifiers (SLAs) are discussed. The components that achieve the function of detecting the bit phase of the input optical signal are concerned and discussed in detail together as a function module named as the optical bit phase detector referred to the general electronic PLL. Therefore, most of the properties of the optical PLL can be analyzed by applying the general phase-locked theory. Here the stability of the optical PLL is discussed. It's shown that the variance of input signal power in the practical application will cause optical PLL system unstable because of its long loop delay. The influence on the output phase jitter of the optical PLL is also investigated.     

Stability analysis and control of the glucose insulin glucagon system in humans

The goal for the treatment of type-1 diabetes mellitus is the development of an artificial pancreas to regulate the blood glucose level in a closed loop design. A system of nonlinear differential equations having five variables (glucose, insulin, β-cell mass, α-cell mass, and glucagon) with seventeen parameters is considered. The Lyapunov function is used to check the stability analysis of the model. Controllability and observability of the linearized model are discussed under two different cases: in case 1 insulin is taken as an input, and in case 2 insulin and glucagon are taken as inputs for the system. This model played an important role in the development of a fully automatic artificial pancreas by stabilizing the control loop system for the glucose-insulin glucagon pump. A proportional integral derivative (PID) controller is designed for an artificial pancreas by using the transfer function. According to the desired value, the algorithm of an artificial pancreas measures the glucose level in the blood of a patient by using a glucose sensor that sends a signal to an insulin glucagon pump to adjust the basal insulin. A closed-loop system is tested in the Simulink environment, and the simulation results show the performance of the designed controller.     

Achieving high bit rate logical stochastic resonance in a bistable system by adjusting parameters

The phenomenon of logical stochastic resonance(LSR) in a nonlinear bistable system is demonstrated by numerical simulations and experiments. However, the bit rates of the logical signals are relatively low and not suitable for practical applications. First, we examine the responses of the bistable system with fixed parameters to different bit rate logic input signals, showing that an arbitrary high bit rate LSR in a bistable system cannot be achieved. Then, a normalized transform of the LSR bistable system is introduced through a kind of variable substitution. Based on the transform, it is found that LSR for arbitrary high bit rate logic signals in a bistable system can be achieved by adjusting the parameters of the system,setting bias value and amplifying the amplitudes of logic input signals and noise properly. Finally, the desired OR and AND logic outputs to high bit rate logic inputs in a bistable system are obtained by numerical simulations. The study might provide higher feasibility of LSR in practical engineering applications.     

Effects of synaptic noise and filtering on the frequency response of spiking neurons

Noise can have a significant impact on the response dynamics of a nonlinear system. For neurons, the primary source of noise comes from background synaptic input activity. If this is approximated as white noise, the amplitude of the modulation of the firing rate in response to an input current oscillating at frequency omega decreases as 1/square root[omega] and lags the input by 45 degrees in phase. However, if filtering due to realistic synaptic dynamics is included, the firing rate is modulated by a finite amount even in the limit omega-->infinity and the phase lag is eliminated. Thus, through its effect on noise inputs, realistic synaptic dynamics can ensure unlagged neuronal responses to high-frequency inputs.     

三稳系统的动态响应及随机共振

以平衡点参数p, q构造出一类对称三稳势函数, 进而提出微弱信号和噪声共同驱动的三稳系统模型. 深入研究并总结参数p, q对势垒高度ΔU₁, ΔU₂及两势垒高度差的影响. 从定常输入的角度提出了系统稳态解曲线的概念, 并进一步研究低频谐波信号输入时系统的输出动态响应. 引入噪声, 三稳系统在合适的参数条件下实现随机共振, 从稳态解曲线的角度分析了噪声诱导的三稳系统随机共振机理. 最后研究了阻尼比k和平衡点参数p, q对系统随机共振的影响.     

Generalized projective synchronization of chaotic systems with unknown dead-zone input: observer-based approach

In this paper we investigate the synchronization problem of drive-response chaotic systems with a scalar coupling signal. By using the scalar transmitted signal from the drive chaotic system, an observer-based response chaotic system with dead-zone nonlinear input is designed. An output feedback control technique is derived to achieve generalized projective synchronization between the drive system and the response system. Furthermore, an adaptive control law is established that guarantees generalized projective synchronization without the knowledge of system nonlinearity, and/or system parameters as well as that of parameters in dead-zone input nonlinearity. Two illustrative examples are given to demonstrate the effectiveness of the proposed synchronization scheme.     

半导体光放大器非线性失真特性实验研究

对半导体光放大器（SOA）用于1 310 nm残留边带幅度调制（AM-VSB）视频光信号放大时的非线性失真特性进行了实验研究.分析了非线性失真机理.给出了当输入光信号波长位于SOA增益谱下降沿且输入光信号功率较大时,SOA所引入的非线性失真主要由其增益随输入光信号功率变化而波动所造成的结论和对应表达式.提出了减小非线性失真的方法.设计了适合于AM-VSB视频光信号放大的SOA并用于有线电视（CATV）系统实验.研究结果表明,在300 mA的工作电流下,SOA在载频647.25 MHz处引入的组合二阶互调失真（CSO）在－42 dB～－38 dB之间,并随输入光信号功率的增加而变大.     

Nonlinear identification of NMR spin systems by adaptive filtering

In this paper, we present two new methods for identifying NMR spin systems. These methods are based on nonlinear adaptive filtering. The spin system is assumed to be time-invariant with memory. The first method uses a truncated discrete Volterra series to describe the nonlinear relationship between excitation (input) and system response (output). First-, second-, and third-order kernels of this series are estimated employing the least mean square (LMS) algorithm. Three parallel filters can then model the NMR spin system so that its output is no more than simple sum of three convolution products between combinations of the input signal and filters coefficients. It is also shown that the contribution of the Volterra second-order term to the total system response is neglected compared with the contributions of the first- and the third-order terms. In the second identification method, the output signal is related to the input signal through a recursive nonlinear difference equation with constant coefficients. The LMS algorithm is used again to estimate the equation coefficients. The two methods are validated with a simulated NMR system model based on Bloch equations. The results and the performances of these methods are analyzed and compared. It is shown that our methods permit a simple identification of NMR spin systems. The field of applications of this study is promising in the optimization of NMR signal detection, especially in the cases of low signal-to-noise ratios where optimum signal filtering and analysis must be performed.     

Nonlinear synthesis of input signals in ultrasonic experimental setups

A method is proposed to find the digital input signals to enter in nonlinear acoustical systems (power amplifiers, transducers, etc.) in order to obtain desired arbitrary response signals. The searched input signals are found by performing a Monte Carlo search guided by a simulated annealing process applied to a hidden model with a small number of parameters. The physical system is actually used in the optimization procedure, in a real-time manner, so that no theoretical model of the system response is required. The main aspects of the algorithm are described and illustrated with several examples.     

Lie symmetry analysis,new group invariant for the (3 + 1)-dimensional and variable coefficients for liquids with gas bubbles models

The explored solutions described some different solutions as, Lump soliton, a solitary wave and exponential solutions. These solutions are investigated through some new Lie infinitesimals for the (3 + 1) dimensional variable coefficients Kudryashov-Sinelshchikov (VCKS). We used the fourth prolongation to investigate fifteen cases of Lie vectors. In each case, there is an infinite number of possibilities of vectors due to the unknown arbitrary functions and the variable coefficients for the considered model. We selected one case and examined the commutative product between multi unknown Lie infinitesimals for the (3 + 1) dimensional (VCKS) equation and this complicated process resulted from some new Lie vectors. The commutative product generates a system of nonlinear ODEs which had been solved manually. Through three stages of Lie symmetry reduction using the equivalence transformation, (VCKS) equation is reduced to solvable nonlinear ODEs using various combinations of optimal Lie vectors. By solving these ODEs, we investigate new analytical solutions for these ODEs. Back substituting to the original variables generates new solutions for (VCKS). Some selected solutions are illustrated through three-dimensional plots.     

Quantifying Information without Entropy: Identifying Intermittent Disturbances in Dynamical Systems

A system’s response to disturbances in an internal or external driving signal can be characterized as performing an implicit computation, where the dynamics of the system are a manifestation of its new state holding some memory about those disturbances. Identifying small disturbances in the response signal requires detailed information about the dynamics of the inputs, which can be challenging. This paper presents a new method called the Information Impulse Function (IIF) for detecting and time-localizing small disturbances in system response data. The novelty of IIF is its ability to measure relative information content without using Boltzmann’s equation by modeling signal transmission as a series of dissipative steps. Since a detailed expression of the informational structure in the signal is achieved with IIF, it is ideal for detecting disturbances in the response signal, i.e., the system dynamics. Those findings are based on numerical studies of the topological structure of the dynamics of a nonlinear system due to perturbated driving signals. The IIF is compared to both the Permutation entropy and Shannon entropy to demonstrate its entropy-like relationship with system state and its degree of sensitivity to perturbations in a driving signal.     

Determination of applicable input range for approximating a nonlinear FGR furnace around the design point

In this paper, the nonlinear dynamic characteristics of a FGR furnace have been analysed around the furnace design point. Based on the steady-state results of full-scale nonlinear CFD simulations, the maximal allowable range on the variations of the furnace inputs can be determined, once for the maximal error bound between nonlinear system and its linear counterpart is specified. It is interesting to note that for a reheating furnace, the nonlinearities associated with the heat load are less severe than that associated with NO emission. With due consideration of the established input signal linear ranges, the linearized dynamic models of the furnace are derived by applying system identification technologies using the data generated from the CFD simulations. Analysis and validation of the models are also carried out. It is concluded that this technique is applicable to weak nonlinear systems around the design point. The results of the analysis provide additional insights on the nature of the nonlinearities as well as guidelines for selecting the input amplitude if system identification techniques are used. So long as the amplitudes of the probing signals satisfy the respective input constraints, the obtained linearized models will be applicable around the design point. Subsequently, these models can be used to design feedback controllers to maintain the furnace operated around the design point.     

Controlling bistability by linear augmentation

In many bistable oscillating systems only one of the attractors is desired to possessing certain system performance. We present a method to drive a bistable system to a desired target attractor by annihilating the other one. This shift from bistability to monostability is achieved by augmentation of the nonlinear oscillator with a linear control system. For a proper choice of the control function one of the attractors disappears at a critical coupling strength in an control-induced boundary crisis. This transition from bistability to monostability is demonstrated with two paradigmatic examples, the autonomous Chua oscillator and a neuronal system with a periodic input signal.     

Signal-to-noise ratio of a dynamical saturating system: Switching from stochastic resonator to signal processor

We consider an isolated dynamical saturating system for processing a noisy sinusoidal signal, and evaluate its performance with the measure of the signal-to-noise ratio. The considered system is linear for small inputs, but exhibits saturation in its response for large inputs. This nonlinearity displays the nonlinear phenomenon of stochastic resonance for a large biased sinusoid in appropriate system parameter regions. Without the stochastic resonance phenomenon, this dynamical saturating system can achieve a signal-to-noise ratio gain exceeding unity for a noisy unbiased sinusoid. These numerical results manifest the nonlinearities and the signal-processing ability of this system acting as a stochastic resonator or a signal processor.     

Resonance, Multi-resonance, and Reverse-resonance Induced by Multiplicative Dichotomous Noise

A constant-potential system driven by multiplicative dichotomous noise and subject to an input oscillatory signal is investigated. Two phenomena of stochastic resonance are observed. One is the response as a function of the noise＇s parameters; the other is that as a function of the input signal frequency. A phenomenon of multi-resonance （there are three or four peaks） is found for the response as a function of a parameter of the noise. A phenomenon of reverse-resonance is found, for which the response of the system to the signal can be weakened by the presence of the noise （there is an optimal minimum）. These results help in studies of the systems with multiplicative dichotomous noise, such as the semiconductor, the proteins motor, the chemical reaction, and so on.     

数字BPM时钟锁相电路的设计与实现

为实现数字BPM时钟系统的锁相,设计了一种基于锁相环同步原理的低抖动、低相位噪声的时钟同步系统。根据锁相环电路工作原理,对数字BPM时钟同步系统的硬件及固件程序进行了设计,实现了外部输入时钟信号与系统内部产生的主工作时钟信号的锁相,并且时钟信号输出的频率及相位均可调整以满足后端ADC采样的要求。测试结果表明,设计可以完成对一定频率范围内变化的外部输入时钟信号的锁相,输出时钟信号抖动满足束流实验要求,为数字BPM后续算法研究提供了基础。     

Switching of one beam by another in a Kerr type nonlinear Mach–Zehnder interferometer

This paper investigates switching of one beam by another in a Kerr type nonlinear Mach–Zehnder interferometer (NMZI) with two input ports and one output port. The present investigation has been carried out using the beam propagation method (BPM). The paper presents a detailed account on the procedures used to choose the parameters of the NMZI to make it behave like a NOT gate (inverter), an AND gate, an amplifier and a wavelength converter. The paper also gives details on the manipulation of the operating inputs of the NMZI to desired values. It is shown that the operating values of both the inputs of the NMZI can simultaneously be increased/decreased by decreasing/increasing the nonlinearity coefficient of nonlinear arm of the NMZI. Variation of NMZI length varies the operating value of only the first input, keeping the second unchanged, while variation of NMZI offset varies the operating value of only the second, keeping the first unchanged. The paper also gives a detailed account on amplification of the NMZI amplifier/wavelength converter. The present investigation is useful from the scientific as well as engineering point of view.     

Melting phenomenon in magneto hydro-dynamics steady flow and heat transfer over a moving surfacein the presence of thermal radiation

The Lie group method is applied to present an analysis of the magneto hydro-dynamics(MHD) steady laminar flow and the heat transfer from a warm laminar liquid flow to a melting moving surface in the presence of thermal radiation.By using the Lie group method,we have presented the transformation groups for the problem apart from the scaling group.The application of this method reduces the partial differential equations(PDEs) with their boundary conditions governing the flow and heat transfer to a system of nonlinear ordinary differential equations(ODEs) with appropriate boundary conditions.The resulting nonlinear system of ODEs is solved numerically using the implicit finite difference method(FDM).The local skin-friction coefficients and the local Nusselt numbers for different physical parameters are presented in a table.