Dynamical analysis,geometric control and digital hardware implementation of a complex-valued laser system with a locally active memristor

In order to make the peak and offset of the signal meet the requirements of artificial equipment,dynamical analysis and geometric control of the laser system have become indispensable.In this paper,a locally active memristor with non-volatile memory is introduced into a complex-valued Lorenz laser system.By using numerical measures,complex dynamical behaviors of the memristive laser system are uncovered.It appears the alternating appearance of quasi-periodic and chaotic oscillations.The mechanism of transformation from a quasi-periodic pattern to a chaotic one is revealed from the perspective of Hamilton energy.Interestingly,initial-values-oriented extreme multi-stability patterns are found,where the coexisting attractors have the same Lyapunov exponents.In addition,the introduction of a memristor greatly improves the complexity of the laser system.Moreover,to control the amplitude and offset of the chaotic signal,two kinds of geometric control methods including amplitude control and rotation control are designed.The results show that these two geometric control methods have revised the size and position of the chaotic signal without changing the chaotic dynamics.Finally,a digital hardware device is developed and the experiment outputs agree fairly well with those of the numerical simulations.

Complex-Valued Neural Networks:A Comprehensive Survey

Complex-valued neural networks(CVNNs)have shown their excellent efficiency compared to their real counterparts in speech enhancement,image and signal processing.Researchers throughout the years have made many efforts to improve the learning algorithms and activation functions of CVNNs.Since CVNNs have proven to have better performance in handling the naturally complex-valued data and signals,this area of study will grow and expect the arrival of some effective improvements in the future.Therefore,there exists an obvious reason to provide a comprehensive survey paper that systematically collects and categorizes the advancement of CVNNs.In this paper,we discuss and summarize the recent advances based on their learning algorithms,activation functions,which is the most challenging part of building a CVNN,and applications.Besides,we outline the structure and applications of complex-valued convolutional,residual and recurrent neural networks.Finally,we also present some challenges and future research directions to facilitate the exploration of the ability of CVNNs.

WIDELY LINEAR RLS CONSTANT MODULUS ALGORITHM FOR COMPLEX-VALUED NONCIRCULAR SIGNALS

Based on the constant modulus criterion, a new Widely Linear(WL) blind equalizer and a novel widely linear recursive least square constant modulus algorithm are proposed to improve the blind equalization performance for complex-valued noncircular signals. The new algorithm takes advantage of the WL filtering theory by taking full use of second-order statistical information of the complex-valued noncircular signals. Therefore, the weight vector contains the complete second-order information of the real and imaginary parts to decrease the residual inter-symbol interference effectively. Theoretical analysis and simulation results show that the proposed scheme can significantly improve the equalization performance for complex-valued noncircular signals compared with traditional blind equalization algorithms.

Finite-time complex projective synchronization of fractional-order complex-valued uncertain multi-link network and its image encryption application

Multi-link networks are universal in the real world such as relationship networks,transportation networks,and communication networks.It is significant to investigate the synchronization of the network with multi-link.In this paper,considering the complex network with uncertain parameters,new adaptive controller and update laws are proposed to ensure that complex-valued multilink network realizes finite-time complex projective synchronization(FTCPS).In addition,based on fractional-order Lyapunov functional method and finite-time stability theory,the criteria of FTCPS are derived and synchronization time is given which is associated with fractional order and control parameters.Meanwhile,numerical example is given to verify the validity of proposed finite-time complex projection strategy and analyze the relationship between synchronization time and fractional order and control parameters.Finally,the network is applied to image encryption,and the security analysis is carried out to verify the correctness of this method.

Adaptive synchronization of a class of fractional-order complex-valued chaotic neural network with time-delay

This paper is concerned with the adaptive synchronization of fractional-order complex-valued chaotic neural networks(FOCVCNNs)with time-delay.The chaotic behaviors of a class of fractional-order complex-valued neural network are investigated.Meanwhile,based on the complex-valued inequalities of fractional-order derivatives and the stability theory of fractional-order complex-valued systems,a new adaptive controller and new complex-valued update laws are proposed to construct a synchronization control model for fractional-order complex-valued chaotic neural networks.Finally,the numerical simulation results are presented to illustrate the effectiveness of the developed synchronization scheme.

Finite-time Mittag-Leffler synchronization of fractional-order complex-valued memristive neural networks with time delay

Without dividing the complex-valued systems into two real-valued ones, a class of fractional-order complex-valued memristive neural networks(FCVMNNs) with time delay is investigated. Firstly, based on the complex-valued sign function, a novel complex-valued feedback controller is devised to research such systems. Under the framework of Filippov solution, differential inclusion theory and Lyapunov stability theorem, the finite-time Mittag-Leffler synchronization(FTMLS) of FCVMNNs with time delay can be realized. Meanwhile, the upper bound of the synchronization settling time(SST) is less conservative than previous results. In addition, by adjusting controller parameters, the global asymptotic synchronization of FCVMNNs with time delay can also be realized, which improves and enrich some existing results. Lastly,some simulation examples are designed to verify the validity of conclusions.

Learning Dynamics of the Complex-Valued Neural Network in the Neighborhood of Singular Points

In this paper, the singularity and its effect on learning dynamics in the complex-valued neural network are elucidated. It has learned that the linear combination structure in the updating rule of the complex-valued neural network increases the speed of moving away from the singular points, and the complex-valued neural network cannot be easily influenced by the singular points, whereas the learning of the usual real-valued neural network can be attracted in the neighborhood of singular points, which causes a standstill in learning. Simulation results on the learning dynamics of the three-layered real-valued and complex-valued neural networks in the neighborhood of singularities support the analytical results.

Periodic Solution for a Complex-Valued Network Model with Discrete Delay

For a tridiagonal two-layer real six-neuron model,the Hopf bifurcation was investigated by studying the eigenvalue equations of the related linear system in the literature.In the present paper,we extend this two-layer real six-neuron network model into a complex-valued delayed network model.Based on the mathematical analysis method,some sufficient conditions to guarantee the existence of periodic oscillatory solutions are established under the assumption that the activation function can be separated into its real and imaginary parts.Our sufficient conditions obtained by the mathe­matical analysis method in this paper are simpler than those obtained by the Hopf bifurcation method.Computer simulation is provided to illustrate the correctness of the theoretical results.

A small microring array that performs large complex-valued matrix-vector multiplication

As an important computing operation,photonic matrix-vector multiplication is widely used in photonic neutral networks and signal processing.However,conventional incoherent matrix-vector multiplication focuses on real-valued operations,which cannot work well in complex-valued neural networks and discrete Fourier transform.In this paper,we propose a systematic solution to extend the matrix computation of microring arrays from the real-valued field to the complex-valued field,and from small-scale(i.e.,4×4)to large-scale matrix computation(i.e.,16×16).Combining matrix decomposition and matrix partition,our photonic complex matrix-vector multiplier chip can support arbitrary large-scale and complex-valued matrix computation.We further demonstrate Walsh-Hardmard transform,discrete cosine transform,discrete Fourier transform,and image convolutional processing.Our scheme provides a path towards breaking the limits of complex-valued computing accelerator in conventional incoherent optical architecture.More importantly,our results reveal that an integrated photonic platform is of huge potential for large-scale,complex-valued,artificial intelligence computing and signal processing.

The Module-Phase Synchronization of Complex-Valued Neural Networks with Time-Varying Delay and Stochastic Perturbations

The problem of exponential module-phase synchronization of complex-valued neural networks(CVNNs)with time-varying delay and stochastic perturbations was investigated.The model of CVNNs with time-varying delay and stochastic perturbations was considered.The error system was deduced and the module-phase synchronization was defined.Based on the principle of Lyapunov stability theory,the appropriate controller was designed to control the CVNNs.Finally,the effectiveness and reliability of the method were verified by the numerical simulations.

Dynamics and synchronization of a complex-valued star network

Complex networks have been extensively investigated in recent years.However,the dynamics,especially chaos and bifurcation,of the complex-valued complex network are rarely studied.In this paper,a star network of coupled complex-valued van der Pol oscillators is proposed to reveal the mechanism of star coupling.By the aid of bifurcation diagram,Lyapunov exponent spectrum and phase portrait in this study,chaos,hyper-chaos,and multi-existing chaotic attractors are observed from the star network,although there are only periodic states in a complex-valued van der Pol oscillator.Complexity versus coupling strength and nonlinear coefficient shows that the bigger the network size,the larger the parameter range within the chaotic(hyper-chaotic)region.It is revealed that the chaotic bifurcation path is highly robust against the size variation of the star network,and it always evolves to chaos directly from period-1 and quasi-periodic states,respectively.Moreover,the coexistence of chaotic phase synchronization and complete synchronization among the peripherals is also found from the star network,which is a symmetrybreaking phenomenon.

Complex-Valued Convolutional Neural Networks Design and Its Application on UAV DOA Estimation in Urban Environments

Direction-of-arrival(DOA)estimation is an important task in many unmanned aerial vehicle(UAV)applications.However,the complicated electromagnetic wave propagation in urban environments substantially deteriorates the performance of many conventional model-driven DOA estimation approaches.To alleviate this,a deep learning based DOA estimation approach is proposed in this paper.Specifically,a complex-valued convolutional neural network(CCNN)is designed to fit the electromagnetic UAV signal with complex envelope better.In the CCNN design,we construct some mapping functions using quantum probabilities,and further analyze some factors which may impact the convergence of complex-valued neural networks.Numerical simulations show that the proposed CCNN converges faster than the real convolutional neural network,and the DOA estimation result is more accurate and robust.

An approach of motion compensation and ISAR imaging for micro-motion targets

Inverse synthetic aperture radar(ISAR)imaging of the target with the non-rigid body is very important in the field of radar signal processing.In this paper,a motion compensation method combined with the preprocessing and global technique is proposed to reduce the influence of micro-motion components in the fast time domain,and the micro-Doppler(m-D)signal in the slow time domain is separated by the improved complex-valued empirical-mode decomposition(CEMD)algorithm,which makes the m-D signal more effectively distinguishable from the signal for the main body by translating the target to the Doppler center.Then,a better focused ISAR image of the target with the non-rigid body can be obtained consequently.Results of the simulated and raw data demonstrate the effectiveness of the algorithm.

复变函数的多值性问题探析

主要分析了复变函数多值性的问题,讨论了函数多值性的一些具体应用以及函数多值性和单值性相互转换的一些方法.

Grinding Chatter Detection and Identication Based on BEMD and LSSVM

Grinding chatter is a self?induced vibration which is unfavorable to precision machining processes. This paper proposes a forecasting method for grinding state identification based on bivarition empirical mode decomposition(BEMD) and least squares support vector machine(LSSVM), which allows the monitoring of grinding chatter over time. BEMD is a promising technique in signal processing research which involves the decomposition of two?dimen?sional signals into a series of bivarition intrinsic mode functions(BIMFs). BEMD and the extraction criterion of its true BIMFs are investigated by processing a complex?value simulation chatter signal. Then the feature vectors which are employed as an amplification for the chatter premonition are discussed. Furthermore, the methodology is tested and validated by experimental data collected from a CNC guideway grinder KD4020 X16 in Hangzhou Hangji Machine Tool Co., Ltd. The results illustrate that the BEMD is a superior method in terms of processing non?stationary and nonlinear signals. Meanwhile, the peak to peak, real?time standard deviation and instantaneous energy are proven to be e ec?tive feature vectors which reflect the di erent grinding states. Finally, a LSSVM model is established for grinding status classification based on feature vectors, giving a prediction accuracy rate of 96%.

A Model-Driven Approach to Enhance Faster-than-Nyquist Signaling over Nonlinear Channels

In order to increase the capacity of future satellite communication systems,faster-than-Nyquist(FTN)signaling is increasingly consideredI..Existing methods for compensating for the high power amplifier(HPA)nonlinearity require perfect knowledge of the HPA model.To address this issue,we analyze the FTN symbol distribution and propose a complex-valued deep neural network(CVDNN)aided compensation scheme for the HPA nonlinearity,which does not require perfect knowledge of the HPA model and can learn the HPA nonlinearity during the training process.A model-driven network for nonlinearity compensation is proposed to further enhance the performance.Furthermore,two training sets based on the FTN symbol distribution are designed for training the network.Extensive simulations show that the Gaussian distribution is a good approximation of the FTN symbol distribution.The proposed model-driven network trained by employing a Gaussian distribution to approximate an FTN signaling can achieve a performance gain of 0.5 dB compared with existing methods without HPA's parameters at the receiver.The proposed neural network is also applicable for non-linear compensation in other systems,including orthogonal frequency-division multiplexing(OFDM).

Polynomial synchronization of complexvalued inertial neural networks with multiproportional delays

This paper investigates the polynomial synchronization(PS)problem of complex-valued inertial neural networks with multi-proportional delays.It is analyzed based on the non-separation method.Firstly,an exponential transformation is applied and an appropriate controller is designed.Then,a new sufficient criterion for PS of the considered system is derived by the Lyapunov function approach and some inequalities techniques.In the end,a numerical example is given to illustrate the effectiveness of the obtained result.

An Implicit Solver for the Time-Dependent Kohn-Sham Equation

The implicit numerical methods have the advantages on preserving the physical properties of the quantum system when solving the time-dependent Kohn-Sham equation.However,the efficiency issue prevents the practical applications of those implicit methods.In this paper,an implicit solver based on a class of Runge-Kutta methods and the finite element method is proposed for the time-dependent Kohn-Sham equation.The efficiency issue is partially resolved by three approaches,i.e.,an h-adaptive mesh method is proposed to effectively restrain the size of the discretized problem,a complex-valued algebraic multigrid solver is developed for efficiently solving the derived linear system from the implicit discretization,as well as the OpenMP based parallelization of the algorithm.The numerical convergence,the ability on preserving the physical properties,and the efficiency of the proposed numerical method are demonstrated by a number of numerical experiments.

Accretivity of the General Second Order Linear Differential Operator

For the general second order linear differential operator ■ with complex-valued distributional coefficients a_(jk), b_j, and c in an open set Ω ? R^n(n ≥ 1), we present conditions which ensure that-L^0 is accretive, i.e., Re<-L_0φ, φ >≥ 0 for all φ∈ C_0~∞(Ω).