Exponential synchronization of discontinuous neural networks with time-varying mixed delays via state feedback and impulsive control

This paper investigates drive-response synchronization for a class of neural networks with time-varying discrete and distributed delays (mixed delays) as well as discontinuous activations. Strict mathematical proof shows the global existence of Filippov solutions to neural networks with discontinuous activation functions and the mixed delays. State feedback controller and impulsive controller are designed respectively to guarantee global exponential synchronization of the neural networks. By using Lyapunov function and new analysis techniques, several new synchronization criteria are obtained. Moreover, lower bound on the convergence rate is explicitly estimated when state feedback controller is utilized. Results of this paper are new and some existing ones are extended and improved. Finally, numerical simulations are given to verify the effectiveness of the theoretical results.     

Local synchronization of one-to-one coupled neural networks with discontinuous activations

In this paper, local synchronization is considered for coupled delayed neural networks with discontinuous activation functions. Under the framework of Filippov solution and in the sense of generalized derivative, a novel sufficient condition is obtained to ensure the synchronization based on the Lyapunov exponent and the detailed analysis in Danca (Int J Bifurcat Chaos 12(8):1813–1826, 2002; Chaos Solitons Fractals 22:605–612, 2004). Simulation results are given to illustrate the theoretical results.     

A linear model for characterization of synchronization frequencies of neural networks

The synchronization frequency of neural networks and its dynamics have important roles in deciphering the working mechanisms of the brain. It has been widely recognized that the properties of functional network synchronization and its dynamics are jointly determined by network topology, network connection strength, i.e., the connection strength of different edges in the network, and external input signals, among other factors. However, mathematical and computational characterization of the relationships between network synchronization frequency and these three important factors are still lacking. This paper presents a novel computational simulation framework to quantitatively characterize the relationships between neural network synchronization frequency and network attributes and input signals. Specifically, we constructed a series of neural networks including simulated small-world networks, real functional working memory network derived from functional magnetic resonance imaging, and real large-scale structural brain networks derived from diffusion tensor imaging, and performed synchronization simulations on these networks via the Izhikevich neuron spiking model. Our experiments demonstrate that both of the network synchronization strength and synchronization frequency change according to the combination of input signal frequency and network self-synchronization frequency. In particular, our extensive experiments show that the network synchronization frequency can be represented via a linear combination of the network self-synchronization frequency and the input signal frequency. This finding could be attributed to an intrinsically-preserved principle in different types of neural systems, offering novel insights into the working mechanism of neural systems.     

Pinning synchronization of coupled inertial delayed neural networks

The paper is devoted to the investigation of synchronization for an array of linearly and diffusively coupled inertial delayed neural networks (DNNs). By placing feedback control on a small fraction of network nodes, the entire coupled DNNs can be synchronized to a common objective trajectory asymptotically. Two different analysis methods, including matrix measure strategy and Lyapunov–Krasovskii function approach, are employed to provide sufficient criteria for the synchronization control problem. Comparisons of these two techniques are given at the end of the paper. Finally, an illustrative example is provided to show the effectiveness of the obtained theoretical results.     

Finite-time and fixed-time synchronization analysis of inertial memristive neural networks with time-varying delays

This paper investigates the finite-time synchronization and fixed-time synchronization problems of inertial memristive neural networks with time-varying delays. By utilizing the Filippov discontinuous theory and Lyapunov stability theory, several sufficient conditions are derived to ensure finite-time synchronization of inertial memristive neural networks. Then, for the purpose of making the setting time independent of initial condition, we consider the fixed-time synchronization. A novel criterion guaranteeing the fixed-time synchronization of inertial memristive neural networks is derived. Finally, three examples are provided to demonstrate the effectiveness of our main results.     

Learning and coding of concepts in neural networks

Our environment consists of virtually an infinite number of scenarios in which we have to function. In order to respond properly to an incoming stimulus, the brain has first to analyze it, and to find out the basic familiar elements that are part of it. In other words, by using a library which contains a relatively small number of basic concepts, the brain analyzes the multitude of incoming events. Some of those basic concepts are innate, but many of them must be learned, in order to accommodate for the arbitrary environment around us. A classifying box is defined as the neural network that finds out the familiar concepts that are present in an incoming stimulus. Models for classifying boxes are introduced, and possible mechanisms by which they may establish their libraries of concepts are suggested, and then compared and evaluated by computer simulations.     

Synchronization properties of networks of electrically coupled neurons in the presence of noise and heterogeneities

We investigate how synchrony can be generated or induced in networks of electrically coupled integrate-and-fire neurons subject to noisy and heterogeneous inputs. Using analytical tools, we find that in a network under constant external inputs, synchrony can appear via a Hopf bifurcation from the asynchronous state to an oscillatory state. In a homogeneous net work, in the oscillatory state all neurons fire in synchrony, while in a heterogeneous network synchrony is looser, many neurons skipping cycles of the oscillation. If the transmission of action potentials via the electrical synapses is effectively excitatory, the Hopf bifurcation is supercritical, while effectively inhibitory transmission due to pronounced hyperpolarization leads to a subcritical bifurcation. In the latter case, the network exhibits bistability between an asynchronous state and an oscillatory state where all the neurons fire in synchrony. Finally we show that for time-varying external inputs, electrical coupling enhances the synchronization in an asynchronous network via a resonance at the firing-rate frequency.

Function projective synchronization of memristor-based Cohen–Grossberg neural networks with time-varying delays

This paper deals with the problem of function projective synchronization for a class of memristor-based Cohen–Grossberg neural networks with time-varying delays. Based on the theory of differential equations with discontinuous right-hand side, some novel criteria are obtained to realize the function projective synchronization of addressed networks by combining open loop control and linear feedback control. As some special cases, several control strategies are given to ensure the realization of complete synchronization, anti-synchronization and the stabilization of the considered memristor-based Cohen–Grossberg neural network. Finally, a numerical example and its simulations are provided to demonstrate the effectiveness of the obtained results.     

Predicting secondary structures of membrane proteins with neural networks

Back-propagation, feed-forward neural networks are used to predict the secondary structures of membrane proteins whose structures are known to atomic resolution. These networks are trained on globular proteins and can predict globular protein structures having no homology to those of the training set with correlation coefficients (C) of 0.45, 0.32 and 0.43 for a-helix, -strand and random coil structures, respectively. When tested on membrane proteins, neural networks trained on globular proteins do, on average, correctly predict (Q_i) 62%, 38% and 69% of the residues in the -helix, -strand and random coil structures. These scores rank higher than those obtained with the currently used statistical methods and are comparable to those obtained with the joint approaches tested so far on membrane proteins. The lower success score for -strand as compared to the other structures suggests that the sample of -strand patterns contained in the training set is less representative than those of a-helix and random coil. Our analysis, which includes the effects of the network parameters and of the structural composition of the training set on the prediction, shows that regular patterns of secondary structures can be successfully extrapolated from globular to membrane proteins. Correspondence to: R. Casadio     

Exponential synchronization for fuzzy cellular neural networks with time-varying delays and nonlinear impulsive effects

In this paper, the globally exponential synchronization of delayed fuzzy cellular neural networks with nonlinear impulsive effects are concerned. By utilizing inequality techniques and Lyapunov functional method, some sufficient conditions on the exponential synchronization are obtained based on p-norm. Finally, a simulation example is given to illustrate the effectiveness of the theoretical results.     

Application of neural networks for the prediction of cartilage stress in a musculoskeletal system

Traditional finite element (FE) analysis is computationally demanding. The computational time becomes prohibitively long when multiple loading and boundary conditions need to be considered such as in musculoskeletal movement simulations involving multiple joints and muscles. Presented in this study is an innovative approach that takes advantage of the computational efficiency of both the dynamic multibody (MB) method and neural network (NN) analysis. A NN model that captures the behavior of musculoskeletal tissue subjected to known loading situations is built, trained, and validated based on both MB and FE simulation data. It is found that nonlinear, dynamic NNs yield better predictions over their linear, static counterparts. The developed NN model is then capable of predicting stress values at regions of interest within the musculoskeletal system in only a fraction of the time required by FE simulation.     

电突触耦合神经元的相位同步及放电节律的转化

研究了两个参数失配较大情况下,处于不同放电模式的两个电突触耦合Hindmarsh-rose(HR)神经元的相位同步问题,发现在适当耦合强度下可以实现相同步并呈现出复杂的放电节律.利用峰峰间期(Interspikeinterval,ISI)和平均放电频率证实了相同步的发生,给出并分析了不同放电状态的神经元在电突触耦合下实现相同步后的神经放电节律.从相同步的角度显示,神经元同步后呈现簇放电特征或峰放电特征,除与两耦合神经元独自放电模式有关外,还与电突触耦合强度有一定的内在关系.     

Dynamics of recurrent neural networks with delayed unreliable synapses: metastable clustering

The influence of unreliable synapses on the dynamic properties of a neural network is investigated for a homogeneous integrate-and-fire network with delayed inhibitory synapses. Numerical and analytical calculations show that the network relaxes to a state with dynamic clusters of identical size which permanently exchange neurons. We present analytical results for the number of clusters and their distribution of firing times which are determined by the synaptic properties. The number of possible configurations increases exponentially with network size. In addition to states with a maximal number of clusters, metastable ones with a smaller number of clusters survive for an exponentially large time scale. An externally excited cluster survives for some time, too, thus clusters may encode information.     

Synchronization of chaotic nonlinear continuous neural networks with time-varying delay

In this paper, the synchronization problem for delayed continuous time nonlinear complex neural networks is considered. The delay dependent state feed back synchronization gain matrix is obtained by considering more general case of time-varying delay. Using Lyapunov stability theory, the sufficient synchronization criteria are derived in terms of Linear Matrix Inequalities (LMIs). By decomposing the delay interval into multiple equidistant subintervals, Lyapunov-Krasovskii functionals (LKFs) are constructed on these intervals. Employing these LKFs, new delay dependent synchronization criteria are proposed in terms of LMIs for two cases with and without derivative of time-varying delay. Numerical examples are illustrated to show the effectiveness of the proposed method.     

New stability criteria for uncertain neural networks with interval time-varying delays

This paper is concerned with the stability analysis for neural networks with interval time-varying delays and parameter uncertainties. An approach combining the Lyapunov-Krasovskii functional with the differential inequality and linear matrix inequality techniques is taken to investigate this problem. By constructing a new Lyapunov-Krasovskii functional and introducing some free weighting matrices, some less conservative delay-derivative-dependent and delay-derivative-independent stability criteria are established in term of linear matrix inequality. And the new criteria are applicable to both fast and slow time-varying delays. Three numerical examples show that the proposed criterion are effective and is an improvement over some existing results in the literature.     

Power-rate synchronization of coupled genetic oscillators with unbounded time-varying delay

In this paper, a new synchronization problem for the collective dynamics among genetic oscillators with unbounded time-varying delay is investigated. The dynamical system under consideration consists of an array of linearly coupled identical genetic oscillators with each oscillators having unbounded time-delays. A new concept called power-rate synchronization, which is different from both the asymptotical synchronization and the exponential synchronization, is put forward to facilitate handling the unbounded time-varying delays. By using a combination of the Lyapunov functional method, matrix inequality techniques and properties of Kronecker product, we derive several sufficient conditions that ensure the coupled genetic oscillators to be power-rate synchronized. The criteria obtained in this paper are in the form of matrix inequalities. Illustrative example is presented to show the effectiveness of the obtained results.     

Partial phase synchronization of neural populations due to random Poisson inputs

We show that populations of identical uncoupled neurons exhibit partial phase synchronization when stimulated with independent, random unidirectional current spikes with interspike time intervals drawn from a Poisson distribution. We characterize this partial synchronization using the phase distribution of the population, and consider analytical approximations and numerical simulations of phase-reduced models and the corresponding conductance-based models of typical Type I (Hindmarsh-Rose) and Type II (Hodgkin-Huxley) neurons, showing quantitatively how the extent of the partial phase synchronization depends on the magnitude and mean interspike frequency of the stimulus. Furthermore, we present several simple examples that disprove the notion that phase synchrony must be strongly related to spike synchrony. Instead, the importance of partial phase synchrony is shown to lie in its influence on the response of the population to stimulation, which we illustrate using first spike time histograms.     

The neural correlate of consciousness

I propose that we are only aware of changes in our underlying cognition. This hypothesis is based on four lines of evidence. (1) Without changes in visual input (including fixational eye movements), static images fade from awareness. (2) Consciousness appears to be continuous, but is actually broken up into discrete cycles of cognition. Without continuity, conscious awareness disintegrates into a series of isolated cycles. The simplest mechanism for creating continuity is to track the changes between the cycles. (3) While these conscious vectors are putative, they have a clear source: the dorsolateral prefrontal cortex (DLPFC). The DLPFC is active during awareness of changes, and this awareness is disrupted by repetitive transcranial magnetic stimulation. (4) When the DLPFC and the orbital and inferior parietal cortices are deactivated during dreaming, conscious awareness is absent even though the rest of the brain is active. Moreover, Lau and Passingham showed that activation of the DLPFC, but no other brain region, correlates with awareness. In summary, if the DLPFC and conscious vectors are the neural correlate of consciousness, then we are only aware of changes in our underlying cognition. The glue that holds conscious awareness together is conscious awareness.