Neural mass activity, bifurcations, and epilepsy

In this letter, we propose a general framework for studying neural mass models defined by ordinary differential equations. By studying the bifurcations of the solutions to these equations and their sensitivity to noise, we establish an important relation, similar to a dictionary, between their behaviors and normal and pathological, especially epileptic, cortical patterns of activity. We then apply this framework to the analysis of two models that feature most phenomena of interest, the Jansen and Rit model, and the slightly more complex model recently proposed by Wendling and Chauvel. This model-based approach allows us to test various neurophysiological hypotheses on the origin of pathological cortical behaviors and investigate the effect of medication. We also study the effects of the stochastic nature of the inputs, which gives us clues about the origins of such important phenomena as interictal spikes, interictal bursts, and fast onset activity that are of particular relevance in epilepsy.     

Grazing bifurcation and mode-locking in reconstructing chaotic dynamics with a leaky integrate-and-fire model

We examined the firing patterns of a chaotically forced leaky integrate-and-fire (LIF) model, and the validity of reconstructing input chaotic dynamics from an observed spike sequence. We generated inputs to the model from the Rössler system at various values of the bifurcation parameter, and carried out numerical simulations of the LIF model forced by each input. For both chaotic and periodic inputs, therotation numbers and the Lyapunov exponents were calculated to investigate the mode-locked behavior of the system. Similar behaviors as in the periodically forced LIF model were also observed in the chaotically forced LIF model. We observed (i)grazing bifurcation with the emergence of qualitatively distinct behaviors separated by a certain border in the parameter space, and (ii) modelocked regions where the output spike sequences are modelocked to the chaotic inputs. We found that thegrazing bifurcation is related to the reconstruction of chaotic dynamics with the LIF. Our results can explain why the shape of the partially reconstructed ISI attractor, which was observed in previous studies.     

Bifurcation study of neuron firing activity of the modified Hindmarsh–Rose model

In this paper, the effects of different parameters on the dynamic behavior of the nonlinear dynamical system are investigated based on modified Hindmarsh–Rose neural nonlinear dynamical system model. We have calculated and analyzed dynamic characteristics of the model under different parameters by using single parameter bifurcation diagram, time response diagram and two parameter bifurcation diagram. The results show that the period-adding bifurcation (with or without chaos), period-doubling bifurcation and intermittent chaos phenomenon (periodic and intermittent chaotic) can be observed more clearly and directly from the two parameter bifurcation diagram, and the optimal parameters matching interval can also be found easily.     

Oscillatory and chaotic dynamics in neural networks under varyingoperating conditions

This paper studies the effects of a time-dependent operating environment on the dynamics of a neural network. In the previous paper Wang et al. (1990) studied an exactly solvable model of a higher order neural network. We identified a bifurcation parameter for the system, i.e., the rescaled noise level, which represents the combined effects of incomplete connectivity, interference among stored patterns, and additional stochastic noise. When this bifurcation parameter assumes different but static (time-independent) values, the network shows a spectrum of dynamics ranging from fixed points, to oscillations, to chaos. This paper shows that varying operating conditions described by the time-dependence of the rescaled noise level give rise to many more interesting dynamical behaviours, such as disappearances of fixed points and transitions between periodic oscillations and deterministic chaos. These results suggest that a varying environment, such as the one studied in the present model, may be used to facilitate memory retrieval if dynamic states are used for information storage in a neural network     

Disturbance-generated bifurcations in a simple adaptive system: Simulation evidence

We present complete characterization based on computer simulation of the possible dynamics exhibited by an adaptive control system where the (first order) plant with a single unknown pole has constant disturbance at the input. The adaptive system is taken from the current adaptive control systems literature. Here we show that the system in fact undergoes bifurcations and exhibits rich dynamics. As the constant disturbance is varied, the system undergoes saddle-node bifurcation, (subcritical) Hopf bifurcation, and a saddle connection bifurcation. The last bifurcation means that the system acquires a homoclinic orbit for a specific disturbance. While the first two bifurcations are local, the presence of the homoclinic orbit has the potential, when periodically disturbed, to generate nonlocal complicated behavior. This latter behavior is often referred to as ‘horseshoe chaos’.     

一类二阶时延神经网络的分岔分析和控制

讨论了一类二阶时延网络系统的非线性特性,应用线性化稳定性和分岔理论,提出了该系统从稳定到分岔的条件.结论指出利用延迟时间可以进行分岔控制、极限环幅值控制等,并给出了仿真的具体实例.     

大规模超环神经网络分岔动力学

目前绝大多数神经网络分岔动力学局限于结构简单、低维少节点模型,这与真实的大规模神经网络系统相去甚远.因此,研究大量神经元耦合的高维神经网络模型更具实际应用价值.环状及辐射状结构在神经网络中普遍存在,提出了一类大规模超环时滞神经网络模型,结构包含一个大环和任意多个小环,并且每个环上拥有任意多个神经元.运用特征值法和分岔理...     

Firing patterns transition induced by system size in coupled Hindmarsh-Rose neural system

The effect of system size on the different dynamical states in coupled cell system is numerically investigated, by using the Hindmarsh-Rose (HR) model. We select the external current as a controlling parameter, for the proper coupling intensity, it is found that the system undergoes the transition of neural firing patterns from one state to another one, when the number of neurons in coupled system is set to be a proper value. And if the coupled system is turned below the bifurcation point, we find that such transition behavior can occur both between two different periodic states, or periodic state and chaotic one. These phenomena imply the occurrence of firing patterns transition (FPT) induced by system size in this coupled system. Furthermore, if we select r as a controlling parameter, we can also find the similar transition behavior can also be observed, and find that such transition behaviors may have some inherent relevance with the activity degree. Finally, we simply gave the reason for difference direction of FPT. Our results indicate the HR system may make an effective response to external stimulus by adjusting itself parameter, and using this transition mode.     

A Neural-Network-Based Model for the Dynamic Simulation of the Tire/Suspension System While Traversing Road Irregularities

This paper deals with the simulation of the tire/suspension dynamics by using recurrent neural networks (RNNs). RNNs are derived from the multilayer feedforward neural networks, by adding feedback connections between output and input layers. The optimal network architecture derives from a parametric analysis based on the optimal tradeoff between network accuracy and size. The neural network can be trained with experimental data obtained in the laboratory from simulated road profiles (cleats). The results obtained from the neural network demonstrate good agreement with the experimental results over a wide range of operation conditions. The NN model can be effectively applied as a part of vehicle system model to accurately predict elastic bushings and tire dynamics behavior. Although the neural network model, as a black-box model, does not provide a good insight of the physical behavior of the tire/suspension system, it is a useful tool for assessing vehicle ride and noise, vibration, harshness (NVH) performance due to its good computational efficiency and accuracy.      

Optimal coding predicts attentional modulation of activity in neural systems

Neuronal activity in response to a fixed stimulus has been shown to change as a function of attentional state, implying that the neural code also changes with attention. We propose an information-theoretic account of such modulation: that the nervous system adapts to optimally encode sensory stimuli while taking into account the changing relevance of different features. We show using computer simulation that such modulation emerges in a coding system informed about the uneven relevance of the input features. We present a simple feedforward model that learns a covert attention mechanism, given input patterns and coding fidelity requirements. After optimization, the system gains the ability to reorganize its computational resources (and coding strategy) depending on the incoming attentional signal, without the need of multiplicative interaction or explicit gating mechanisms between units. The modulation of activity for different attentional states matches that observed in a variety of selective attention experiments. This model predicts that the shape of the attentional modulation function can be strongly stimulus dependent. The general principle presented here accounts for attentional modulation of neural activity without relying on special-purpose architectural mechanisms dedicated to attention. This principle applies to different attentional goals, and its implications are relevant for all modalities in which attentional phenomena are observed.     

All fiber-optic neural network using coupled SOA based ring lasers

An all-optical neural network is presented that is based on coupled lasers. Each laser in the network lases at a distinct wavelength, representing one neuron. The network status is determined by the wavelength of the network's light output. Inputs to the network are in the optical power domain. The nonlinear threshold function required for neural-network operation is achieved optically by interaction between the lasers. The behavior of the coupled lasers is explained by a simple laser model developed in the paper. In particular, the winner take all (WTA) neural-network behavior of a system of many lasers is described. An experimental system is implemented using single mode fiber optic components at wavelengths near 1550 nm. A number of functions are implemented to demonstrate the practicality of the new network. The neural network is particularly robust against input wavelength variations.     

Asynchronous states and the emergence of synchrony in large networks of interacting excitatory and inhibitory neurons

We investigate theoretically the conditions for the emergence of synchronous activity in large networks, consisting of two populations of extensively connected neurons, one excitatory and one inhibitory. The neurons are modeled with quadratic integrate-and-fire dynamics, which provide a very good approximation for the subthreshold behavior of a large class of neurons. In addition to their synaptic recurrent inputs, the neurons receive a tonic external input that varies from neuron to neuron. Because of its relative simplicity, this model can be studied analytically. We investigate the stability of the asynchronous state (AS) of the network with given average firing rates of the two populations. First, we show that the AS can remain stable even if the synaptic couplings are strong. Then we investigate the conditions under which this state can be destabilized. We show that this can happen in four generic ways. The first is a saddle-node bifurcation, which leads to another state with different average firing rates. This bifurcation, which occurs for strong enough recurrent excitation, does not correspond to the emergence of synchrony. In contrast, in the three other instability mechanisms, Hopf bifurcations, which correspond to the emergence of oscillatory synchronous activity, occur. We show that these mechanisms can be differentiated by the firing patterns they generate and their dependence on the mutual interactions of the inhibitory neurons and cross talk between the two populations. We also show that besides these codimension 1 bifurcations, the system can display several codimension 2 bifurcations: Takens-Bogdanov, Gavrielov-Guckenheimer, and double Hopf bifurcations.     

Multiple Decision Expert Systems for Performance Analysis of a Boiler System

Artificial neural networks (ANN)-based multiple decision expert systems (MDES) were developed for assessing the performance of a boiler system. Different configurations of ANN were used with different decision combination methods, including a neural combiner, to propose the model. The model was developed using the plant data collected over a period of five months to predict steam temperature, pressure, and mass flow rate, using feed water pressure, feed water temperature, conveyor speed, and incinerator exit temperature as the input parameters. The predictive capability of the model is evaluated in terms of both correlation coefficient (R) and mean absolute percentage error (MAPE). The results observed from this work demonstrate that neural combiner and ANN-based MDES can efficiently predict the data on steam properties consistently, and that the model can serve as an efficient tool for monitoring boiler behavior under real-time conditions. Superiority of the proposed model over others under various scenarios is also demonstrated.     

Bifurcations in a stock market model

A theoretical framework is laid out, where a Stock Exchange is represented as a process under decentralized control. Attention is devoted to a specific case, in which the trading activity is described by a second order dynamical system. Three economically significant modes of behavior are identified. The stock market can (1)_adjust to a stable equilibrium, (2) approach a stable limit cycle, (3) diverge to infinity. The transition from mode (1) to mode (2) is a supercritical Hopf bifurcation, whereas the transition from mode (2) to mode (3) is a homoclinic bifurcation.     

Artificial neural networks in vibration control of rotor-bearing systems

A neural network controller is described and implemented for controlling the vibration of a rotor-bearing system. A multi-layered neural network is used to model the inverse dynamics or the rotor-bearing system on-line. It is learnt by a backpropagation algorithm, and a delta rule, in which the difference between the actual control input to the plant, which is generated from the neural controller, and the input estimated from the inverse-dynamics model by using an actual plant output, is minimized. The results show a satisfactory diminished response of the rotor-bearing system when the controller is applied to the system.     

一类时延神经网络的非线性分析

本文详细讨论了一类由两神经元藕合的时延网络系统,分析了该系统稳定、分叉 的条件,指出利用分叉稳定因子(延迟时间)可以进行分叉控制、极限环幅值控制等,并给出 了仿真的具体实例．     

Stability switches and bifurcation analysis of a neural networkwith continuously delay

A continuously delayed neural network with strong kernel is investigated. We found that a switch from stability to instability may occur for certain range of system parameters and must then be followed by a switch back to stability. We also investigate bifurcation phenomena of this model. Using the mean time delay as a bifurcation parameter, we prove that Hopf bifurcation occurs, i.e., a family of periodic solutions bifurcates from the equilibrium when the bifurcation parameter passes through a critical value. Stability criteria for the bifurcating periodic solutions are obtained. Some computer simulations illustrate correctness of the results     

Fixational instability and natural image statistics: implications for early visual representations

Under natural viewing conditions, small movements of the eye, head and body prevent the maintenance of a steady direction of gaze. It is known that stimuli tend to fade when they are stabilized on the retina for several seconds. However, it is unclear whether the physiological motion of the retinal image serves a visual purpose during the brief periods of natural visual fixation. This study examines the impact of fixational instability on the statistics of the visual input to the retina and on the structure of neural activity in the early visual system. We show that fixational instability introduces a component in the retinal input signals that, in the presence of natural images, lacks spatial correlations. This component strongly influences neural activity in a model of the LGN. It decorrelates cell responses even if the contrast sensitivity functions of simulated cells are not perfectly tuned to counter-balance the power-law spectrum of natural images. A decorrelation of neural activity at the early stages of the visual system has been proposed to be beneficial for discarding statistical redundancies in the input signals. The results of this study suggest that fixational instability might contribute to the establishment of efficient representations of natural stimuli.     

Asymptotic behavior and synchronizability characteristics of a class of recurrent neural networks

We propose an approach to the analysis of the influence of the topology of a neural network on its synchronizability in the sense of equal output activity rates given by a particular neural network model. The model we introduce is a variation of the Zhang model. We investigate the time-asymptotic behavior of the corresponding dynamical system (in particular, the conditions for the existence of an invariant compact asymptotic set) and apply the results of the synchronizability analysis on a class of random scale free networks and to the classical random networks with Poisson connectivity distribution.     

基于组件技术和遗传小波神经网络的智能建模系统研究

本文对已有的人工神经网络、小波分析、遗传算法的建模方法进行组合利用和加以改进,建立了智能信息处理器。该系统将大量的观测数据进行小波去噪等预处理后,作为小波神经网络模型的输入训练样本数据,网络训练中利用遗传算法动态修改网络结构和参数,并避免神经网络训练速度慢、容易陷入局部极值的缺点,从而完成数据挖掘和复杂的非线性建模功能;同时以智能信息处理器为基础,基于GIS平台利用组件技术建立扩展性强的智能建模系统。最后以某灌区水资源管理过程中的径流预报为例进行仿真实验,验证了方案的可行性和有效性。