Chaotic bursting as chaotic itinerancy in coupled neural oscillators

We show that chaotic bursting activity observed in coupled neural oscillators is a kind of chaotic itinerancy. In neuronal systems with phase deformation along the trajectory, diffusive coupling induces a dephasing effect. Because of this effect, an antiphase synchronized solution is stable for weak coupling, while an in-phase solution is stable for very strong coupling. For intermediate coupling, a chaotic bursting activity is generated. It is a mixture of three different states: an antiphase firing state, an in-phase firing state, and a nonfiring resting state. As we construct numerically the deformed torus manifold underlying the chaotic bursting state, it is shown that the three unstable states are connected to give rise to a global chaotic itinerancy structure. Thus we claim that chaotic itinerancy provides an alternative route to chaos via torus breakdown.     

Chaotic itinerancy in coupled dynamical recognizers

We argue that chaotic itinerancy in interaction between humans originates in the fluctuation of predictions provided by the nonconvergent nature of learning dynamics. A simple simulation model called the coupled dynamical recognizer is proposed to study this phenomenon. Daily cognitive phenomena provide many examples of chaotic itinerancy, such as turn taking in conversation. It is therefore an interesting problem to bridge two chaotic itinerant phenomena. A clue to solving this is the fluctuation of prediction, which can be translated as "hot prediction" in the context of cognitive theory. Hot prediction is simply defined as a prediction based on an unstable model. If this approach is correct, the present simulation will reveal some dynamic characteristics of cognitive interactions.     

Chaotic diagonal recurrent neural network

We propose a novel neural network based on a diagonal recurrent neural network and chaos,and its structure and learning algorithm are designed.The multilayer feedforward neural network,diagonal recurrent neural network,and chaotic diagonal recurrent neural network are used to approach the cubic symmetry map.The simulation results show that the approximation capability of the chaotic diagonal recurrent neural network is better than the other two neural networks.     

Chaotic cluster itinerancy and hierarchical cluster trees in electrochemical experiments

Experiments on an array of 64 globally coupled chaotic electrochemical oscillators were carried out. The array is heterogeneous due to small variations in the properties of the electrodes and there is also a small amount of noise. Over some ranges of the coupling parameter, dynamical clustering was observed. The precision-dependent cluster configuration is analyzed using hierarchical cluster trees. The cluster configurations varied with time: spontaneous changes of number of clusters and their configurations were detected. Simple transitions occurred with the switch of a single element or groups of elements. During more complicated transitions subclusters were exchanged among clusters but original cluster configurations were revisited. At weaker coupling the system itinerated among lower-dimensional quasistationary chaotic two-cluster states and higher-dimensional states with many clusters. In this region the transitions showed characteristics of on-off intermittency.     

Positive Lyapunov exponents in the Kramers oscillator

The maximum Lyapunov exponent is computed numerically for the double-well oscillator in a heat bath. Positive exponents are found in a wide range of friction coefficients in the low-damping regime.     

Macroscopic Lyapunov functions for separable stochastic neural networks with detailed balance

We derive macroscopic Lyapunov functions for large, long-range, Ising-spin neural networks with separable symmetric interactions, which evolve in time according to local field alignment. We generalize existing constructions, which correspond todeterministic (zero-temperature) evolution and to specific choices of the interaction structure, to the case ofstochastic evolution and arbitrary separable interaction matrices, for both parallel and sequential spin updating. We find a direct relation between the form of the Lyapunov functions (which describe dynamical processes) and the saddle-point integration that results from performing equilibrium statistical mechanical studies of the present type of model.     

一种具有正弦基函数权值的反馈型神经网络模型

提出了一种新的两层反馈型神经网络模型. 该网络采用正弦基函数作为权值, 神经元激活函数为线性函数, 连接形式为两层反馈型结构. 研究并定义了该反馈型神经网络的能量函数, 分析了网络运行的稳定性问题, 并证明了在Liapunov意义下网络运行的稳定性. 网络运行过程中, 其权值不做调整(但随时间按正弦规律变化), 网络状态不断地转换. 随着网络状态变化其能量不断减小, 最终在达到稳定时能量到达极小点. 由于该反馈型神经网络权值为正弦函数, 特别适合于周期信号的自适应逼近和检测, 为实际中周期性信号检测与处理提供了一种新的、有效的网络模型和方法. 作为应用实例把该网络应用于电力系统中电压凹陷特征量实时检测, 仿真结果表明, 网络用于信号检测不仅有很高的静态精度, 而且有非常好的动态响应特性.     

Construction of the Lyapunov Spectrum in a Chaotic System Displaying Phase Synchronization

We consider a three-dimensional chaotic system consisting of the suspension of Arnold’s cat map coupled with a clock via a weak dissipative interaction. We show that the coupled system displays a synchronization phenomenon, in the sense that the relative phase between the suspension flow and the clock locks to a special value, thus making the motion fall onto a lower dimensional attractor. More specifically, we construct the attractive invariant manifold, of dimension smaller than three, using a convergent perturbative expansion. Moreover, we compute via convergent series the Lyapunov exponents, including notably the central one. The result generalizes a previous construction of the attractive invariant manifold in a similar but simpler model. The main novelty of the current construction relies in the computation of the Lyapunov spectrum, which consists of non-trivial analytic exponents. Some conjectures about a possible smoothening transition of the attractor as the coupling is increased are also discussed.     

Further improvement of the Lyapunov functional and the delay-dependent stability criterion for a neural network with a constant delay

This paper investigates the asymptotical stability problem of a neural system with a constant delay. A new delaydependent stability condition is derived by using the novel augmented Lyapunov–Krasovskii function with triple integral terms, and the additional triple integral terms play a key role in the further reduction of conservativeness. Finally, a numerical example is given to demonstrate the effectiveness and lower conservativeness of the proposed method.     

Chaotic behavior in noninteger-order cellular neural networks

In this paper, a simple system showing chaotic behavior is introduced. It is based on the well-known concept of cellular neural networks (CNNs), which have already given good results in generating complex dynamics. The peculiarity of the CNN model consists in the fact that it replaces the traditional first-order cell with a noninteger-order one. The introduction of the fractional cell, with a suitable choice of the coupling parameters, leads to the onset of chaos in a simple two-cell system. A theoretical approach, based on the harmonic balance theory, has been used to investigate the existence of chaos. A circuit realization of the proposed fractional two-cell chaotic CNN is reported and the corresponding strange attractor is also shown.     

Correlation and complexity analysis of well logs via Lyapunov, Hurst, Lempel-Ziv and neural network algorithms

Well logs produce a wealth of data that can be used to evaluate the production capacity of oil and gas fields. These data are usually concerned with depth series of petrophysical quantities such as the sonic transient time, gamma emission, deep induction resistivity, neutron porosity and bulk density. Here, we perform a correlation and complexity analysis of well log data from the Namorado’s school field using Lyapunov, Hurst, Lempel-Ziv and neural network algorithms. After identifying the most correlated and complex series, we demonstrate that well log data estimates can be confidently performed by neural network algorithms either to complete missing data or to infer complete well logs of a specific quantity.     

基于时变阈值过程神经网络的太阳黑子数预测

太阳黑子活动直接影响着外层空间环境的变化，为保证航天飞行任务的安全必须对其进行有效预测.为此，提出了一种基于时变阈值过程神经网络的时间序列预测模型.为简化模型的计算复杂度，开发了一种基于正交基函数展开的学习算法.文中分析了模型的泛函逼近能力，并以Mackey-Glass时间序列预测为例验证了所提模型及其学习算法的有效性.最后，将该预测模型用于太阳活动第23周太阳黑子数平滑月均值预测，取得了满意的结果，应用结果同时表明：所提预测方法与其他传统预测方法相比预测精度有所提高，具有一定的理论和实用价值. 关键词： 太阳黑子数 时变阈值过程神经网络 时间序列预测 泛函逼近     

Negative Wigner functions of nonlinear dissipative oscillator in the pulsed regime

Preparation of nonclassical states that are described by negative Wigner functions is studied for an anharmonic oscillator under parametric excitation (AOPE). The over-transient pulsed regime of AOPE driven by a train of Gaussian laser pulses is analyzed. The results are obtained by complete consideration of dissipative and decoherence effects.     

Synchronization and structure in an adaptive oscillator network

We analyze the interplay of synchronization and structure evolution in an evolving network of phase oscillators. An initially random network is adaptively rewired according to the dynamical coherence of the oscillators, in order to enhance their mutual synchronization. We show that the evolving network reaches a small-world structure. Its clustering coefficient attains a maximum for an intermediate intensity of the coupling between oscillators, where a rich diversity of synchronized oscillator groups is observed. In the stationary state, these synchronized groups are directly associated with network clusters.     

基于径向基函数神经网络的未知模型混沌系统控制

基于径向基函数神经网络的智能方法对混沌进行控制-该方法不需要被控混沌系统的解析模型，控制的目标可以为周期轨道，也可以为连续变化的目标函数，在模型参数发生摄动和存在测量噪声情况下，控制仍然有效-研究了神经网络误差对控制精度的影响，并给出相关的定理及证明-针对Logistic映射和Henon吸引子的仿真结果，表明了此方法的有效性和可行性- 关键词： 混沌控制 径向基函数神经网络 参数摄动 测量噪声     

Chaotic motion in the resonant separatrix bands of a Mathieu-Duffing oscillator with a twin-well potential

The (M:1)-resonant bands in the left and right potential wells are skew-symmetric, and the (2M:1)-resonant bands of the large orbit motion are symmetric. The analytical conditions for the onset and destruction of a resonant band are developed through the incremental energy approach. The numerical predictions of such onset and destruction are also completed by the energy increment spectrum method. The sub-resonance interaction occurs for strong excitations, which needs to be further investigated. These results are applicable to the small- and large-orbit motions of post-buckled structure under a parametric excitation.     

Importance of itinerancy and quantum fluctuations for the magnetism in ironpnictides

By applying density functional theory, we find strong evidence for an itinerant nature of magnetism in two families of iron pnictides. Furthermore, by employing dynamical mean field theory with continuous time quantum Monte Carlo as an impurity solver, we observe that the antiferromagnetic metal with small magnetic moment naturally arises out of coupling between unfrustrated and frustrated bands. Our results point to a possible scenario for magnetism in iron pnictides where magnetism originates from a strong instability at the momentum vector (π,π,π) while it is reduced by quantum fluctuations due to the coupling between weakly and strongly frustrated bands.     

Chaotic oscillations in a map-based model of neural activity

We propose a discrete time dynamical system (a map) as a phenomenological model of excitable and spiking-bursting neurons. The model is a discontinuous two-dimensional map. We find conditions under which this map has an invariant region on the phase plane, containing a chaotic attractor. This attractor creates chaotic spiking-bursting oscillations of the model. We also show various regimes of other neural activities (subthreshold oscillations, phasic spiking, etc.) derived from the proposed model.