Finite-time stability for fractional-order fuzzy neural network with mixed delays and inertial terms

This paper explored the finite-time stability (FTS) of fractional-order fuzzy inertial neural network with mixed delays. First, the dimension of the model was reduced by the order reduction method. Second, by leveraging the fractional-order finite-time stability theorem, fractional calculus and inequality methods, we established some sufficient conditions to guarantee the FTS of the model under feasible delay-dependent feedback controller and delay-dependent adaptive controller, respectively. Additionally, we derived the settling times (STs) for each control strategy. Finally, we provided two examples to substantiate our findings

Spatiotemporal dynamics of continuum neural fields

We survey recent analytical approaches to studying the spatiotemporal dynamics of continuum neural fields. Neural fields model the large-scale dynamics of spatially structured biological neural networks in terms of nonlinear integrodifferential equations whose associated integral kernels represent the spatial distribution of neuronal synaptic connections. They provide an important example of spatially extended excitable systems with nonlocal interactions and exhibit a wide range of spatially coherent dynamics including traveling waves oscillations and Turing-like patterns

Dynamical properties induced by state-dependent delays in photonic systems

© 2015 Macmillan Publishers Limited. All rights reserved. In many dynamical systems and complex networks time delays appear naturally in feedback loops or coupling connections of individual elements. Moreover, in a whole class of systems, these delay times can depend on the state of the system. Nevertheless, so far the understanding of the impact of such state-dependent delays remains poor with a particular lack of systematic experimental studies. Here we fill this gap by introducing a conceptually simple photonic system that exhibits dynamics of self-organised switching between two loops with two different delay times, depending on the state of the system. On the basis of experiments and modelling on semiconductor lasers with frequency-selective feedback mirrors, we characterize the switching between the states defined by the individual delays. Our approach opens new perspectives for the study of this class of dynamical systems and enables applications in which the self-organized switching can be exploited.This work was supported by MINECO (Spain) under Project TEC2012-36335 (TRIPHOP) and FIS2012-30634 (INTENSE@COSYP), Govern de les Illes Balears via the program Grups Competitius and Formació de Personal Investigador and the European Commission via FEDER and European Social Fund.Peer Reviewe

Spontaneous and stimulus-induced coherent states of critically balanced neuronal networks

How the information microscopically processed by individual neurons is integrated and used in organizing the behavior of an animal is a central question in neuroscience. The coherence of neuronal dynamics over different scales has been suggested as a clue to the mechanisms underlying this integration. Balanced excitation and inhibition may amplify microscopic fluctuations to a macroscopic level, thus providing a mechanism for generating coherent multiscale dynamics. Previous theories of brain dynamics, however, were restricted to cases in which inhibition dominated excitation and suppressed fluctuations in the macroscopic population activity. In the present study, we investigate the dynamics of neuronal networks at a critical point between excitation-dominant and inhibition-dominant states. In these networks, the microscopic fluctuations are amplified by the strong excitation and inhibition to drive the macroscopic dynamics, while the macroscopic dynamics determine the statistics of the microscopic fluctuations. Developing a novel type of mean-field theory applicable to this class of interscale interactions, we show that the amplification mechanism generates spontaneous, irregular macroscopic rhythms similar to those observed in the brain. Through the same mechanism, microscopic inputs to a small number of neurons effectively entrain the dynamics of the whole network. These network dynamics undergo a probabilistic transition to a coherent state, as the magnitude of either the balanced excitation and inhibition or the external inputs is increased. Our mean-field theory successfully predicts the behavior of this model. Furthermore, we numerically demonstrate that the coherent dynamics can be used for state-dependent read-out of information from the network. These results show a novel form of neuronal information processing that connects neuronal dynamics on different scales.Comment: 20 pages 12 figures (main text) + 23 pages 6 figures (Appendix); Some of the results have been removed in the revision in order to reduce the volume. See the previous version for more result

Dynamics meets Morphology: towards Dymorph Computation

In this dissertation, approaches are presented for both technically using and investigating biological principles with oscillators in the context of electrical engineering, in particular neuromorphic engineering. Thereby, dynamics as well as morphology as important neuronal principles were explicitly selected, which shape the information processing in the human brain and distinguish it from other technical systems. The aspects and principles selected here are adaptation during the encoding of stimuli, the comparatively low signal transmission speed, the continuous formation and elimination of connections, and highly complex, partly chaotic, dynamics. The selection of these phenomena and properties has led to the development of a sensory unit that is capable of encoding mechanical stress into a series of voltage pulses by the use of a MOSFET augmented by AlScN. The circuit is based on a leaky integrate and fire neuron model and features an adaptation of the pulse frequency. Furthermore, the slow signal transmission speed of biological systems was the motivation for the investigation of a temporal delay in the feedback of the output pulses of a relaxation oscillator. In this system stable pulse patterns which form due to so-called jittering bifurcations could be observed. In particular, switching between different stable pulse patterns was possible to induce. In the further course of the work, the first steps towards time-varying coupling of dynamic systems are investigated. It was shown that in a system consisting of dimethyl sulfoxid and zinc acetate, oscillators can be used to force the formation of filaments. The resulting filaments then lead to a change in the dynamics of the oscillators. Finally, it is shown that in a system with chaotic dynamics, the extension of it with a memristive device can lead to a transient stabilisation of the dynamics, a behaviour that can be identified as a repeated pass of Hopf bifurcations

Oscillatory mechanisms for controlling information flow in neural circuits

Mammalian brains generate complex, dynamic structures of oscillatory activity, in which distributed regions transiently engage in coherent oscillation, often at specific stages in behavioural or cognitive tasks. Much is now known about the dynamics underlying local circuit synchronisation and the phenomenology of where and when such activity occurs. While oscillations have been implicated in many high level processes, for most such phenomena we cannot say with confidence precisely what they are doing at an algorithmic or implementational level. This thesis presents work towards understanding the dynamics and possible function of large scale oscillatory network activity. We first address the question of how coherent oscillatory activity emerges between local networks by measuring phase response curves of an oscillating network in vitro. The network phase response curves provide mechanistic insight into inter-region synchronisation of local network oscillators. Highly simplified firing models are shown to reproduce the experimental data with remarkable accuracy. We then focus on one hypothesised computational function of network oscillations; flexibly controlling the gain of signal flow between anatomically connected networks. We investigate coding strategies and algorithmic operations that support flexible control of signal flow by oscillations, and their implementation by network dynamics. We identify two readout algorithms which selectively recover population rate coded signal with specific oscillatory modulations while ignoring other distracting inputs. By designing a spiking network model that implements one of these mechanisms, we demonstrate oscillatory control of signal flow in convergent pathways. We then investigate constraints on the structures of oscillatory activity that can be used to accurately and selectively control signal flow. Our results suggest that for inputs to be accurately distinguished from one another their oscillatory modulations must be close to orthogonal. This has implications for interpreting in vivo oscillatory activity, and may be an organising principle for the spatio-temporal structure of brain oscillations

Wave-by-wave Forecasting of Sea Surface Elevation for WEC Applications Utilizing NARX Neural Networks

Forecasting of ocean waves over a short duration on the order of tens of seconds was approached with the optimization of wave energy conversion in mind. This study outlines the development of an artificial neural network model, specifically the Nonlinear Autoregressive Network with Exogenous Input (NARX), to predict a wave-by-wave surface elevation time series based entirely on previous observations at the site of interest. Such a model would be computationally less intensive than competing deterministic techniques rooted in wave theory. Furthermore, it could potentially fit irregular patterns without some predetermined function as would be necessary for many other stochastic approaches. In principle, neural networks can be trained to learn previous patterns based on a recent wave record and then utilized in a feedback mode to yield multistep predictions for perhaps up to three wave periods (~45 seconds). The challenge of this approach is error accumulation in the intermediary steps that can lead to poor performance for longer prediction horizons. It was hypothesized that filtering the wave record input via wavelet or Fourier transformations could enhance model performance and hence, explorations of these types of input preprocessing were an integral part of the study. The NARX architecture allowed for an exogenous input time series that could conceivably mitigate error accumulation by providing an additional degree of signal correlation. Accordingly, the investigation also included potential exogenous inputs that could be derived from the original wave record. The work culminated with a band-pass exogenous input delivering a significant forecasting advantage. Yet, providing the zero-phase narrow-band signal posed a challenge when applied in real- time, without the use of future data. A two-prong tactical approach was undertaken to address this challenge but ultimately proved insufficient. Consequently, the success of the NARX wave-by-wave forecasting method under the conditions of a real-world application will depend upon a better solution to the zero-phase filtering challenge