Exponential stability for markovian jumping stochastic BAM neural networks with mode-dependent probabilistic time-varying delays and impulse control

Abstract
In this article, an exponential stability analysis of Markovian jumping stochastic bidirectional associative memory (BAM) neural networks with mode-dependent probabilistic time-varying delays and impulsive control is investigated. By establishment of a stochastic variable with Bernoulli distribution, the information of probabilistic time-varying delay is considered and transformed into one with deterministic time-varying delay and stochastic parameters. By fully taking the inherent characteristic of such kind of stochastic BAM neural networks into account, a novel Lyapunov-Krasovskii functional is constructed with as many as possible positive definite matrices which depends on the system mode and a triple-integral term is introduced for deriving the delay-dependent stability conditions. Furthermore, mode-dependent mean square exponential stability criteria are derived by constructing a new Lyapunov-Krasovskii functional with modes in the integral terms and using some stochastic analysis techniques. The criteria are formulated in terms of a set of linear matrix inequalities, which can be checked efficiently by use of some standard numerical packages. Finally, numerical examples and its simulations are given to demonstrate the usefulness and effectiveness of the proposed results.

Optimal feature subset selection for neuron spike sorting using the genetic algorithm

It is crucial for a neuron spike sorting algorithm to cluster data from different neurons efficiently. In this study, the search capability of the Genetic Algorithm (GA) is exploited for identifying the optimal feature subset for neuron spike sorting with a clustering algorithm. Two important objectives of the optimization process are considered: to reduce the number of features and increase the clustering performance. Specifically, we employ a binary GA with the silhouette evaluation criterion as the fitness function for neuron spike sorting using the Super-Paramagnetic Clustering (SPC) algorithm. The clustering results of SPC with and without the GA-based feature selector are evaluated using benchmark synthetic neuron spike data sets. The outcome indicates the usefulness of the GA in identifying a smaller feature set with improved clustering performance.

Statistical modelling of artificial neural network for sorting temporally synchronous spikes

Artificial neural network (ANN) models are able to predict future events based on current data. The usefulness of an ANN lies in the capacity of the model to learn and adjust the weights following previous errors during training. In this study, we carefully analyse the existing methods in neuronal spike sorting algorithms. The current methods use clustering as a basis to establish the ground truths, which requires tedious procedures pertaining to feature selection and evaluation of the selected features. Even so, the accuracy of clusters is still questionable. Here, we develop an ANN model to specially address the present drawbacks and major challenges in neuronal spike sorting. New enhancements are introduced into the conventional backpropagation ANN for determining the network weights, input nodes, target node, and error calculation. Coiflet modelling of noise is employed to enhance the spike shape features and overshadow noise. The ANN is used in conjunction with a special spiking event detection technique to prioritize the targets. The proposed enhancements are able to bolster the training concept, and on the whole, contributing to sorting neuronal spikes with close approximations.

Novel criteria for exponential stability of linear neutral time-varying differential systems

Using a novel approach, we get explicit criteria for exponential stability of linear neutral time-varying differential systems. A brief discussion to the obtained results is given. To the best of our knowledge, the results of this paper are new.

On the existence and exponential attractivity of a unique positive almost periodic solution to an impulsive hematopoiesis model with delays

Abstract In this paper, a generalized model of hematopoiesis with delays and impulses isconsidered. By employing the contraction mapping principle and a novel type of impulsivedelay inequality, we prove the existence of a unique positive almost periodic solution of themodel. It is also proved that, under the proposed conditions in this paper, the unique positivealmost periodic solution is globally exponentially attractive. A numerical example is givento illustrate the effectiveness of the obtained results.

Unified selective sorting approach to analyse multi-electrode extracellular data

Extracellular data analysis has become a quintessential method for understanding the neurophysiological responses to stimuli. This demands stringent techniques owing to the complicated nature of the recording environment. In this paper, we highlight the challenges in extracellular multi-electrode recording and data analysis as well as the limitations pertaining to some of the currently employed methodologies. To address some of the challenges, we present a unified algorithm in the form of selective sorting. Selective sorting is modelled around hypothesized generative model, which addresses the natural phenomena of spikes triggered by an intricate neuronal population. The algorithm incorporates Cepstrum of Bispectrum, ad hoc clustering algorithms, wavelet transforms, least square and correlation concepts which strategically tailors a sequence to characterize and form distinctive clusters. Additionally, we demonstrate the influence of noise modelled wavelets to sort overlapping spikes. The algorithm is evaluated using both raw and synthesized data sets with different levels of complexity and the performances are tabulated for comparison using widely accepted qualitative and quantitative indicators.

Exponential stability of time-delay systems via new weighted integral inequalities

In this paper, new weighted integral inequalities (WIIs) are first derived based on Jensen's integral inequalities in single and double forms. It is theoretically shown that the newly derived inequalities in this paper encompass both the Jensen inequality and its most recent improvement based on Wirtinger's integral inequality. The potential capability of WIIs is demonstrated through applications to exponential stability analysis of some classes of time-delay systems in the framework of linear matrix inequalities (LMIs). The effectiveness and least conservativeness of the derived stability conditions using WIIs are shown by various numerical examples.

Exponential stability of non-autonomous neural networks with heterogeneous time-varying delays and destabilizing impulses

In this paper, the problem of global exponential stability analysis of a class of non-autonomous neural networks with heterogeneous delays and time-varying impulses is considered. Based on the comparison principle, explicit conditions are derived in terms of testable matrix inequalities ensuring that the system is globally exponentially stableunder destabilizing impulsive effects. Numerical examples are given to demonstrate the effectiveness of the obtained results.

A novel approach to exponential stability of nonlinear non-autonomous difference equations with variable delays

In this paper, by using a novel approach, we first prove a new generalization of discrete-type Halanay inequality. Based on our new generalized inequality, a novel criterion for the exponential stability of a certain class of nonlinear non-autonomous difference equations is proposed. Numerical examples are given to illustrate the effectiveness of the obtained results.

Exponential stabilization of non-autonomous delayed neural networks via Riccati equations

This paper concerns with the problem of exponential stabilization for a class of non-autonomous neural networks with mixed discrete and distributed time-varying delays. Two cases of discrete time-varying delay, namely (i) slowly time-varying; and (ii) fast time-varying, are considered. By constructing an appropriate Lyapunov-Krasovskii functional in case (i) and utilizing the Razumikhin technique in case (ii), we establish some new delay-dependent conditions for designing a memoryless state feedback controller which stabilizes the system with an exponential convergence of the resulting closed-loop system. The proposed conditions are derived through solutions of some types of Riccati differential equations. Applications to control a class of autonomous neural networks with mixed time-varying delays are also discussed in this paper. Some numerical examples are provided to illustrate the effectiveness of the obtained results.

A novel approach to exponential stability of continuous-time Roesser systems with directional time-varying delays

This paper addresses the problem of exponential stability analysis of two-dimensional (2D) linearcontinuous-time systems with directional time-varying delays. An abstract Lyapunov-like theorem whichensures that a 2D linear system with delays is exponentially stable for a prescribed decay rate is exploitedfor the first time. In light of the abstract theorem, and by utilizing new 2D weighted integral inequalitiesproposed in this paper, new delay-dependent exponential stability conditions are derived in terms oftractable matrix inequalities which can be solved by various computational tools to obtain maximumallowable bound of delays and exponential decay rate. Two numerical examples are given to illustrate theeffectiveness of the obtained results.

On global exponential stability of positive neural networks with time-varying delay

This paper presents a new result on the existence, uniqueness and global exponential stability of a positive equilibrium of positiveneural networks in the presence of bounded time-varying delay. Based on some novel comparison techniques, a testable conditionis derived to ensure that all the state trajectories of the system converge exponentially to a unique positive equilibrium. Theeffectiveness of the obtained results is illustrated by a numerical example.