Stability Of Recurrent Neural Networks Research Articles

Robustness analysis of stability of Takagi-Sugeno type fuzzy neural network

<abstract><p>In this paper, inequality techniques, stochastic analysis and algebraic methods are used to analyze the robustness of the stability of recurrent neural networks containing Takagi-Sugeno fuzzy rules. By solving the transcendental equations, the upper bounds of time delay and noise intensity are given, and the dynamic relationship between the two disturbance factors is derived. Finally, numerical examples are given to verify the results of this paper.</p></abstract>

Further Results on Exponentially Robust Stability of Uncertain Connection Weights of Neutral-Type Recurrent Neural Networks

Further results on the robustness of the global exponential stability of recurrent neural network with piecewise constant arguments and neutral terms (NPRNN) subject to uncertain connection weights are presented in this paper. Estimating the upper bounds of the two categories of interference factors and establishing a measuring mechanism for uncertain dual connection weights are the core tasks and challenges. Hence, on the one hand, the new sufficient criteria for the upper bounds of neutral terms and piecewise arguments to guarantee the global exponential stability of NPRNN are provided. On the other hand, the allowed enclosed region of dual connection weights is characterized by a four-variable transcendental equation based on the preceding stable NPRNN. In this way, two interference factors and dual uncertain connection weights are mutually restricted in the model of parameter-uncertainty NPRNN, which leads to a dynamic evolution relationship. Finally, the numerical simulation comparisons with stable and unstable cases are provided to verify the effectiveness of the deduced results.

Exploration on Robustness of Exponentially Global Stability of Recurrent Neural Networks with Neutral Terms and Generalized Piecewise Constant Arguments

With a view to the interference of piecewise constant arguments (PCAs) and neutral terms (NTs) to the original system and the significant applications in the signal transmission process, we explore the robustness of the exponentially global stability (EGS) of recurrent neural network (RNN) with PCAs and NTs (NPRNN). The following challenges arise: what the range of PCAs and the scope of NTs can NPRNN tolerate to be exponentially stable. So we derive two important indicators: maximum interval length of PCAs and the scope of neutral term (NT) compression coefficient here for NPRNN to be exponentially stable. Additionally, we theoretically proved that if the interval length of PCAs and the bound of NT compression coefficient are all lower than the given results herein, the disturbed NPRNN will still remain global exponential stability. Finally, there are two numerical examples to verify the deduced results’ effectiveness here.

Stability of internal states in recurrent neural networks trained on regular languages

We provide an empirical study of the stability of recurrent neural networks trained to recognize regular languages. Noise is used to force the recurrent neurons into saturation. In the saturated regime, analysis of the network activation reveals the formation of clusters that resemble discrete states in a finite state machine. We demonstrate that transitions between these activation clusters in response to input symbols are deterministic and stable. The networks display a stationary behavior for arbitrarily long strings and, when random perturbations are applied, they can recover, and their evolution converges to the original clusters. This observation reinforces the interpretation of the networks as finite automata, with neurons or groups of neurons coding specific and meaningful input patterns.

Multiple and Complete Stability of Recurrent Neural Networks With Sinusoidal Activation Function.

This article presents new theoretical results on multistability and complete stability of recurrent neural networks with a sinusoidal activation function. Sufficient criteria are provided for ascertaining the stability of recurrent neural networks with various numbers of equilibria, such as a unique equilibrium, finite, and countably infinite numbers of equilibria. Multiple exponential stability criteria of equilibria are derived, and the attraction basins of equilibria are estimated. Furthermore, criteria for complete stability and instability of equilibria are derived for recurrent neural networks without time delay. In contrast to the existing stability results with a finite number of equilibria, the new criteria, herein, are applicable for both finite and countably infinite numbers of equilibria. Two illustrative examples with finite and countably infinite numbers of equilibria are elaborated to substantiate the results.

Robust Exponential Stability of Recurrent Neural Networks with Deviating Argument and Stochastic Disturbance

It is well known that deviating argument and stochastic disturbance may derail the stability of recurrent neural networks (RNNs). This paper discusses the robustness of global exponential stability (GES) of RNNs accompanied with deviating argument and stochastic disturbance. For a given global exponentially stable RNNs, it is interesting to know how much the length of the interval of piecewise function and the interference intensity so that the disturbed system may still be exponentially stable. The available upper boundary of the range of piecewise variables and the interference intensity in the disturbed RNNs to keep GES are the solutions of some transcendental equations. Finally, some examples are provided to demonstrate the efficacy of the inferential results.

Region Stability and Stabilization of Recurrent Neural Network with Parameter Disturbances

This paper mainly focuses on global region stability and stabilization analysis for recurrent neural networks with certain or uncertain parameter disturbances. Firstly, it presents global region stability results for recurrent neural networks with certain parameter disturbances by state partition and mathematical analysis methods. Next, it designs one adaptive controller to stabilize network states to the desired region for recurrent neural networks with uncertain parameter disturbances. At last, it gives two numerical examples for verifying obtained results.

Firing rate homeostasis counteracts changes in stability of recurrent neural networks caused by synapse loss in Alzheimer's disease.

The impairment of cognitive function in Alzheimer’s disease is clearly correlated to synapse loss. However, the mechanisms underlying this correlation are only poorly understood. Here, we investigate how the loss of excitatory synapses in sparsely connected random networks of spiking excitatory and inhibitory neurons alters their dynamical characteristics. Beyond the effects on the activity statistics, we find that the loss of excitatory synapses on excitatory neurons reduces the network’s sensitivity to small perturbations. This decrease in sensitivity can be considered as an indication of a reduction of computational capacity. A full recovery of the network’s dynamical characteristics and sensitivity can be achieved by firing rate homeostasis, here implemented by an up-scaling of the remaining excitatory-excitatory synapses. Mean-field analysis reveals that the stability of the linearised network dynamics is, in good approximation, uniquely determined by the firing rate, and thereby explains why firing rate homeostasis preserves not only the firing rate but also the network’s sensitivity to small perturbations.

Global exponential asymptotic stability of RNNs with mixed asynchronous time-varying delays

The present article addresses the exponential stability of recurrent neural networks (RNNs) with distributive and discrete asynchronous time-varying delays. Some novel algebraic conditions are obtained to ensure that for the model there exists a unique balance point, and it is global exponential asymptotically stable. Meanwhile, it also reveals the difference about the equilibrium point between systems with and without distributed asynchronous delay. One numerical example and its Matlab software simulations are given to illustrate the correctness of the present results.

Robust Stability of Recurrent Neural Networks With Time-Varying Delays and Input Perturbation.

This paper addresses the robust stability of recurrent neural networks (RNNs) with time-varying delays and input perturbation, where the time-varying delays include discrete and distributed delays. By employing the new ψ -type integral inequality, several sufficient conditions are derived for the robust stability of RNNs with discrete and distributed delays. Meanwhile, the robust boundedness of neural networks is explored by the bounded input perturbation and L1 -norm constraint. Moreover, RNNs have a strong anti-jamming ability to input perturbation, and the robustness of RNNs is suitable for associative memory. Specifically, when input perturbation belongs to the specified and well-characterized space, the results cover both monostability and multistability as special cases. It is revealed that there is a relationship between the stability of neural networks and input perturbation. Compared with the existing results, these conditions proposed in this paper improve and extend the existing stability in some literature. Finally, the numerical examples are given to substantiate the effectiveness of the theoretical results.

Synchronization stability for recurrent neural networks with time-varying delays

Synchronization stability for recurrent neural networks with time-varying delays

On Complete Stability of Recurrent Neural Networks With Time-Varying Delays and General Piecewise Linear Activation Functions.

This paper addresses the problem of complete stability of delayed recurrent neural networks with a general class of piecewise linear activation functions. By applying an appropriate partition of the state space and iterating the defined bounding functions, some sufficient conditions are obtained to ensure that an n -neuron neural network is completely stable with exactly ∏i=1n(2Ki-1) equilibrium points, among which ∏i=1nKi equilibrium points are locally exponentially stable and the others are unstable, where Ki (i=1,…,n) are non-negative integers which depend jointly on activation functions and parameters of neural networks. The results of this paper include the existing works on the stability analysis of recurrent neural networks with piecewise linear functions as special cases and hence can be considered as the improvement and extension of the existing stability results in the literature. A numerical example is provided to illustrate the derived theoretical results.

Improved Stability Criterion for Recurrent Neural Networks With Time-Varying Delays.

In this brief, the problem of delay-dependent stability of recurrent neural networks with time-varying delays is studied. A newly augmented Lyapunov-Krasovskii functional (LKF) that considers the information of the nonzero lower bound of time-varying delays is developed. Moreover, the information of the delayed state terms is not considered as elements of augmented vectors when constructing the LKF. An improved stability criterion with the framework of linear matrix inequalities is derived by employing the integral inequality and reciprocally convex combination. With the comparison to the existing ones, the developed stability criterion for neural networks has less conservatism and complexity. Finally, two widely used numerical examples are given to show the effectiveness and superiority of the obtained stability criterion.

Delay-dependent Stability of Recurrent Neural Networks with Time-varying Delay

Delay-dependent Stability of Recurrent Neural Networks with Time-varying Delay

Decomposition approach to the stability of recurrent neural networks with asynchronous time delays in quaternion field

In this paper, the global exponential stability for recurrent neural networks (QVNNs) with asynchronous time delays is investigated in quaternion field. Due to the non-commutativity of quaternion multiplication resulting from Hamilton rules: ij=−ji=k, jk=−kj=i, ki=−ik=j, ijk=i2=j2=k2=−1, the QVNN is decomposed into four real-valued systems, which are studied separately. The exponential convergence is proved directly accompanied with the existence and uniqueness of the equilibrium point to the consider systems. Combining with the generalized ∞-norm and Cauchy convergence property in the quaternion field, some sufficient conditions to guarantee the stability are established without using any Lyapunov–Krasovskii functional and linear matrix inequality. Finally, a numerical example is given to demonstrate the effectiveness of the results.

Stability Proof of Iterative Interference Cancellation for OFDM Signals With Blanking Nonlinearity in Impulsive Noise Channels

Blanking nonlinearity is a widely applied technique for suppressing impulsive noise. However, for orthogonal frequency-division multiplexing signals, the blanking nonlinearity induces intercarrier interference, which must be removed in order to fully exploit the advantage of the blanking nonlinearity and to avoid performance degradation. For this purpose, interference cancellation techniques are attracting a considerable attention. Particularly, the nonlinear iterative ones show a good complexity-performance behavior. Nevertheless, one of the most important features of nonlinear iterative methods in the context of interference cancellation often remains disregarded: The stability. In this correspondence, we prove the asymptotical stability in the sense of Lyapunov of a nonlinear iterative interference cancellation technique for OFDM signals with blanking nonlinearity in impulsive noise channels. This is achieved by reformulating the considered technique as a multithreshold recurrent neural network and by taking advantage of the extensive research on the Lyapunov stability of recurrent neural networks. We show that the considered nonlinear iterative interference cancellation technique either reaches a fixed point or a limit cycle of length two. The obtained results can be utilized to find an upper bound on the required number of iterations to settle on a fixed point.

Stability of Recurrent Neural Networks With Time-Varying Delay via Flexible Terminal Method.

This brief is concerned with the stability criteria for recurrent neural networks with time-varying delay. First, based on convex combination technique, a delay interval with fixed terminals is changed into the one with flexible terminals, which is called flexible terminal method (FTM). Second, based on the FTM, a novel Lyapunov-Krasovskii functional is constructed, in which the integral interval associated with delayed variables is not fixed. Thus, the FTM can achieve the same effect as that of delay-partitioning method, while their implementary ways are different. Guided by FTM, Wirtinger-based integral inequality and free-weight matrix method are employed to develop several stability criteria, respectively. Finally, the feasibility and the effectiveness of the proposed results are tested by two numerical examples.

Delay-dependent exponential stability of recurrent neural networks with Markovian jumping parameters and proportional delays

This paper deals with the global exponential stability problem of a class of recurrent neural networks with Markovian jumping parameters and proportional delays. Here the proportional delay is unbounded time-varying, which is different from unbounded distributed delay. The nonlinear transformation \(z(t)=x({\text {e}}^{t})\) transforms the recurrent neural networks with Markovian jumping parameters and proportional delays into the recurrent neural networks with Markovian jumping parameters, constant delays and variable coefficients. By constructing Lyapunov functional, a linear matrix inequality (LMI) approach is developed to establish a new delay-dependent global exponential stability sufficient condition in the mean square, which is related to the size of the proportional delay factor and can be easily checked by utilizing the numerically efficient MATLAB LMI toolbox, and no tuning of parameters is required. Two numerical examples and their simulations are given to illustrate the effectiveness of the obtained results.

Global exponential periodicity and stability of recurrent neural networks with multi-proportional delays

In this paper, a class of recurrent neural networks with multi-proportional delays is studied. The nonlinear transformation transforms a class of recurrent neural networks with multi-proportional delays into a class of recurrent neural networks with constant delays and time-varying coefficients. By constructing Lyapunov functional and establishing the delay differential inequality, several delay-dependent and delay-independent sufficient conditions are derived to ensure global exponential periodicity and stability of the system. And several examples and their simulations are given to illustrate the effectiveness of obtained results.

Further results on robustness analysis of global exponential stability of recurrent neural networks with time delays and random disturbances

In this paper, further results on robustness analysis of global exponential stability of recurrent neural networks (RNNs) subjected to time delays and random disturbances are provided. Novel exponential stability criteria for the RNNs are derived, and upper bounds of the time delay and noise intensity are characterized by solving transcendental equations containing adjustable parameters. Through the selection of the adjustable parameters, the upper bounds are improved. It shows that our results generalize and improve the corresponding results of recent works. In addition, some numerical examples are given to show the effectiveness of the results we obtained.