Multistability Of Recurrent Neural Networks Research Articles

Multistability of recurrent neural networks with general periodic activation functions and unbounded time-varying delays

This paper investigates the multistability of recurrent neural networks (RNNs) with unbounded time-varying delays whose activation functions are general periodic functions. The activation function can be linear, nonlinear, or have multiple corner points, as long as it satisfies Lipschitz continuous condition. According to the characteristics of the parameters of the RNNs and the state space division method, the number of equilibrium points (EPs) of the RNNs is split into three categories, which can be unique, finite, or countable infinite. Some sufficient conditions for determining the number of EPs are presented, the criterion of asymptotically stable EPs is deduced, and the attraction basins of stable EPs are estimated. Furthermore, the multistability results in this paper are an extension of some previous results. The theoretical results are validated using three numerical simulation examples.

Multistability of Recurrent Neural Networks With Piecewise-Linear Radial Basis Functions and State-Dependent Switching Parameters

This paper presents new theoretical results on the multistability of switched recurrent neural networks with radial basis functions and state-dependent switching. By partitioning state space, applying Brouwer fixed-point theorem and constructing a Lyapunov function, the number of the equilibria and their locations are estimated and their stability/instability are analyzed under some reasonable assumptions on the decomposition of index set and switching threshold. It is shown that the switching threshold plays an important role in increasing the number of stable equilibria and different multistability results can be obtained under different ranges of switching threshold. The results suggest that switched recurrent neural networks would be superior to conventional ones in terms of increased storage capacity when used as associative memories. Two examples are discussed in detail to substantiate the effectiveness of the theoretical analysis.

Multistability of Recurrent Neural Networks With Nonmonotonic Activation Functions and Unbounded Time-Varying Delays

This paper is concerned with the coexistence of multiple equilibrium points and dynamical behaviors of recurrent neural networks with nonmonotonic activation functions and unbounded time-varying delays. Based on a state space partition by using the geometrical properties of the activation functions, it is revealed that an -neuron neural network can exhibit equilibrium points with . In particular, several sufficient criteria are proposed to ascertain the asymptotical stability of equilibrium points for recurrent neural networks. These theoretical results cover both monostability and multistability. Furthermore, the attraction basins of asymptotically stable equilibrium points are estimated. It is shown that the attraction basins of the stable equilibrium points can be larger than their originally partitioned subsets. Finally, the results are illustrated by using the simulation results of four examples.

Multistability of recurrent neural networks with time-varying delays and nonincreasing activation function

In this paper, we are concerned with a class of recurrent neural networks (RNNs) with nonincreasing activation function. First, based on the fixed point theorem, it is shown that under some conditions, such an n-dimensional neural network with nondecreasing activation function can have at least (4k+3)n equilibrium points. Then, it proves that there is only (4k+3)n equilibria under some conditions, among which (2k+2)n equilibria are locally stable. Besides, by analysis and study of RNNs with nondecreasing activation function, we can also obtain the same number of equilibria for RNNs with nonincreasing activation function. Finally, two simulation examples are given to show effectiveness of the obtained results.

Multistability of Recurrent Neural Networks With Nonmonotonic Activation Functions and Mixed Time Delays

This paper presents new theoretical results on the multistability analysis of a class of recurrent neural networks with nonmonotonic activation functions and mixed time delays. Several sufficient conditions are derived for ascertaining the existence of 3 <sup xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">n</sup> equilibrium points and the exponential stability of 2 <sup xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">n</sup> equilibrium points via state space partition by using the geometrical properties of activation functions and algebraic properties of nonsingular M-matrix. Compared with existing results, the conditions herein are much more computable with one order less linear matrix inequalities. Furthermore, the attraction basins of these exponentially stable equilibrium points are estimated. It is revealed that the attraction basins of the 2 <sup xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">n</sup> equilibrium points can be larger than their originally partitioned subspaces. Three numerical examples are elaborated with typical nonmonotonic activation functions to substantiate the efficacy and characteristics of the theoretical results.

Multistability of Recurrent Neural Networks With Time-varying Delays and the Piecewise Linear Activation Function

In this brief, stability of multiple equilibria of recurrent neural networks with time-varying delays and the piecewise linear activation function is studied. A sufficient condition is obtained to ensure that n-neuron recurrent neural networks can have (4k - 1)(n) equilibrium points and (2k)(n) of them are locally exponentially stable. This condition improves and extends the existing stability results in the literature. Simulation results are also discussed in one illustrative example.