Mittag-Leffler stability analysis of multiple equilibrium points in impulsive fractional-order quaternion-valued neural networks

2020 ◽  
Vol 21 (2) ◽  
pp. 234-246 ◽  
Author(s):  
K. Udhayakumar ◽  
R. Rakkiyappan ◽  
Jin-de Cao ◽  
Xue-gang Tan
Keyword(s):  
Neural Networks ◽  
Stability Analysis ◽  
Fractional Order ◽  
Equilibrium Points ◽  
Multiple Equilibrium ◽  
Multiple Equilibrium Points

scholarly journals Multistability and Multiperiodicity for a General Class of Delayed Cohen-Grossberg Neural Networks with Discontinuous Activation Functions

2013 ◽  
Vol 2013 ◽  
pp. 1-11 ◽  
Author(s):  
Yanke Du ◽  
Yanlu Li ◽  
Rui Xu
Keyword(s):  
Neural Networks ◽  
Periodic Orbits ◽  
General Class ◽  
Equilibrium Points ◽  
Sufficient Conditions ◽  
Multiple Equilibrium ◽  
Activation Functions ◽  
Discontinuous Activation ◽  
Discontinuous Activation Functions ◽  
Multiple Equilibrium Points

A general class of Cohen-Grossberg neural networks with time-varying delays, distributed delays, and discontinuous activation functions is investigated. By partitioning the state space, employing analysis approach and Cauchy convergence principle, sufficient conditions are established for the existence and locally exponential stability of multiple equilibrium points and periodic orbits, which ensure thatn-dimensional Cohen-Grossberg neural networks withk-level discontinuous activation functions can haveknequilibrium points orknperiodic orbits. Finally, several examples are given to illustrate the feasibility of the obtained results.

Analysis of Complete Stability for Discrete-Time Cellular Neural Networks with Piecewise Linear Output Functions

2009 ◽  
Vol 21 (5) ◽  
pp. 1434-1458 ◽  
Author(s):  
Xuemei Li
Keyword(s):  
Neural Networks ◽  
Discrete Time ◽  
Piecewise Linear ◽  
Equilibrium Points ◽  
Cellular Neural Networks ◽  
Multiple Equilibrium ◽  
Small Perturbations ◽  
Feedback Matrix ◽  
Multiple Equilibrium Points ◽  
Stability Results

This letter discusses the complete stability of discrete-time cellular neural networks with piecewise linear output functions. Under the assumption of certain symmetry on the feedback matrix, a sufficient condition of complete stability is derived by finite trajectory length. Because the symmetric conditions are not robust, the complete stability of networks may be lost under sufficiently small perturbations. The robust conditions of complete stability are also given for discrete-time cellular neural networks with multiple equilibrium points and a unique equilibrium point. These complete stability results are robust and available.

scholarly journals Multi-stability analysis of fractional-order quaternion-valued neural networks with time delay

2021 ◽  
Vol 7 (3) ◽  
pp. 3603-3629
Author(s):  
S. Kathiresan ◽  
◽  
Ardak Kashkynbayev ◽  
K. Janani ◽  
R. Rakkiyappan ◽  
...  
Keyword(s):  
Neural Networks ◽  
Stability Analysis ◽  
Time Delay ◽  
Fractional Order ◽  
Equilibrium Points ◽  
Activation Functions ◽  
Geometrical Properties ◽  
Intermediate Value ◽  
Complex Valued ◽  
Theoretical Results

<abstract><p>This paper addresses the problem of multi-stability analysis for fractional-order quaternion-valued neural networks (QVNNs) with time delay. Based on the geometrical properties of activation functions and intermediate value theorem, some conditions are derived for the existence of at least $ (2\mathcal{K}_p^R+1)^n, (2\mathcal{K}_p^I+1)^n, (2\mathcal{K}_p^J+1)^n, (2\mathcal{K}_p^K+1)^n $ equilibrium points, in which $ [(\mathcal{K}_p^R+1)]^n, [(\mathcal{K}_p^I+1)]^n, [(\mathcal{K}_p^J+1)]^n, [(\mathcal{K}_p^K+1)]^n $ of them are uniformly stable while the other equilibrium points become unstable. Thus the developed results show that the QVNNs can have more generalized properties than the real-valued neural networks (RVNNs) or complex-valued neural networks (CVNNs). Finally, two simulation results are given to illustrate the effectiveness and validity of our obtained theoretical results.</p></abstract>

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