Periodic Motions and Equilibria of Neural Networks with Piecewise Constant Argument

2013 ◽  
pp. 85-91
Author(s):  
Marat Akhmet ◽  
Enes Yılmaz
Keyword(s):  
Neural Networks ◽  
Periodic Motions ◽  
Piecewise Constant ◽  
Piecewise Constant Argument ◽  
Constant Argument

scholarly journals Existence and Exponential Stability of Solutions for Stochastic Cellular Neural Networks with Piecewise Constant Argument

2014 ◽  
Vol 2014 ◽  
pp. 1-11 ◽  
Author(s):  
Xiaoai Li
Keyword(s):  
Neural Networks ◽  
Exponential Stability ◽  
Sufficient Conditions ◽  
Cellular Neural Networks ◽  
Piecewise Constant ◽  
Piecewise Constant Argument ◽  
Inequality Technique ◽  
Generalized Type ◽  
Moment Exponential Stability ◽  
Constant Argument

By using the concept of differential equations with piecewise constant argument of generalized type, a model of stochastic cellular neural networks with piecewise constant argument is developed. Sufficient conditions are obtained for the existence and uniqueness of the equilibrium point for the addressed neural networks.pth moment exponential stability is investigated by means of Lyapunov functional, stochastic analysis, and inequality technique. The results in this paper improve and generalize some of the previous ones. An example with numerical simulations is given to illustrate our results.

Global Exponential Stability of Cohen-Grossberg Neural Networks with Piecewise Constant Argument of Generalized Type and Impulses

2016 ◽  
Vol 28 (1) ◽  
pp. 229-255 ◽  
Author(s):  
Qiang Xi
Keyword(s):  
Neural Networks ◽  
Exponential Stability ◽  
Global Exponential Stability ◽  
Sufficient Conditions ◽  
Uniqueness Of Solutions ◽  
Piecewise Constant ◽  
Piecewise Constant Argument ◽  
Lyapunov Function Method ◽  
Generalized Type ◽  
Constant Argument

In this letter, we consider a model of Cohen-Grossberg neural networks with piecewise constant argument of generalized type and impulses. Sufficient conditions ensuring the existence and uniqueness of solutions are obtained. Based on constructing a new differential inequality with piecewise constant argument and impulse and using the Lyapunov function method, we derive sufficient conditions ensuring the global exponential stability of equilibrium point, with approximate exponential convergence rate. An example is given to illustrate the validity and advantage of the theoretical results.

scholarly journals Unpredictable Oscillations for Hopfield-Type Neural Networks with Delayed and Advanced Arguments

Mathematics ◽  
2021 ◽  
Vol 9 (5) ◽  
pp. 571
Author(s):  
Marat Akhmet ◽  
Duygu Aruğaslan Çinçin ◽  
Madina Tleubergenova ◽  
Zakhira Nugayeva
Keyword(s):  
Neural Networks ◽  
Differential Equations ◽  
Strong Evidence ◽  
Time Varying ◽  
Excitation Wave ◽  
Piecewise Constant ◽  
Piecewise Constant Argument ◽  
Chaotic Signals ◽  
First Time ◽  
Constant Argument

This is the first time that the method for the investigation of unpredictable solutions of differential equations has been extended to unpredictable oscillations of neural networks with a generalized piecewise constant argument, which is delayed and advanced. The existence and exponential stability of the unique unpredictable oscillation are proven. According to the theory, the presence of unpredictable oscillations is strong evidence for Poincaré chaos. Consequently, the paper is a contribution to chaos applications in neuroscience. The model is inspired by chaotic time-varying stimuli, which allow studying the distribution of chaotic signals in neural networks. Unpredictable inputs create an excitation wave of neurons that transmit chaotic signals. The technique of analysis includes the ideas used for differential equations with a piecewise constant argument. The results are illustrated by examples and simulations. They are carried out in MATLAB Simulink to demonstrate the simplicity of the diagrammatic approaches.

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