scholarly journals Fixed Point and Asymptotic Analysis of Cellular Neural Networks

2012 ◽  
Vol 2012 ◽  
pp. 1-12 ◽  
Author(s):  
Xianghong Lai ◽  
Yutian Zhang
Keyword(s):  
Neural Networks ◽  
Fixed Point ◽  
Existence And Uniqueness ◽  
Fixed Point Theory ◽  
Sufficient Conditions ◽  
Point Theory ◽  
Cellular Neural Networks ◽  
Time Varying ◽  
Trivial Equilibrium ◽  
The Stability

We firstly employ the fixed point theory to study the stability of cellular neural networks without delays and with time-varying delays. Some novel and concise sufficient conditions are given to ensure the existence and uniqueness of solution and the asymptotic stability of trivial equilibrium at the same time. Moreover, these conditions are easily checked and do not require the differentiability of delays.

scholarly journals Stability of Impulsive Neural Networks with Time-Varying and Distributed Delays

2013 ◽  
Vol 2013 ◽  
pp. 1-10 ◽  
Author(s):  
Qi Luo ◽  
Xinjie Miao ◽  
Qian Wei ◽  
Zhengxin Zhou
Keyword(s):  
Neural Networks ◽  
Existence And Uniqueness ◽  
Global Exponential Stability ◽  
Fixed Point Theory ◽  
Sufficient Conditions ◽  
Point Theory ◽  
Distributed Delays ◽  
Time Varying ◽  
Trivial Equilibrium ◽  
The Stability

This work is devoted to investigating the stability of impulsive cellular neural networks with time-varying and distributed delays. We use the new method of fixed point theory to obtain some new and concise sufficient conditions to ensure the existence and uniqueness of solution and the global exponential stability of trivial equilibrium. The presented algebraic criteria are easily checked and do not require the differentiability of delays.

scholarly journals Asymptotic Stability of Impulsive Cellular Neural Networks with Infinite Delays via Fixed Point Theory

2013 ◽  
Vol 2013 ◽  
pp. 1-10
Author(s):  
Yutian Zhang ◽  
Yuanhong Guan
Keyword(s):  
Neural Networks ◽  
Fixed Point ◽  
Asymptotic Stability ◽  
Fixed Point Theory ◽  
Sufficient Conditions ◽  
Point Theory ◽  
Cellular Neural Networks ◽  
Infinite Delays ◽  
Trivial Equilibrium ◽  
The Stability

We employ the new method of fixed point theory to study the stability of a class of impulsive cellular neural networks with infinite delays. Some novel and concise sufficient conditions are presented ensuring the existence and uniqueness of solution and the asymptotic stability of trivial equilibrium at the same time. These conditions are easily checked and do not require the boundedness and differentiability of delays.

scholarly journals Mean-Square Exponential Stability Analysis of Stochastic Neural Networks with Time-Varying Delays via Fixed Point Method

2014 ◽  
Vol 2014 ◽  
pp. 1-9
Author(s):  
Tianxiang Yao ◽  
Xianghong Lai
Keyword(s):  
Neural Networks ◽  
Fixed Point ◽  
Exponential Stability ◽  
Fixed Point Theory ◽  
Sufficient Conditions ◽  
Point Theory ◽  
Stability Study ◽  
Stochastic Neural Networks ◽  
Time Varying ◽  
Mean Square

This work addresses the stability study for stochastic cellular neural networks with time-varying delays. By utilizing the new research technique of the fixed point theory, we find some new and concise sufficient conditions ensuring the existence and uniqueness as well as mean-square global exponential stability of the solution. The presented algebraic stability criteria are easily checked and do not require the differentiability of delays. The paper is finally ended with an example to show the effectiveness of the obtained results.

scholarly journals Fixed point theory in the setting of $(\alpha,\beta,\psi,\phi)$-interpolative contractions

2021 ◽  
Vol 2021 (1) ◽  
Author(s):  
Erdal Karapınar ◽  
Andreea Fulga ◽  
Antonio Francisco Roldán López de Hierro
Keyword(s):  
Fixed Point ◽  
Existence And Uniqueness ◽  
Fixed Point Theory ◽  
Sufficient Conditions ◽  
Point Theory ◽  
Necessary And Sufficient Conditions ◽  
Alpha Beta ◽  
Necessary And Sufficient

AbstractIn this manuscript we introduce the notion of $(\alpha,\beta,\psi,\phi)$ ( α , β , ψ , ϕ ) -interpolative contraction that unifies and generalizes significant concepts: Proinov type contractions, interpolative contractions, and ample spectrum contraction. We investigate the necessary and sufficient conditions to guarantee existence and uniqueness of the fixed point of such mappings.

scholarly journals Finite-Time Stabilization of Memristive Cohen-Grossberg Neural Networks with Time-Varying Delay

Complexity ◽  
2018 ◽  
Vol 2018 ◽  
pp. 1-15
Author(s):  
Ge Li ◽  
Yaqiong Li ◽  
Zhaohui Yuan
Keyword(s):  
Neural Networks ◽  
Finite Time ◽  
Fixed Point Theory ◽  
Sufficient Conditions ◽  
Point Theory ◽  
Time Varying ◽  
Finite Time Stability ◽  
Time Varying Delay ◽  
Finite Time Stabilization ◽  
Varying Delay

In this paper, the finite-time stabilization problem for memristive Cohen-Grossberg neural networks with time-varying delay is discussed. By using the novel fixed point theory of set-valued maps, we establish the existence theorem of equilibrium point. In order to realize the finite-time stabilization, two different kinds of discontinuous state feedback controllers whether including time-varying delay are designed. Based on the extended Filippov framework and two different kinds of methods whether using finite-time stability theory, some novel sufficient conditions and the upper bound of the settling time for finite-time stabilization are proposed. Finally, two numerical examples are given to demonstrate the validity of theoretical results.

scholarly journals Global Exponential Stability and Periodicity of Nonautonomous Impulsive Neural Networks with Time-Varying Delays and Reaction-Diffusion Terms

Complexity ◽  
2021 ◽  
Vol 2021 ◽  
pp. 1-13
Author(s):  
Weiyi Hu ◽  
Kelin Li
Keyword(s):  
Neural Networks ◽  
Exponential Stability ◽  
Global Exponential Stability ◽  
Fixed Point Theory ◽  
Sufficient Conditions ◽  
Reaction Diffusion ◽  
Point Theory ◽  
Time Varying ◽  
Nonautonomous Systems ◽  
Inequality Techniques

In this paper, we investigate the global exponential stability and periodicity of nonautonomous cellular neural networks with reaction-diffusion, impulses, and time-varying delays. By establishing a new differential inequality for nonautonomous systems, using the properties of M-matrix and inequality techniques, some new sufficient conditions for the global exponential stability of the system are obtained. Moreover, sufficient conditions for the periodic solutions of the system are obtained by using the Poincare mapping and the fixed point theory. The validity and superiority of the main results are verified by numerical examples and simulations.

Modeling the dynamics of hepatitis E via the Caputo–Fabrizio derivative

2019 ◽  
Vol 14 (3) ◽  
pp. 311 ◽  
Author(s):  
Muhammad Altaf Khan ◽  
Zakia Hammouch ◽  
Dumitru Baleanu
Keyword(s):  
Fixed Point ◽  
Existence And Uniqueness ◽  
Numerical Scheme ◽  
Arbitrary Order ◽  
Fixed Point Theory ◽  
Hepatitis E ◽  
Point Theory ◽  
Existence And Uniqueness Results ◽  
Uniqueness Results ◽  
Essential Properties

A virus that causes hepatitis E is known as (HEV) and regarded on of the reason for lever inflammation. In mathematical aspects a very low attention has been paid to HEV dynamics. Therefore, the present work explores the HEV dynamics in fractional derivative. The Caputo–Fabriizo derivative is used to study the dynamics of HEV. First, the essential properties of the model will be presented and then describe the HEV model with CF derivative. Application of fixed point theory is used to obtain the existence and uniqueness results associated to the model. By using Adams–Bashfirth numerical scheme the solution is obtained. Some numerical results and tables for arbitrary order derivative are presented.

scholarly journals Existence and exponential stability of a periodic solution for fuzzy cellular neural networks with time-varying delays

2011 ◽  
Vol 21 (4) ◽  
pp. 649-658 ◽  
Author(s):  
Qianhong Zhang ◽  
Lihui Yang ◽  
Daixi Liao
Keyword(s):  
Neural Networks ◽  
Periodic Solution ◽  
Exponential Stability ◽  
Differential Inequality ◽  
Sufficient Conditions ◽  
Coincidence Degree ◽  
Cellular Neural Networks ◽  
Time Varying ◽  
Fuzzy Cellular Neural Networks ◽  
Inequality Technique

Existence and exponential stability of a periodic solution for fuzzy cellular neural networks with time-varying delays Fuzzy cellular neural networks with time-varying delays are considered. Some sufficient conditions for the existence and exponential stability of periodic solutions are obtained by using the continuation theorem based on the coincidence degree and the differential inequality technique. The sufficient conditions are easy to use in pattern recognition and automatic control. Finally, an example is given to show the feasibility and effectiveness of our methods.

Exponential stability and periodicity of memristor-based recurrent neural networks with time-varying delays

2017 ◽  
Vol 10 (02) ◽  
pp. 1750027 ◽  
Author(s):  
Wei Zhang ◽  
Chuandong Li ◽  
Tingwen Huang
Keyword(s):  
Neural Networks ◽  
Exponential Stability ◽  
Sufficient Conditions ◽  
Functional Approach ◽  
Linear Matrix ◽  
Time Varying ◽  
Matrix Inequality ◽  
Matrix Inequalities ◽  
Inclusion Theory ◽  
The Stability

In this paper, the stability and periodicity of memristor-based neural networks with time-varying delays are studied. Based on linear matrix inequalities, differential inclusion theory and by constructing proper Lyapunov functional approach and using linear matrix inequality, some sufficient conditions are obtained for the global exponential stability and periodic solutions of memristor-based neural networks. Finally, two illustrative examples are given to demonstrate the results.

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