scholarly journals Neural Networks Models based on the tensor-matrix theory

2021 ◽  
pp. 23-28
Author(s):  
V.I. Slyusar ◽  
Keyword(s):  
Neural Networks ◽  
Matrix Theory

scholarly journals Exponential Stability and Periodicity of Fuzzy Delayed Reaction-Diffusion Cellular Neural Networks with Impulsive Effect

2013 ◽  
Vol 2013 ◽  
pp. 1-9 ◽  
Author(s):  
Guowei Yang ◽  
Yonggui Kao ◽  
Changhong Wang
Keyword(s):  
Neural Networks ◽  
Exponential Stability ◽  
Matrix Theory ◽  
Sufficient Conditions ◽  
Neumann Boundary ◽  
Reaction Diffusion ◽  
Cellular Neural Networks ◽  
Impulsive Effect ◽  
Time Varying ◽  
Delayed Reaction

This paper considers dynamical behaviors of a class of fuzzy impulsive reaction-diffusion delayed cellular neural networks (FIRDDCNNs) with time-varying periodic self-inhibitions, interconnection weights, and inputs. By using delay differential inequality,M-matrix theory, and analytic methods, some new sufficient conditions ensuring global exponential stability of the periodic FIRDDCNN model with Neumann boundary conditions are established, and the exponential convergence rate index is estimated. The differentiability of the time-varying delays is not needed. An example is presented to demonstrate the efficiency and effectiveness of the obtained results.

scholarly journals Complete Periodic Synchronization of Memristor-Based Neural Networks with Time-Varying Delays

2013 ◽  
Vol 2013 ◽  
pp. 1-12 ◽  
Author(s):  
Huaiqin Wu ◽  
Luying Zhang ◽  
Sanbo Ding ◽  
Xueqing Guo ◽  
Lingling Wang
Keyword(s):  
Neural Networks ◽  
Periodic Solution ◽  
Matrix Theory ◽  
Adaptive Controller ◽  
Network System ◽  
Time Varying ◽  
State Dependent ◽  
Coincidence Theorem ◽  
Error System ◽  
Theoretical Results

This paper investigates the complete periodic synchronization of memristor-based neural networks with time-varying delays. Firstly, under the framework of Filippov solutions, by usingM-matrix theory and the Mawhin-like coincidence theorem in set-valued analysis, the existence of the periodic solution for the network system is proved. Secondly, complete periodic synchronization is considered for memristor-based neural networks. According to the state-dependent switching feature of the memristor, the error system is divided into four cases. Adaptive controller is designed such that the considered model can realize global asymptotical synchronization. Finally, an illustrative example is given to demonstrate the validity of the theoretical results.

scholarly journals Large-dimensional random matrix theory and its applications in deep learning and wireless communications

2021 ◽  
pp. 2230001
Author(s):  
Jungang Ge ◽  
Ying-Chang Liang ◽  
Zhidong Bai ◽  
Guangming Pan
Keyword(s):  
Neural Networks ◽  
Deep Learning ◽  
Wireless Communications ◽  
Random Matrix Theory ◽  
Random Matrix ◽  
Communication Systems ◽  
Quantum Physics ◽  
Matrix Theory ◽  
Research Field ◽  
Analysis And Design

Large-dimensional (LD) random matrix theory, RMT for short, which originates from the research field of quantum physics, has shown tremendous capability in providing deep insights into large-dimensional systems. With the fact that we have entered an unprecedented era full of massive amounts of data and large complex systems, RMT is expected to play more important roles in the analysis and design of modern systems. In this paper, we review the key results of RMT and its applications in two emerging fields: wireless communications and deep learning. In wireless communications, we show that RMT can be exploited to design the spectrum sensing algorithms for cognitive radio systems and to perform the design and asymptotic analysis for large communication systems. In deep learning, RMT can be utilized to analyze the Hessian, input–output Jacobian and data covariance matrix of the deep neural networks, thereby to understand and improve the convergence and the learning speed of the neural networks. Finally, we highlight some challenges and opportunities in applying RMT to the practical large-dimensional systems.

scholarly journals Global Robust Exponential Stability and Periodic Solutions for Interval Cohen-Grossberg Neural Networks with Mixed Delays

2013 ◽  
Vol 2013 ◽  
pp. 1-10 ◽  
Author(s):  
Yanke Du ◽  
Rui Xu
Keyword(s):  
Neural Networks ◽  
Exponential Stability ◽  
Matrix Theory ◽  
Complex Dynamics ◽  
Sufficient Conditions ◽  
Functional Method ◽  
Linear Matrix ◽  
Mixed Delays ◽  
Robust Exponential Stability ◽  
Global Robust Exponential Stability

A class of interval Cohen-Grossberg neural networks with time-varying delays and infinite distributed delays is investigated. By employing H-matrix and M-matrix theory, homeomorphism techniques, Lyapunov functional method, and linear matrix inequality approach, sufficient conditions are established for the existence, uniqueness, and global robust exponential stability of the equilibrium point and the periodic solution to the neural networks. Our results improve some previously published ones. Finally, numerical examples are given to illustrate the feasibility of the theoretical results and further to exhibit that there is a characteristic sequence of bifurcations leading to a chaotic dynamics, which implies that the system admits rich and complex dynamics.

scholarly journals Exponential Stability for Discrete-Time Stochastic BAM Neural Networks with Discrete and Distributed Delays

2011 ◽  
Vol 2011 ◽  
pp. 1-23
Author(s):  
R. Raja ◽  
R. Sakthivel ◽  
S. Marshal Anthoni
Keyword(s):  
Neural Networks ◽  
Exponential Stability ◽  
Discrete Time ◽  
Global Exponential Stability ◽  
Matrix Theory ◽  
Sufficient Conditions ◽  
Time Varying ◽  
Bam Neural Networks ◽  
Analysis Problem ◽  
The Stability

This paper deals with the stability analysis problem for a class of discrete-time stochastic BAM neural networks with discrete and distributed time-varying delays. By constructing a suitable Lyapunov-Krasovskii functional and employing M-matrix theory, we find some sufficient conditions ensuring the global exponential stability of the equilibrium point for stochastic BAM neural networks with time-varying delays. The conditions obtained here are expressed in terms of LMIs whose feasibility can be easily checked by MATLAB LMI Control toolbox. A numerical example is presented to show the effectiveness of the derived LMI-based stability conditions.

Exponential stability of anti-periodic solutions for neural networks with multiple discrete and distributed delays

2008 ◽  
Vol 223 (3) ◽  
pp. 299-308 ◽  
Author(s):  
X Liu ◽  
J Cao
Keyword(s):  
Neural Networks ◽  
Exponential Stability ◽  
Periodic Solutions ◽  
Matrix Theory ◽  
Lyapunov Method ◽  
Sufficient Conditions ◽  
Distributed Delays ◽  
Generalized Neural Networks ◽  
Discrete Delays ◽  
Analysis Of Stability

In this paper, the anti-periodic solutions are considered for generalized neural networks with multiple discrete delays and distributed delays. Several new sufficient conditions are established for ensuring the existence and exponential stability of anti-periodic solutions based on the Lyapunov method and M-matrix theory. It is shown that, by means of the techniques developed, the analysis of stability for anti-periodic solutions is different from the familiar periodic ones. The obtained results generalize and improve the earlier works. Two numerical examples are given to illustrate the effectiveness of the proposed theories.

Globally Exponentially Stability of Discrete-Time Recurrent Neural Networks with Unsaturating Linear Activation Functions

2011 ◽  
Vol 467-469 ◽  
pp. 731-736
Author(s):  
Zong Bing Lin ◽  
Qian Rong Tan ◽  
Jun Li
Keyword(s):  
Neural Networks ◽  
Discrete Time ◽  
Recurrent Neural Networks ◽  
Matrix Theory ◽  
Activation Functions ◽  
Energy Functions ◽  
Matrix Eigenvalue ◽  
Definition Of

Globally exponentially stability (GES) of a class of discrete- time recurrent neural networks with unsaturating linear activation functions is studied. Based on matrix eigenvalue, a new definition of GES is presented. By applying matrix theory, some conditions for GES are obtained. Simultaneously, those conditions are proved without energy functions.

scholarly journals Robust Exponential Stability of Switched Complex-Valued Neural Networks with Interval Parameter Uncertainties and Impulses

Complexity ◽  
2018 ◽  
Vol 2018 ◽  
pp. 1-12 ◽  
Author(s):  
Xiaohui Xu ◽  
Huanbin Xue ◽  
Yiqiang Peng ◽  
Quan Xu ◽  
Jibin Yang
Keyword(s):  
Neural Networks ◽  
Exponential Stability ◽  
Matrix Theory ◽  
Sufficient Conditions ◽  
Average Dwell Time ◽  
Interval Parameter ◽  
Parameter Uncertainties ◽  
Robust Exponential Stability ◽  
The Stability ◽  
Complex Valued

In this paper, dynamic behavior analysis has been discussed for a class of switched complex-valued neural networks with interval parameter uncertainties and impulse disturbance. Sufficient conditions for guaranteeing the existence, uniqueness, and global robust exponential stability of the equilibrium point have been obtained by using the homomorphism mapping theorem, the scalar Lyapunov function method, the average dwell time method, and M-matrix theory. Since there is no result concerning the stability problem of switched neural networks defined in complex number domain, the stability results we describe in this paper generalize the existing ones. The effectiveness of the proposed results is illustrated by a numerical example.

scholarly journals Novel Criteria of Stability for Delayed Memristive Quaternionic Neural Networks: Directly Quaternionic Method

Mathematics ◽  
2021 ◽  
Vol 9 (11) ◽  
pp. 1291
Author(s):  
Jie Pan ◽  
Lianglin Xiong
Keyword(s):  
Neural Networks ◽  
Existence And Uniqueness ◽  
Variable Coefficient ◽  
Matrix Theory ◽  
Computing Complexity ◽  
Derivative Formula ◽  
Inequality Techniques ◽  
The Fixed Point Theorem ◽  
The Stability ◽  
Theoretical Results

In this paper, we fixate on the stability of varying-time delayed memristive quaternionic neural networks (MQNNs). With the help of the closure of the convex hull of a set the theory of differential inclusion, MQNN are transformed into variable coefficient continuous quaternionic neural networks (QNNs). The existence and uniqueness of the equilibrium solution (ES) for MQNN are concluded by exploiting the fixed-point theorem. Then a derivative formula of the quaternionic function’s norm is received. By utilizing the formula, the M-matrix theory, and the inequality techniques, some algebraic standards are gained to affirm the global exponential stability (GES) of the ES for the MQNN. Notably, compared to the existing work on QNN, our direct quaternionic method operates QNN as a whole and markedly reduces computing complexity and the gained results are more apt to be verified. The two numerical simulation instances are provided to evidence the merits of the theoretical results.

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