scholarly journals Existence, Uniqueness and Exponential Stability of Periodic Solution for Discrete-Time Delayed BAM Neural Networks Based on Coincidence Degree Theory and Graph Theoretic Method

Mathematics ◽  
2019 ◽  
Vol 7 (11) ◽  
pp. 1055 ◽  
Author(s):  
Manickam Iswarya ◽  
Ramachandran Raja ◽  
Grienggrai Rajchakit ◽  
Jinde Cao ◽  
Jehad Alzabut ◽  
...  

In this work, a general class of discrete time bidirectional associative memory (BAM) neural networks (NNs) is investigated. In this model, discrete and continuously distributed time delays are taken into account. By utilizing this novel method, which incorporates the approach of Kirchhoff’s matrix tree theorem in graph theory, Continuation theorem in coincidence degree theory and Lyapunov function, we derive a few sufficient conditions to ensure the existence, uniqueness and exponential stability of the periodic solution of the considered model. At the end of this work, we give a numerical simulation that shows the effectiveness of this work.

Author(s):  
Qianhong Zhang ◽  
Lihui Yang ◽  
Daixi Liao

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.


2005 ◽  
Vol 2005 (3) ◽  
pp. 281-297 ◽  
Author(s):  
Hong Xiang ◽  
Ke-Ming Yan ◽  
Bai-Yan Wang

By using coincidence degree theory as well as a priori estimates and Lyapunov functional, we study the existence and global stability of periodic solution for discrete delayed high-order Hopfield-type neural networks. We obtain some easily verifiable sufficient conditions to ensure that there exists a unique periodic solution, and all theirs solutions converge to such a periodic solution.


2007 ◽  
Vol 17 (01) ◽  
pp. 35-42 ◽  
Author(s):  
YONGHUI XIA ◽  
JINDE CAO ◽  
MUREN LIN

Sufficient conditions are obtained for the existence and global exponential stability of a unique periodic solution of a class of impulsive tow-neuron networks with variable and unbounded delays. The approaches are based on Mawhin's continuation theorem of coincidence degree theory and Lyapunov functions.


2013 ◽  
Vol 291-294 ◽  
pp. 2412-2415
Author(s):  
Hui Li ◽  
Yi Fei Wang

In this paper, we investigate of a class of predator-prey system with rate stocking and time delay, the existence positive periodic solution by using coincidence degree theory. We obtain the sufficient conditions which guarantee existence of the positive periodic solution of the periodic system. Some new results obtained.


2009 ◽  
Vol 2009 ◽  
pp. 1-18 ◽  
Author(s):  
Yongkun Li ◽  
Lili Zhao ◽  
Ping Liu

On time scales, by using the continuation theorem of coincidence degree theory and constructing some suitable Lyapunov functions, the periodicity and the exponential stability are investigated for a class of delayed high-order Hopfield neural networks (HHNNs), which are new and complement of previously known results. Finally, an example is given to show the effectiveness of the proposed method and results.


2011 ◽  
Vol 2011 ◽  
pp. 1-23
Author(s):  
R. Raja ◽  
R. Sakthivel ◽  
S. Marshal Anthoni

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.


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