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 Projective synchronization analysis for BAM neural networks with time-varying delay via novel control

2021 ◽  
Vol 26 (1) ◽  
pp. 41-56
Author(s):  
Malika Sader ◽  
Fuyong Wang ◽  
Zhongxin Liu ◽  
Zhongxin Chen
Keyword(s):  
Neural Networks ◽  
Adaptive Controller ◽  
Projective Synchronization ◽  
Time Varying ◽  
Bam Neural Networks ◽  
Application Process ◽  
Time Varying Delay ◽  
Synchronization Problem ◽  
Varying Delay ◽  
Theoretical Results

In this paper, the projective synchronization of BAM neural networks with time-varying delays is studied. Firstly, a type of novel adaptive controller is introduced for the considered neural networks, which can achieve projective synchronization. Then, based on the adaptive controller, some novel and useful conditions are obtained to ensure the projective synchronization of considered neural networks. To our knowledge, different from other forms of synchronization, projective synchronization is more suitable to clearly represent the nonlinear systems’ fragile nature. Besides, we solve the projective synchronization problem between two different chaotic BAM neural networks, while most of the existing works only concerned with the projective synchronization chaotic systems with the same topologies. Compared with the controllers in previous papers, the designed controllers in this paper do not require any activation functions during the application process. Finally, an example is provided to show the effectiveness of the theoretical results.

Complete periodic adaptive antisynchronization of memristor-based neural networks with mixed time-varying delays

2014 ◽  
Vol 92 (11) ◽  
pp. 1337-1349 ◽  
Author(s):  
Huaiqin Wu ◽  
Ruoxia Li ◽  
Sanbo Ding ◽  
Xiaowei Zhang ◽  
Rong Yao
Keyword(s):  
Neural Networks ◽  
Adaptive Controller ◽  
Time Varying ◽  
Slave System ◽  
Control Parameters ◽  
Analysis Theory ◽  
Master System ◽  
Coincidence Theorem ◽  
Adaptive Laws ◽  
Unknown Control

This paper is concerned with the complete periodic antisynchronization issue of memristor-based neural networks with mixed time-varying delays. Under the framework of Filippov solutions of the differential equations with discontinuous right-hand side, based on Mawhin-like coincidence theorem in set-valued analysis theory, the proof of the existence of periodic solution is presented. By applying the Lyapunov–Krasovskii functional approach, adaptive controller is designed and unknown control parameters of the slave system are determined by adaptive laws, and the complete periodic adaptive antisynchronization condition is addressed to ensure the slave system global antisynchronization with the master system. An illustrative example is given to demonstrate the effectiveness of the obtained results.

Periodic solutions for stochastic Cohen–Grossberg neural networks with time-varying delays

2020 ◽  
Vol 0 (0) ◽  
Author(s):  
Wanqin Wu ◽  
Li Yang ◽  
Yaping Ren
Keyword(s):  
Neural Networks ◽  
Periodic Solution ◽  
Exponential Stability ◽  
Fixed Points ◽  
Periodic Solutions ◽  
Sufficient Conditions ◽  
Stochastic Neural Networks ◽  
Time Varying ◽  
Deterministic Systems ◽  
Theoretical Results

AbstractThis paper is concerned with the periodic solutions for a class of stochastic Cohen–Grossberg neural networks with time-varying delays. Since there is a non-linearity in the leakage terms of stochastic Cohen–Grossberg neural networks, some techniques are needed to overcome the difficulty in dealing with the nonlinearity. By applying fixed points principle and Gronwall–Bellman inequality, some sufficient conditions on the existence and exponential stability of periodic solution for the stochastic neural networks are established. Moreover, a numerical example is presented to validate the theoretical results. Our results are also applicable to the existence and exponential stability of periodic solution for the corresponding deterministic systems.

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.

ATTRACTABILITY AND LOCATION OF EQUILIBRIUM POINT OF CELLULAR NEURAL NETWORKS WITH TIME-VARYING DELAYS

2004 ◽  
Vol 14 (05) ◽  
pp. 337-345 ◽  
Author(s):  
ZHIGANG ZENG ◽  
DE-SHUANG HUANG ◽  
ZENGFU WANG
Keyword(s):  
Neural Networks ◽  
Exponential Stability ◽  
Equilibrium Point ◽  
Global Exponential Stability ◽  
Cellular Neural Networks ◽  
Stability Conditions ◽  
Time Varying ◽  
The Stability ◽  
Theoretical Results

This paper presents new theoretical results on global exponential stability of cellular neural networks with time-varying delays. The stability conditions depend on external inputs, connection weights and delays of cellular neural networks. Using these results, global exponential stability of cellular neural networks can be derived, and the estimate for location of equilibrium point can also be obtained. Finally, the simulating results demonstrate the validity and feasibility of our proposed approach.

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.

Synchronization of time-varying time delayed neutral-type neural networks for finite-time in complex field

2021 ◽  
Vol 8 (3) ◽  
pp. 486-498
Author(s):  
N. Jayanthi ◽  
◽  
R. Santhakumari ◽  
Keyword(s):  
Neural Networks ◽  
Finite Time ◽  
State Feedback ◽  
Neutral Type ◽  
State Feedback Control ◽  
Projective Synchronization ◽  
Time Varying ◽  
Master System ◽  
Complex Valued ◽  
Theoretical Results

This paper deals with the problem of finite-time projective synchronization for a class of neutral-type complex-valued neural networks (CVNNs) with time-varying delays. A simple state feedback control protocol is developed such that slave CVNNs can be projective synchronized with the master system in finite time. By employing inequalities technique and designing new Lyapunov--Krasovskii functionals, various novel and easily verifiable conditions are obtained to ensure the finite-time projective synchronization. It is found that the settling time can be explicitly calculated for the neutral-type CVNNs. Finally, two numerical simulation results are demonstrated to validate the theoretical results of this paper.

scholarly journals Robust Almost Periodic Dynamics for Interval Neural Networks with Mixed Time-Varying Delays and Discontinuous Activation Functions

2013 ◽  
Vol 2013 ◽  
pp. 1-13
Author(s):  
Huaiqin Wu ◽  
Sanbo Ding ◽  
Xueqing Guo ◽  
Lingling Wang ◽  
Luying Zhang
Keyword(s):  
Neural Networks ◽  
Periodic Solution ◽  
Time Varying ◽  
Almost Periodic ◽  
Activation Functions ◽  
Robust Exponential Stability ◽  
Discontinuous Activation ◽  
Interval Neural Networks ◽  
Discontinuous Activation Functions ◽  
Global Robust Exponential Stability

The robust almost periodic dynamical behavior is investigated for interval neural networks with mixed time-varying delays and discontinuous activation functions. Firstly, based on the definition of the solution in the sense of Filippov for differential equations with discontinuous right-hand sides and the differential inclusions theory, the existence and asymptotically almost periodicity of the solution of interval network system are proved. Secondly, by constructing appropriate generalized Lyapunov functional and employing linear matrix inequality (LMI) techniques, a delay-dependent criterion is achieved to guarantee the existence, uniqueness, and global robust exponential stability of almost periodic solution in terms of LMIs. Moreover, as special cases, the obtained results can be used to check the global robust exponential stability of a unique periodic solution/equilibrium for discontinuous interval neural networks with mixed time-varying delays and periodic/constant external inputs. Finally, an illustrative example is given to demonstrate the validity of the theoretical results.

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