Global Mittag–Leffler stabilization of fractional-order bidirectional associative memory neural networks

2016 ◽  
Vol 177 ◽  
pp. 489-496 ◽  
Author(s):  
Ailong Wu ◽  
Zhigang Zeng ◽  
Xingguo Song
Keyword(s):  
Neural Networks ◽  
Fractional Order ◽  
Associative Memory ◽  
Bidirectional Associative Memory

Mittag–Leffler synchronization for impulsive fractional-order bidirectional associative memory neural networks via optimal linear feedback control

2021 ◽  
Vol 26 (2) ◽  
pp. 207-226
Author(s):  
Jiazhe Lin ◽  
Rui Xu ◽  
Liangchen Li
Keyword(s):  
Neural Networks ◽  
Fractional Order ◽  
Associative Memory ◽  
Actuator Saturation ◽  
Sufficient Conditions ◽  
Linear Feedback ◽  
Impulsive Effect ◽  
Bidirectional Associative Memory ◽  
Optimal Linear ◽  
Predictor Corrector

In this paper, we are concerned with the synchronization scheme for fractional-order bidirectional associative memory (BAM) neural networks, where both synaptic transmission delay and impulsive effect are considered. By constructing Lyapunov functional, sufficient conditions are established to ensure the Mittag–Leffler synchronization. Based on Pontryagin’s maximum principle with delay, time-dependent control gains are obtained, which minimize the accumulative errors within the limitation of actuator saturation during the Mittag–Leffler synchronization. Numerical simulations are carried out to illustrate the feasibility and effectiveness of theoretical results with the help of the modified predictor-corrector algorithm and the forward-backward sweep method.

scholarly journals Stability Analysis of Fractional-Order Bidirectional Associative Memory Neural Networks with Mixed Time-Varying Delays

Complexity ◽  
2019 ◽  
Vol 2019 ◽  
pp. 1-22
Author(s):  
Zhanying Yang ◽  
Jie Zhang
Keyword(s):  
Neural Networks ◽  
Stability Analysis ◽  
Fractional Order ◽  
Associative Memory ◽  
Analytical Techniques ◽  
Mean Value Theorem ◽  
Sufficient Condition ◽  
Time Varying ◽  
Bidirectional Associative Memory ◽  
Practical Applications

This paper studies the stability analysis of fractional-order bidirectional associative memory neural networks with mixed time-varying delays. The orders of these systems lie in the interval 1,2. Firstly, a sufficient condition is derived to ensure the finite-time stability of systems by resorting to some analytical techniques and some elementary inequalities. Next, a sufficient condition is obtained to guarantee the global asymptotic stability of systems based on the Laplace transform, the mean value theorem, the generalized Gronwall inequality, and some properties of Mittag–Leffler functions. In particular, these obtained conditions are expressed as some algebraic inequalities which can be easily calculated in practical applications. Finally, some numerical examples are given to verify the feasibility and effectiveness of the obtained main results.

scholarly journals Mittag-Leffler synchronization of delayed fractional-order bidirectional associative memory neural networks with discontinuous activations: state feedback control and impulsive control schemes

2017 ◽  
Vol 473 (2204) ◽  
pp. 20170322 ◽  
Author(s):  
Xiaoshuai Ding ◽  
Jinde Cao ◽  
Xuan Zhao ◽  
Fuad E. Alsaadi
Keyword(s):  
Neural Networks ◽  
Fractional Order ◽  
Associative Memory ◽  
State Feedback ◽  
Impulsive Control ◽  
State Feedback Control ◽  
Bidirectional Associative Memory ◽  
Discontinuous Activations ◽  
The Fixed Point Theorem ◽  
Discontinuous Activation Functions

This paper is concerned with the drive–response synchronization for a class of fractional-order bidirectional associative memory neural networks with time delays, as well as in the presence of discontinuous activation functions. The global existence of solution under the framework of Filippov for such networks is firstly obtained based on the fixed-point theorem for condensing map. Then the state feedback and impulsive controllers are, respectively, designed to ensure the Mittag-Leffler synchronization of these neural networks and two new synchronization criteria are obtained, which are expressed in terms of a fractional comparison principle and Razumikhin techniques. Numerical simulations are presented to validate the proposed methodologies.

scholarly journals Anti-periodic solutions for fractional-order bidirectional associative memory neural networks with delays

2019 ◽  
Vol 23 (Suppl. 6) ◽  
pp. 2169-2177
Author(s):  
Munevver Tuz ◽  
Gulden Suroglu
Keyword(s):  
Neural Networks ◽  
Periodic Solutions ◽  
Fractional Order ◽  
Associative Memory ◽  
Lyapunov Functional ◽  
Sufficient Conditions ◽  
Functional Method ◽  
Bidirectional Associative Memory ◽  
Inequality Technique ◽  
Lyapunov Functional Method

This paper concerns fractional-order bidirectional associative memory neural networks with distributed delays. Based on inequality technique and Lyapunov functional method, some novel sufficient conditions are obtained for the existence and exponential stability of anti-periodic solutions are established. An example is given to show the feasibility main results.

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