scholarly journals Global Stability Analysis of Fractional-Order Quaternion-Valued Bidirectional Associative Memory Neural Networks

Mathematics ◽  
2020 ◽  
Vol 8 (5) ◽  
pp. 801 ◽  
Author(s):  
Usa Humphries ◽  
Grienggrai Rajchakit ◽  
Pramet Kaewmesri ◽  
Pharunyou Chanthorn ◽  
Ramalingam Sriraman ◽  
...  
Keyword(s):  
Asymptotic Stability ◽  
Fractional Order ◽  
Associative Memory ◽  
Global Asymptotic Stability ◽  
Sufficient Conditions ◽  
Linear Matrix ◽  
Activation Functions ◽  
Bidirectional Associative Memory ◽  
Lmi Approach ◽  
Global Stability Analysis

We study the global asymptotic stability problem with respect to the fractional-order quaternion-valued bidirectional associative memory neural network (FQVBAMNN) models in this paper. Whether the real and imaginary parts of quaternion-valued activation functions are expressed implicitly or explicitly, they are considered to meet the global Lipschitz condition in the quaternion field. New sufficient conditions are derived by applying the principle of homeomorphism, Lyapunov fractional-order method and linear matrix inequality (LMI) approach for the two cases of activation functions. The results confirm the existence, uniqueness and global asymptotic stability of the system’s equilibrium point. Finally, two numerical examples with their simulation results are provided to show the effectiveness of the obtained results.

Robust stability analysis for delayed Cohen-Grossberg-type bidirectional associative memory neural networks with norm-bounded uncertainties

2009 ◽  
Vol 223 (5) ◽  
pp. 693-707
Author(s):  
Y Wang ◽  
P Hu
Keyword(s):  
Neural Networks ◽  
Associative Memory ◽  
Robust Stability ◽  
Sufficient Conditions ◽  
Linear Matrix ◽  
Bidirectional Associative Memory ◽  
Parameter Uncertainties ◽  
Robust Stability Analysis ◽  
Global Robust Stability ◽  
Bounded Uncertainties

In this paper, the problem of global robust stability is discussed for uncertain Cohen-Grossberg-type (CG-type) bidirectional associative memory (BAM) neural networks (NNs) with delays. The parameter uncertainties are supposed to be norm bounded. The sufficient conditions for global robust stability are derived by employing a Lyapunov-Krasovskii functional. Based on these, the conditions ensuring global asymptotic stability without parameter uncertainties are established. All conditions are expressed in terms of linear matrix inequalities (LMIs). In addition, two examples are provided to illustrate the effectiveness of the results obtained.

LMI-BASED ASYMPTOTIC STABILITY ANALYSIS OF NEURAL NETWORKS WITH TIME-VARYING DELAYS

2008 ◽  
Vol 18 (03) ◽  
pp. 257-265 ◽  
Author(s):  
TAO LI ◽  
CHANGYIN SUN ◽  
XIANLIN ZHAO ◽  
CHONG LIN
Keyword(s):  
Neural Networks ◽  
Asymptotic Stability ◽  
Global Asymptotic Stability ◽  
Linear Matrix ◽  
Time Varying ◽  
Matrix Inequality ◽  
Stability Criteria ◽  
Activation Functions ◽  
Different Types ◽  
Conservative Result

The problem of the global asymptotic stability for a class of neural networks with time-varying delays is investigated in this paper, where the activation functions are assumed to be neither monotonic, nor differentiable, nor bounded. By constructing suitable Lyapunov functionals and combining with linear matrix inequality (LMI) technique, new global asymptotic stability criteria about different types of time-varying delays are obtained. It is shown that the criteria can provide less conservative result than some existing ones. Numerical examples are given to demonstrate the applicability of the proposed approach.

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.

Dynamic Analysis of a Delayed Fractional-Order SIR Model with Saturated Incidence and Treatment Functions

2018 ◽  
Vol 28 (14) ◽  
pp. 1850180 ◽  
Author(s):  
Xinhe Wang ◽  
Zhen Wang ◽  
Xia Huang ◽  
Yuxia Li
Keyword(s):  
Asymptotic Stability ◽  
Equilibrium Point ◽  
Fractional Order ◽  
Global Asymptotic Stability ◽  
Sufficient Conditions ◽  
Endemic Equilibrium ◽  
Local Asymptotic Stability ◽  
Proposed Model ◽  
Saturated Incidence ◽  
Theoretical Results

In this paper, a delayed fractional-order SIR (susceptible, infected, and removed) epidemic model with saturated incidence and treatment functions is presented. Firstly, the non-negativity and boundedness of solutions of the proposed model are proved. Next, some sufficient conditions are established to ensure the local asymptotic stability of the disease-free equilibrium point [Formula: see text] and the endemic equilibrium point [Formula: see text] for any delay. Meanwhile, global asymptotic stability of the endemic equilibrium point [Formula: see text] is investigated by constructing a suitable Lyapunov function. Some sufficient conditions are established for the global asymptotic stability of this endemic equilibrium point. Finally, some numerical simulations are illustrated to verify the correctness of the theoretical results.

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