Projective synchronization of fractional-order memristive neural networks with switching jumps mismatch

2017 ◽  
Vol 471 ◽  
pp. 402-415 ◽  
Author(s):  
Lingzhong Zhang ◽  
Yongqing Yang ◽  
Fei Wang
Keyword(s):  
Neural Networks ◽  
Fractional Order ◽  
Projective Synchronization ◽  
Memristive Neural Networks ◽  
Switching Jumps Mismatch

scholarly journals Finite-Time Projective Synchronization of Fractional-Order Memristive Neural Networks with Mixed Time-Varying Delays

Complexity ◽  
2020 ◽  
Vol 2020 ◽  
pp. 1-27
Author(s):  
Meng Hui ◽  
Chen Wei ◽  
Jiao Zhang ◽  
Herbert Ho-Ching Iu ◽  
Ni Luo ◽  
...  
Keyword(s):  
Neural Networks ◽  
Lyapunov Function ◽  
Fractional Order ◽  
Finite Time ◽  
Settling Time ◽  
Projective Synchronization ◽  
Time Varying ◽  
Memristive Neural Networks ◽  
Synchronization Problem ◽  
Fractional Differential

This paper is concerned with the finite-time projective synchronization problem of fractional-order memristive neural networks (FMNNs) with mixed time-varying delays. Firstly, under the frame of fractional-order differential inclusion and the set-valued map, several criteria are derived to ensure finite-time projective synchronization of FMNNs. Meanwhile, three properties are established to deal with different forms of the finite-time fractional differential inequation, which greatly extend some results on estimation of settling time of FMNNs. In addition to the traditional Lyapunov function with 1-norm form in Theorem 1, a more general and flexible Lyapunov function based on p-norm is constructed in Theorem 2 to analyze the finite-time projective synchronization problem, and the estimation of settling time has been verified less conservative than previous results. Finally, numerical examples are provided to demonstrate the effectiveness of the derived theoretical results.

scholarly journals Projective Synchronization of Nonidentical Fractional-Order Memristive Neural Networks

2019 ◽  
Vol 2019 ◽  
pp. 1-11 ◽  
Author(s):  
Chong Chen ◽  
Zhixia Ding
Keyword(s):  
Neural Networks ◽  
Fractional Order ◽  
Sliding Mode ◽  
Direct Method ◽  
Projective Synchronization ◽  
Sliding Mode Controller ◽  
Memristive Neural Networks ◽  
Lyapunov Direct Method ◽  
Sliding Motion ◽  
Fractional Order Integral

This paper investigates projective synchronization of nonidentical fractional-order memristive neural networks (NFMNN) via sliding mode controller. Firstly, based on the sliding mode control theory, a new fractional-order integral sliding mode controller is designed to ensure the occurrence of sliding motion. Furthermore, according to fractional-order differential inequalities and fractional-order Lyapunov direct method, the trajectories of the system converge to the sliding mode surface to carry out sliding mode motion, and some sufficient criteria are obtained to achieve global projective synchronization of NFMNN. In addition, the conclusions extend and improve some previous works on the synchronization of fractional-order memristive neural networks (FMNN). Finally, a simulation example is given to verify the effectiveness and correctness of the obtained results.

scholarly journals Global Mittag–Leffler Stability and Stabilization Analysis of Fractional-Order Quaternion-Valued Memristive Neural Networks

Mathematics ◽  
2020 ◽  
Vol 8 (3) ◽  
pp. 422 ◽  
Author(s):  
Grienggrai Rajchakit ◽  
Pharunyou Chanthorn ◽  
Pramet Kaewmesri ◽  
Ramalingam Sriraman ◽  
Chee Peng Lim
Keyword(s):  
Neural Networks ◽  
Fractional Order ◽  
Differential Inclusions ◽  
State Feedback ◽  
Control Law ◽  
Memristive Neural Networks ◽  
Numerical Examples ◽  
Quaternion Multiplication ◽  
Stabilizing Control ◽  
Stability And Stabilization

This paper studies the global Mittag–Leffler stability and stabilization analysis of fractional-order quaternion-valued memristive neural networks (FOQVMNNs). The state feedback stabilizing control law is designed in order to stabilize the considered problem. Based on the non-commutativity of quaternion multiplication, the original fractional-order quaternion-valued systems is divided into four fractional-order real-valued systems. By using the method of Lyapunov fractional-order derivative, fractional-order differential inclusions, set-valued maps, several global Mittag–Leffler stability and stabilization conditions of considered FOQVMNNs are established. Two numerical examples are provided to illustrate the usefulness of our analytical results.

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