| Citation: |
Lili Jia, Zongxin Lei, Changyou Wang, Yuqian Zhou, Tao Jiang, Yuanhua Du, Qiuyan Zhang. PROJECTION SYNCHRONIZATION OF FUNCTIONAL FRACTIONAL-ORDER NEURAL NETWORKS WITH VARIABLE COEFFICIENTS[J]. Journal of Applied Analysis & Computation, 2023, 13(2): 1070-1087. doi: 10.11948/20220491
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PROJECTION SYNCHRONIZATION OF FUNCTIONAL FRACTIONAL-ORDER NEURAL NETWORKS WITH VARIABLE COEFFICIENTS
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Abstract
In this paper, the projection synchronization problem of functional fractional-order neural networks with variable coefficients and Caputo derivatives is studied. Firstly, a simple global projection synchronization scheme is designed according to the open-loop and adaptive feedback control. Secondly, by constructing a suitable Lyapunov function and utilizing the properties of delayed fractional-order differential inequalities, some criteria for the global projective synchronization of the variable coefficient functional neural networks with Caputo derivatives are obtained. Finally, a numerical example with many numerical simulations is employed to demonstrate the correctness and validity of the proposed method in this paper.
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References
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Lili Jia, Zongxin Lei, Changyou Wang, Yuqian Zhou, Tao Jiang, Yuanhua Du, Qiuyan Zhang. PROJECTION SYNCHRONIZATION OF FUNCTIONAL FRACTIONAL-ORDER NEURAL NETWORKS WITH VARIABLE COEFFICIENTS[J]. Journal of Applied Analysis & Computation, 2023, 13(2): 1070-1087. doi: 10.11948/20220491
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Figure 1.
Synchronization errors of the master-slave systems (4.1) and (4.2) with
$ \beta = -2 $ -
Figure 2.
Evolutions of the master-slave systems (4.1) and (4.2) with
$ \beta = -2 $ -
Figure 3.
Synchronization errors of the master-slave systems (4.1) and (4.2) with
$ \beta = 3 $ -
Figure 4.
Evolutions of the master-slave systems (4.1) and (4.2) with
$ \beta = 3 $ -
Figure 5.
Synchronization errors of the systems (4.1) and (4.2) with different initial values and
$ \beta = -2 $ -
Figure 6.
Evolutions of the master-slave systems (4.1) and (4.2) with different initial values and
$ \beta = -2 $ -
Figure 7.
Synchronization errors of the systems (4.1) and (4.2) with different fractional orders and
$ \beta = -2 $ -
Figure 8.
Evolutions of the master-slave systems (4.1) and (4.2) with different fractional orders and
$ \beta = -2 $ -
Figure 9.
Synchronization errors of the systems (4.1) and (4.2) with different delays and
$ \beta = -2 $ -
Figure 10.
Evolutions of the master-slave systems (4.1) and (4.2) with different delays and
$ \beta = -2 $ -
Figure 11.
Synchronization errors of the systems (4.1) and (4.2) with different initial values and
$ \beta = 3 $ -
Figure 12.
Evolutions of the master-slave systems (4.1) and (4.2) with different initial values and
$ \beta = 3 $ -
Figure 13.
Synchronization errors of the systems (4.1) and (4.2) with different fractional orders and
$ \beta = 3 $ -
Figure 14.
Evolutions of the master-slave systems (4.1) and (4.2) with different fractional orders and
$ \beta = 3 $ -
Figure 15.
Synchronization errors of the systems (4.1) and (4.2) with different delays and
$ \beta = 3 $ -
Figure 16.
Evolutions of the master-slave systems (4.1) and (4.2) with different delays and
$ \beta = 3 $