Quasi-projective and finite-time synchronization of fractional-order memristive complex-valued delay neural networks via hybrid control

Jiaqing Zhu; Guodong Zhang; Leimin Wang; Jiaqing Zhu; Guodong Zhang; Leimin Wang

doi:10.3934/math.2024370

AIMS Mathematics

2024, Volume 9, Issue 3: 7627-7644. doi: 10.3934/math.2024370

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Quasi-projective and finite-time synchronization of fractional-order memristive complex-valued delay neural networks via hybrid control

1.
College of Mathematics and statistics, South-Central Minzu University, Wuhan 430074, China
2.
School of Automation, China University of Geosciences, Wuhan 430074, China

Received: 29 December 2023 Revised: 29 January 2024 Accepted: 04 February 2024 Published: 22 February 2024
MSC : 34A08, 34D06, 34K37, 93C23

We focused on the quasi-projective synchronization (QPS) and finite-time synchronization (FNTS) for a class of fractional-order memristive complex-valued delay neural networks (FOMCVDNNs). Rather than decomposing the complex-valued system into its real and imaginary components, we adopted a more streamlined approach by introducing a lemma associated with the complex-valued sign function. This innovative technique enabled us to design a simpler discontinuous controller. Then, based on the finite-time Lemma, measurable selection theorem, Lyapunov function theory, properties of the Mittag-Leffler function, and the fractional-order Razumikhin theorem, various substantial results were derived using a novel hybrid control scheme. In conclusion, we presented numerical simulations to illustrate the practical effectiveness of our theoretical findings.
- quasi-projective synchronization,
- finite-time synchronization,
- fractional-order,
- complex-valued,
- hybrid control
Citation: Jiaqing Zhu, Guodong Zhang, Leimin Wang. Quasi-projective and finite-time synchronization of fractional-order memristive complex-valued delay neural networks via hybrid control[J]. AIMS Mathematics, 2024, 9(3): 7627-7644. doi: 10.3934/math.2024370

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Abstract

We focused on the quasi-projective synchronization (QPS) and finite-time synchronization (FNTS) for a class of fractional-order memristive complex-valued delay neural networks (FOMCVDNNs). Rather than decomposing the complex-valued system into its real and imaginary components, we adopted a more streamlined approach by introducing a lemma associated with the complex-valued sign function. This innovative technique enabled us to design a simpler discontinuous controller. Then, based on the finite-time Lemma, measurable selection theorem, Lyapunov function theory, properties of the Mittag-Leffler function, and the fractional-order Razumikhin theorem, various substantial results were derived using a novel hybrid control scheme. In conclusion, we presented numerical simulations to illustrate the practical effectiveness of our theoretical findings.

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