A Razumikhin approach to stability and synchronization criteria for fractional order time delayed gene regulatory networks

Pratap Anbalagan; Evren Hincal; Raja Ramachandran; Dumitru Baleanu; Jinde Cao; Michal Niezabitowski; Pratap Anbalagan; Evren Hincal; Raja Ramachandran; Dumitru Baleanu; Jinde Cao; Michal Niezabitowski

doi:10.3934/math.2021268

AIMS Mathematics

2021, Volume 6, Issue 5: 4526-4555. doi: 10.3934/math.2021268

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Research article

A Razumikhin approach to stability and synchronization criteria for fractional order time delayed gene regulatory networks

1.
Department of Mathematics, Alagappa University, Karaikudi-630 004, India
2.
Department of Mathematics, Near East University TRNC, Mersin 10, Turkey
3.
Ramanujan Centre for Higher Mathematics, Alagappa University, Karaikudi-630 004, India
4.
Department of Mathematics, Cankaya University, Ankara 06530, Turkey, and Institute of Space Sciences, Magurele-Bucharest, R 76900, Romania
5.
School of Mathematics, Southeast University, Nanjing 211189, China
6.
Yonsei Frontier Lab, Yonsei University, Seoul 03722, South Korea
7.
Faculty of Automatic Control, Electronics and Computer Science, and Department of Automatic Control, and Robotics, Silesian University of Technology, Akademicka 16, 44-100 Gliwice, Poland

Received: 26 October 2020 Accepted: 09 February 2021 Published: 22 February 2021
MSC : 26A33, 34K37

This manuscript is concerned with the stability and synchronization for fractional-order delayed gene regulatory networks (FODGRNs) via Razumikhin approach. First of all, the existence of FODGRNs are established by using homeomorphism theory, 2-norm based on the algebraic method and Cauchy Schwartz inequality. The uniqueness of this work among the existing stability results are, the global Mittag-Leffler stability of FODGRNs is explored based on the fractional-order Lyapunov Razumikhin approach. In the meanwhile, two different controllers such as linear feedback and adaptive feedback control, are designed respectively. With the assistance of fractional Razumikhin theorem and our designed controllers, we have established the global Mittag-Leffler synchronization and adaptive synchronization for addressing master-slave systems. Finally, three numerical cases are given to justify the applicability of our stability and synchronization results.
- gene regulatory networks,
- fractional-order,
- existence and stability,
- synchronization,
- linear feedback control,
- adaptive feedback control
Citation: Pratap Anbalagan, Evren Hincal, Raja Ramachandran, Dumitru Baleanu, Jinde Cao, Michal Niezabitowski. A Razumikhin approach to stability and synchronization criteria for fractional order time delayed gene regulatory networks[J]. AIMS Mathematics, 2021, 6(5): 4526-4555. doi: 10.3934/math.2021268

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Abstract

This manuscript is concerned with the stability and synchronization for fractional-order delayed gene regulatory networks (FODGRNs) via Razumikhin approach. First of all, the existence of FODGRNs are established by using homeomorphism theory, 2-norm based on the algebraic method and Cauchy Schwartz inequality. The uniqueness of this work among the existing stability results are, the global Mittag-Leffler stability of FODGRNs is explored based on the fractional-order Lyapunov Razumikhin approach. In the meanwhile, two different controllers such as linear feedback and adaptive feedback control, are designed respectively. With the assistance of fractional Razumikhin theorem and our designed controllers, we have established the global Mittag-Leffler synchronization and adaptive synchronization for addressing master-slave systems. Finally, three numerical cases are given to justify the applicability of our stability and synchronization results.

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