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

• Published in: AIMS mathematics Vol. 6; no. 5; pp. 4526 - 4555
• Main Authors: Anbalagan, Pratap, Hincal, Evren, Ramachandran, Raja, Baleanu, Dumitru, Cao, Jinde, Niezabitowski, Michal
• Format: Journal Article
• Language: English
• Published: AIMS Press 01.01.2021
• Subjects: adaptive feedback control; existence and stability; fractional-order; gene regulatory networks; linear feedback control; synchronization
• ISSN: 2473-6988; 2473-6988
• DOI: 10.3934/math.2021268

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.