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

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-Letter 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-Letter 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.

Automated summary

This manuscript focuses on the stability and synchronization of fractional-order delayed gene regulatory networks (FODGRNs) using the Razumikhin approach. Unique to this work is the exploration of global Mittag-Letter stability of FODGRNs based on the fractional-order Lyapunov Razumikhin approach. By designing controllers and utilizing the fractional Razumikhin theorem, global Mittag-Letter synchronization and adaptive synchronization for master-slave systems were achieved, with the applicability of the results justified through numerical cases.