Input-to-state stability of stochastic Markovian jump genetic regulatory networks

The development of gene circuits in logic modules that start enormous output distributions with low signal-to-noise ratios is a difficult problem in engineering. As a result, the gene model depicts the transcription and translation of a single gene produced in the modification of noise in isolated logic modules. Our goal is to construct such networks with all types of connectivity. Further, the impacts of noise on further complex genetic networks have been investigated using stochastic gene models. Using this information as a foundation, our research investigates the input-to-state stability investigation for stochastic Markovian jump genetic regulatory networks with time-varying delay components. The goal of this article is to develop genetic networks with temporal delays, which are crucial for genetic regulation because slow biochemical processes like gene transcription and translation need time to occur. Additionally, the Markovian chain is essential for demonstrating how a system shifts from one mode to another with known transition probabilities. In the stochastic case, some complex systems with random disturbance will occur. Due to this significance the genetic regulatory network with stochastic case is applied to identify the complex behaviour among genes and proteins of the micro perspective. By establishing the Lyapunov functional with Ito's and Dynkin's formula, new stability conditions are derived and which is effectively solved by MATLAB toolbox. The efficiency of the suggested technique is demonstrated using a numerical example. (c) 2023 International Association for Mathematics and Computers in Simulation (IMACS). Published by Elsevier B.V. All rights reserved.