Finite-time boundary synchronization of space-time discretized stochastic fuzzy genetic regulatory networks with time delays

This paper presents an investigation into the phenomenon of global mean-squared finite-time synchronization within the context of two distinct schemes: The asymptotic and exponential forms. The subject matter encompasses space-time discrete stochastic fuzzy genetic regulatory networks, wherein Dirichlet controlled boundary values and time delays are taken into account. The findings presented therein pertain to global mean-squared finite-time synchronization for the aforementioned discrete stochastic fuzzy networks, which incorporate the Lyapunov-Krasovskii functional with a double sum representing the delay-dependent components. In addition, this study demonstrates that improved global mean-squared finite-time synchronization of space-time discrete stochastic fuzzy genetic regulatory networks with boundary controls can be achieved by optimizing the small diffusion intensities, the small fuzzy MIN and MAX parameters, and the large degradation rates of mRNA and proteins. It was unexpected to discover that the sizes of the time lags exert a direct influence on the value of the convergent rate of global mean-squared finite-time exponential synchronization of the networks. This paper presents a framework for exploring the issues of global mean-squared finite-time asymptotic and exponential synchronization for space-time discrete stochastic fuzzy genetic regulatory networks via the Dirichlet controlled boundaries. To conclude, an illustrative example is provided to demonstrate the efficacy of the aforementioned method.