Projective exponential synchronization of uncertain Markov jumping discrete-time and -space fuzzy genetic regulatory networks

This study investigates global projective synchronization in discrete-time uncertain Markov jumping fuzzy genetic regulatory networks, providing deeper insight into the synchronization mechanisms of these complex systems. By constructing an advanced Lyapunov–Krasovskii functional featuring a double-summation structure to rigorously capture delay-dependent characteristics, the analysis establishes sufficient conditions for achieving global projective synchronization. The results further demonstrate that synchronization performance in spatiotemporal discrete Markov jumping fuzzy networks can be substantially improved through carefully designed diffusion intensities, smaller fuzzy MIN and MAX parameters, and elevated degradation rates of mRNA and protein. These findings not only enhance the theoretical understanding of synchronization in high-dimensional biological networks but also offer practical design guidelines for optimizing synchronization behavior in real-world applications. Overall, this work provides a comprehensive and impactful contribution to the study of genetic regulatory networks and synchronization theory.