New Results on Global Exponential Stability of Genetic Regulatory Networks with Diffusion Effect and Time-Varying Hybrid Delays

Taking into account the spatial diffusion effect, this paper deals with the stability problem of genetic regulatory networks with both time-varying discrete delays (DDs) and distributed delays (DTDs). By virtue of the theories of delayed partial differential equation and Lyapunov stability, new algebraic conditions are established to guarantee the global exponential stability of the genetic regulatory networks with spatial diffusion (SDGRNs) with time-varying hybrid delays. The obtained conditions are generalized and easily calculated based on the system parameters. Besides, some extended results are presented for SDGRNs without diffusion effect or DTDs. Finally, the effectiveness and feasibility of the theoretical results are illustrated by two numerical examples and the corresponding simulation results.