Finite-time synchronization of neuronal networks based on double-power sliding mode control
Finite-time synchronization control of discrete neuronal networks with piecewise nonlinear characteristics is a critical and challenging issue in complex network dynamic research. This paper investigates the finite-time synchronization problem of discrete neuronal networks constructed by the Rulkov map, and proposes a novel double-power finite-time sliding mode control (SMC) strategy. Different from single-power SMC schemes with inherent performance trade-offs, the designed control law integrates super-power and sub-power terms organically. The super-power term accelerates the convergence of sliding variables when system errors are large, while the sub-power term guarantees precise finite-time convergence of system states near the equilibrium point, effectively solving the contradiction between transient response speed and steady-state synchronization accuracy in traditional SMC. A terminal sliding surface matching the discrete network dynamic characteristics is established for each neuron node, and the control law is derived based on system error dynamics with a coupling compensation term added to adapt to the dynamic adjustment of large-scale network coupling relationships. Based on Lyapunov stability theory and discrete finite-time stability theorems, the finite-time convergence of both the reaching phase and sliding phase of the control system is strictly proved, and the explicit upper bound of network synchronization time is deduced, which quantitatively reveals the correlation between synchronization efficiency and system initial states as well as control parameters. Numerical simulations on an 80-node randomly connected network demonstrate the effectiveness of the proposed scheme in achieving rapid error convergence and accurate synchronization, and a systematic parameter study reveals the dominant influence of the low-power gain and the high-power exponent on the synchronization time.