This paper addresses the problem of ensuring finite-time synchronization for fractional-order heterogeneous dynamical networks via aperiodic intermittent control, where uncertain impulsive disturbances are introduced at the instants triggered by the control actions applied to the system. Under aperiodic time-triggered and event-triggered intermittent control, a Lyapunov function iteration method, based on the traditional Lyapunov method, was developed to analyze the criteria for finite-time synchronization. Several sufficient conditions were proposed to ensure finite-time synchronization. First, within the framework of finite-time and time-triggered control, the relationship between the control period width, impulsive disturbances, and configuration control parameters was established to guarantee finite-time synchronization. Second, an event-triggered mechanism was introduced into the intermittent control, where the sequence of impulsive disturbance instants was determined by a pre-designed trigger threshold. The relationship between impulsive disturbances, the event-triggered threshold, and the control period width was established. These two relationships can potentially increase the flexibility of the designed control periods and control width. Moreover, the Zeno phenomenon can be eliminated in the event-triggered mechanism. Finally, two simulations were presented to illustrate the feasibility and effectiveness of the theoretical results.

This paper discusses the robustness of neutral fuzzy cellular neural networks with stochastic disturbances and time delays. This work questions whether fuzzy cellular neural networks, which initially remains stable, can be stabilised again when the system is subjected to three simultasneous perturbations i.e., neutral items, random disturbances, and time delays. First, by using inequality techniques such as Gronwall's Lemma, the Itŏ formula, and the property of integrals, the transcendental equations that contain the contraction coefficient of the neutral terms, the intensity of the random disturbances, and the time delays are derived. Then, the upper bounds of the neutral terms, random disturbances, and time delays are estimated by solving the transcendental equations for multifactor perturbations, which ensures that the disturbed fuzzy cellular neural network can be stabilised again. Finally, the validity of the results is verified by numerical examples.

In this paper, the fixed/predefined-time generalized synchronization problem of stochastic complex dynamical networks with delays is studied for the first time. First, based on the feedback controller without linear terms, the results show that the controlled system has strong stability. Second, stochastic analysis methods, inequality techniques, and an extension of the existing fixed/predefined-time stability lemma ( $\eta$ range extension) are used to make the results of this paper more general. The sufficient conditions for generalized synchronization are established, and the settling time independent of the initial values are given. To illustrate the theoretical results, a numerical example is given.