This manuscript investigated the stability of Hopfield neural networks with time-varying transmission delays and leakage delays, and specially discussed the impact of the time-varying delays' dynamic characteristics on network stability. First, to characterize the dynamic features of time-varying delays transitioning continuously between short and large delays, two key parameters were introduced: a critical threshold for distinguishing whether the time-varying delays are short or large delays, and the ratio of the measure of the union of time periods, in which the time-varying delays appear as short delays, to the measure of the whole time interval. Then, by utilizing the Lyapunov stability method, some sufficient conditions for the global exponential stability of the neural networks were derived. It is pointed out that when the measure of time periods in which the time-varying delays appear as short delays is large enough, the above two parameters related to the time-varying delays' dynamic characteristics will have an important impact on the system stability, and the upper bound that the time-varying delays can achieve in the whole time interval will no longer be the dominant factor influencing stability. Additionally, the relationship between the leakage delays and the stabilization ability of the negative feedback terms was explored. Two admissible upper bounds were presented, below which the leakage delays do not completely undermine the capacity of negative feedback terms to stabilize the neural networks. Finally, some simulation experiments were conducted to validate our theoretical findings.

Avian influenza is an infectious viral disease caused by type A virus, which occurs frequently around the world and causes serious economic losses. Therefore, the adaptive control problem is explored in this paper for an avian influenza model in consideration of slaughtering to poultry, educational campaigns to the susceptible human and treatment to the infected human. First, by analyzing the transmission mechanism of avian influenza, a nonlinear adaptive control problem of avian influenza model is formulated, where some errors between model parameters and real values are allowed. Then, the parameters are estimated by constructing adaptive laws, which can be effectively used to design the applicative controllers to achieve the control goals. Besides, the stability of controlled model is analyzed with the aid of Lyapunov stability theory. Finally, numerical examples are proposed to verify the effectiveness and robustness of the designed controllers.

Based on a neural field network model with impulsive and random disturbances, a preview control method that makes full use of known future information is proposed to reduce the static error of the target signal and the transient oscillatory behavior of the controlled system when it receives random disturbance inputs. The preview controller for epileptic seizures is constructed, and the feasibility and effectiveness of clinical single-target and multi-target stimulation in epilepsy regulation are explored from a computational perspective. In addition, a performance index function is proposed to evaluate the energy consumption of controller with and without preview under different input (target) strategies. Suggestions for different strategies are given in terms of the individualized disease environment of patients. From the perspective of seizure control effectiveness and performance consumption, the results show that the preview controller has a greater advantage. The theory of preview control is applied to the control of epileptic seizures for the first time, and the conclusions of the multifaceted study provide some references for clinical trials and controller applications.