This study addresses the consensus problem of multi-agent systems (MAS) subject to external disturbance. Considering the presence of external disturbance factors, a theoretical analysis of consensus for distributed MAS is conducted. First, a state observer and an adaptive disturbance observer are designed to estimate both the node states and disturbance states of each agent in the system. Subsequently, a dynamic event-triggered control strategy is formulated based on the estimated values from the observers. Notably, the dynamic event-triggered strategy incorporates dynamically adjustable parameters, offering enhanced flexibility compared to conventional static event-triggered strategies. Using Lyapunov stability theory and inequality techniques, sufficient conditions for achieving consensus in disturbed MAS are derived. Finally, a numerical example is provided to demonstrate the effectiveness of the observers, control strategies, and theoretical results. This work provides new solutions for the consensus control of heterogeneous MAS with external disturbance, where both the obsever and the dynamic event-triggered controller are equipped with adjustable parameters, rendering the approach more practical for real-world applications.

It is shown that many neurological diseases are caused by the changes of firing patterns induced by bifurcations. Therefore, the bifurcation control may provide a potential therapeutic method of these neurodegenerative diseases. In this paper, we investigate the Hopf bifurcation control of the Morris-Lecar (ML) model with Homoclinic (Hc) bifurcation type by introducing a dynamic state-feedback control. The results indicate that the linear term can change the ML model from Hc bifurcation type to SNIC bifurcation type without changing the firing patterns. The cooperation of linear and cubic term can transform the ML model from the Hc bifurcation type to the Hopf bifurcation type, resulting in the transformation of firing patterns from type I to type II. Besides, we utilize the Poincare Birkhoff (PB) normal form method to derive the analytical expression of the bifurcation stability index for the controlled ML model with Hc bifurcation type, and the results show that the cubic term can regulate the criticality of the Hopf bifurcation. Numerical simulation results are consistent with the theoretical analysis.