In this paper, a new synchronization problem for the collective dynamics among genetic oscillators with unbounded time-varying delay is investigated. The dynamical system under consideration consists of an array of linearly coupled identical genetic oscillators with each oscillators having unbounded time-delays. A new concept called power-rate synchronization, which is different from both the asymptotical synchronization and the exponential synchronization, is put forward to facilitate handling the unbounded time-varying delays. By using a combination of the Lyapunov functional method, matrix inequality techniques and properties of Kronecker product, we derive several sufficient conditions that ensure the coupled genetic oscillators to be power-rate synchronized. The criteria obtained in this paper are in the form of matrix inequalities. Illustrative example is presented to show the effectiveness of the obtained results.

This paper is concerned with output consensus of heterogeneous multi-agent systems under sparse attacks. The leader agent is only available to a small fraction nodes. To estimate the leader's signal, a distributed observer is proposed, which is of the integral type and possesses good robustness and high convergence rate. Unlike the existing literature on distributed observer, this paper introduces a novel event-triggered strategy that utilizes the agents' measurement error state instead of the norm of the state errors. It is theoretically and numerically demonstrated that the triggering times and communication loads between agents can be significantly reduced by using this strategy, and a positive lower bound on the triggering time interval is also computed. Furthermore, an adaptive scheme with pinning strategy is considered to ensure the output consensus with uniformly ultimately bounded in the presence of false data attacks. Finally, a numerical example is given to illustrate the effectiveness of the results.

In this paper, by using a pinning impulse controller and a hybrid controller respectively, the research difficulties of asymptotic synchronization and finite time cluster synchronization of time-varying delayed neural networks are studied. On the ground of Lyapunov stability theorem and Lyapunov-Razumikhin method, a novel sufficient criterion on asymptotic cluster synchronization of time-varying delayed neural networks is obtained. Utilizing Finite time stability theorem and hybrid control technology, a sufficient criterion on finite-time cluster synchronization is also obtained. In order to deal with time-varying delay and save control cost, pinning pulse control is introduced to promote the realization of asymptotic cluster synchronization. Following the idea of pinning control scheme, we design a progressive hybrid control to promote the realization of finite time cluster synchronization. Finally, an example is given to illustrate the theoretical results.

Weibo's wide reach and openness make it a platform for both influence and the spread of rumors, causing negative social impacts. Therefore, studying the dissemination of rumors on Weibo holds important practical significance. This research takes the recent "Starch Sausage Incident" as a case study, expanding the traditional SIR model by incorporating a rational population, resulting in the SIRW model. Utilizing web scraping techniques to collect Weibo data, the study conducted data preprocessing and performed sentiment analysis using a GRU model. By combining sentiment results with user profile information, the research analyzed the cumulative numbers in various compartments over different time periods. Parameters were fitted using the least squares method, and the results indicate that the model performs well. Considering the characteristics of Weibo, the study employed a BA scale-free complex network for visual simulation and analyzed the impact of the degree and number of initial infected nodes on rumor propagation. Through robustness analysis, the research explored effective strategies for interrupting rumor transmission from the perspectives of large nodes and bridge nodes, proposing targeted public opinion control recommendations. The study demonstrates that a higher initial proportion of rational individuals significantly restricts rumor spread; conversely, a moderate number of rumors may enhance individuals' rationality and discernment. During different stages of rumor propagation, targeting hub nodes or bridge nodes can markedly improve the effectiveness of disruption.