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In this paper, group consensus of second-order multi-agent systems with nonlinear dynamics is investigated. First, we design the distributed protocols for achieving group consensus, in which the strengths of the interactions among the agents are enhanced through tuning the coupling strengths. Further, taking the difference of the edges among agents into account, edge-based distributed protocols through tuning coupling weights of a fraction of edges are designed. Remarkably, only the edges of spanning tree in each group are pinned and the coupling strengths or weights of pinned edges are enhanced according to the updated laws. Both the types of distributed protocols are proved analytically and verified by numerical illustrations.

Cluster synchronization is an important dynamical behavior in community networks and deserves further investigations. A community network with distributed time delays is investigated in this paper. For achieving cluster synchronization, an impulsive control scheme is introduced to design proper controllers and an adaptive strategy is adopted to make the impulsive controllers unified for different networks. Through taking advantage of the linear matrix inequality technique and constructing Lyapunov functions, some synchronization criteria with respect to the impulsive gains, instants, and system parameters without adaptive strategy are obtained and generalized to the adaptive case. Finally, numerical examples are presented to demonstrate the effectiveness of the theoretical results.

Mathematical epidemiology that describes the complex dynamics on social networks has become increasingly popular. However, a few methods have tackled the problem of coupling network topology with complex incidence mechanisms. Here, we propose a simplicial susceptible-infected-recovered-susceptible (SIRS) model to investigate the epidemic spreading via combining the network higher-order structure with a nonlinear incidence rate. A network-based social system is reshaped to a simplicial complex, in which the spreading or infection occurs with nonlinear reinforcement characterized by the simplex dimensions. Compared with the previous simplicial susceptible-infected-susceptible (SIS) models, the proposed SIRS model can not only capture the discontinuous transition and the bistability of a complex system but also capture the periodic phenomenon of epidemic outbreaks. More significantly, the two thresholds associated with the bistable region and the critical value of the reinforcement factor are derived. We further analyze the stability of equilibrium points of the proposed model and obtain the condition of existence of the bistable states and limit cycles. This work expands the simplicial SIS models to SIRS models and sheds light on a novel perspective of combining the higher-order structure of complex systems with nonlinear incidence rates.

Background Oxytocin (OT) plays an important role in regulating gastric function. How OT regulates stress‐induced gastric ulcers is not understood. We investigated OT's protective role in stress‐induced gastric ulcers, with a focus on OT's interaction with the ventral tegmental area (VTA) to nucleus accumbens (NAc) dopamine pathway. Methods Drugs administration into the rats brain nuclei by brain stereotaxic apparatus, to examine related changes in gastric ulcer index, pH of gastric content, and mucus secretion, and to determine complex interactions between OT and DA systems in the regulation of stress and gastric functions. Key Results Neurons in the VTA were co‐immunoreactive for the OT receptor (OTR) and DA. In a rat model of stress‐induced ulcer, water‐immersion restricted stress, direct administration of OT into the VTA significantly reduced gastric ulcer index and increased the pH of gastric content and mucus secretion. OT's effects were eliminated by pretreatment with the OTR antagonist atosiban in the VTA and weakened with pretreatment of the DA D2 receptor (DA D2R) antagonist raclopride in the NAc. In OTR gene knockout (Oxtr−/−) mice, OT's protective effect was lost. OT administered to the VTA of dorsal motor nucleus of the vagus (DMV)‐lesioned rats had minimal protective effects on gastric mucosa. Conclusions and Inferences This study provides important data necessary for a deeper understanding of the complex interactions between OT and DA systems in the regulation of stress and gastric functions. It provides relevant mechanistic clues into OT's role as a protective factor against stress‐induced changes to gastric function.

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