Codimension two and three bifurcations of a predator–prey system with group defense and prey refuge

A predator–prey system with nonmonotonic functional response and prey refuge is considered. We mainly obtain that the system has the bifurcations of cusp-type codimension two and three, these illustrate that the dynamic behaviors of the model with prey refuge will become more complicated than the system with no refuge

Cluster Consensus on Discrete-Time Multi-Agent Networks

Nowadays, multi-agent networks are ubiquitous in the real world. Over the last decade, consensus has received an increasing attention from various disciplines. This paper investigates cluster consensus for discrete-time multi-agent networks. By utilizing a special coupling matrix and the Kronecker product, a criterion based on linear matrix inequality (LMI) is obtained. It is shown that the addressed discrete-time multi-agent networks achieve cluster consensus if a certain LMI is feasible. Finally, an example is given to demonstrate the effectiveness of the proposed criterion

Consensus of Multiagent Networks with Intermittent Interaction and Directed Topology

Intermittent interaction control is introduced to solve the consensus problem for second-order multiagent networks due to the limited sensing abilities and environmental changes periodically. And, we get some sufficient conditions for the agents to reach consensus with linear protocol from the theoretical findings by using the Lyapunov control approach. Finally, the validity of the theoretical results is validated through the numerical example

Bogdanov–Takens and triple zero bifurcations in general differential systems with m delays

This paper mainly concerns the derivation of the normal forms of the Bogdanov–Takens (BT) and triple zero bifurcations for differential systems with m discrete delays. The feasible algorithms to determine the existence of the corresponding bifurcations of the system at the origin are given. By using center manifold reduction and normal form theory, the coefficient formulas of normal forms are derived and some examples are presented to illustrate our main results