Emergent collective behaviors on coopetition networks

• Coopetition networks are modeled by directed signed graphs with structural balance.
• The collective dynamics are modeled by multiagent system with local interaction rule.
• Sufficient conditions were given for different convergence of the multiagent system.

Cooperation and competition are two typical interactional relationships for intra-networks and inter-networks. This paper investigates the modeling of coopetition networks and the collective dynamics on such networks. The coopetition networks are firstly modeled by directed signed graphs. The evolutionary relationships among individuals on the coopetition networks are described by a neighbor-based dynamics model, which is also called multi-agent system (MAS). Then, under a weak connectivity assumption that the signed network has a spanning tree, some sufficient conditions are derived for the consensus, polarization or fragmentation behaviors of the MAS with the help of the structural balance theory. At the same time, signless Laplacian matrix and signed Laplacian matrix are introduced to analyze the collective dynamics of the MAS on coopetition networks. Finally, simulation results are provided to demonstrate the emergence of diverse collective behaviors on coopetition networks.