Pinning Adaptive Passivity and Bipartite Synchronization of Leaderless Fractional Spatiotemporal Networks

In this article, by developing a direct error approach, the pinning passivity of leaderless fractional spatiotemporal networks and the leaderless bipartite synchronization of fractional spatiotemporal networks over a signed topological graph are investigated respectively. Above all, a fractional-order edge-based adaptive pinning strategy is designed based on the spanning tree to achieve the passivity of leaderless systems with Dirichlet boundary condition. Next, the fractional spatiotemporal networks with signed graph are discussed and some conditions are obtained to realize leaderless bipartite synchronization based on the derived passivity results and gauge transformation. Note that, the passivity and synchronization of networks are directly investigated without defining any reference state. The developed criteria are eventually verified by several illustrative examples.