101 research outputs found
Pinning Complex Networks by a Single Controller
In this paper, without assuming symmetry, irreducibility, or linearity of the
couplings, we prove that a single controller can pin a coupled complex network
to a homogenous solution. Sufficient conditions are presented to guarantee the
convergence of the pinning process locally and globally. An effective approach
to adapt the coupling strength is proposed. Several numerical simulations are
given to verify our theoretical analysis
Cluster synchronization in networks of coupled non-identical dynamical systems
In this paper, we study cluster synchronization in networks of coupled
non-identical dynamical systems. The vertices in the same cluster have the same
dynamics of uncoupled node system but the uncoupled node systems in different
clusters are different. We present conditions guaranteeing cluster
synchronization and investigate the relation between cluster synchronization
and the unweighted graph topology. We indicate that two condition play key
roles for cluster synchronization: the common inter-cluster coupling condition
and the intra-cluster communication. From the latter one, we interpret the two
well-known cluster synchronization schemes: self-organization and driving, by
whether the edges of communication paths lie at inter or intra-cluster. By this
way, we classify clusters according to whether the set of edges inter- or
intra-cluster edges are removable if wanting to keep the communication between
pairs of vertices in the same cluster. Also, we propose adaptive feedback
algorithms on the weights of the underlying graph, which can synchronize any
bi-directed networks satisfying the two conditions above. We also give several
numerical examples to illustrate the theoretical results
Event-triggered Consensus for Multi-agent Systems with Asymmetric and Reducible Topologies
This paper studies the consensus problem of multi-agent systems with
asymmetric and reducible topologies. Centralized event-triggered rules are
provided so as to reduce the frequency of system's updating. The diffusion
coupling feedbacks of each agent are based on the latest observations from its
in-neighbors and the system's next observation time is triggered by a criterion
based on all agents' information. The scenario of continuous monitoring is
first considered, namely all agents' instantaneous states can be observed. It
is proved that if the network topology has a spanning tree, then the
centralized event-triggered coupling strategy can realize consensus for the
multi-agent system. Then the results are extended to discontinuous monitoring,
where the system computes its next triggering time in advance without having to
observe all agents' states continuously. Examples with numerical simulation are
provided to show the effectiveness of the theoretical results
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