109,772 research outputs found
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
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
Topological semimetals with Riemann surface states
Riemann surfaces are geometric constructions in complex analysis that may
represent multi-valued holomorphic functions using multiple sheets of the
complex plane. We show that the energy dispersion of surface states in
topological semimetals can be represented by Riemann surfaces generated by
holomorphic functions in the two-dimensional momentum space, whose constant
height contours correspond to Fermi arcs. This correspondence is demonstrated
in the recently discovered Weyl semimetals and leads us to predict new types of
topological semimetals, whose surface states are represented by double- and
quad-helicoid Riemann surfaces. The intersection of multiple helicoids, or the
branch cut of the generating function, appears on high-symmetry lines in the
surface Brillouin zone, where surface states are guaranteed to be doubly
degenerate by a glide reflection symmetry. We predict the heterostructure
superlattice [(SrIrO)(CaIrO)] to be a topological semimetal
with double-helicoid Riemann surface states.Comment: Four pages, four figures and two pages of appendice
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