TY - JOUR
T1 - Understanding the enhanced synchronization of delay-coupled networks with fluctuating topology
AU - D'Huys, Otti
AU - Rodríguez-Laguna, Javier
AU - Jiménez, Manuel
AU - Korutcheva, Elka
AU - Kinzel, Wolfgang
PY - 2018/12/1
Y1 - 2018/12/1
N2 - We study the dynamics of networks with coupling delay, from which the
connectivity changes over time. The synchronization properties are shown
to depend on the interplay of three time scales: the internal time scale
of the dynamics, the coupling delay along the network links and time
scale at which the topology changes. Concentrating on a linearized
model, we develop an analytical theory for the stability of a
synchronized solution. In two limit cases, the system can be reduced to
an "effective" topology: in the fast switching approximation, when the
network fluctuations are much faster than the internal time scale and
the coupling delay, the effective network topology is the arithmetic
mean over the different topologies. In the slow network limit, when the
network fluctuation time scale is equal to the coupling delay, the
effective adjacency matrix is the geometric mean over the adjacency
matrices of the different topologies. In the intermediate regime, the
system shows a sensitive dependence on the ratio of time scales, and on
the specific topologies, reproduced as well by numerical simulations.
Our results are shown to describe the synchronization properties of
fluctuating networks of delay-coupled chaotic maps.
AB - We study the dynamics of networks with coupling delay, from which the
connectivity changes over time. The synchronization properties are shown
to depend on the interplay of three time scales: the internal time scale
of the dynamics, the coupling delay along the network links and time
scale at which the topology changes. Concentrating on a linearized
model, we develop an analytical theory for the stability of a
synchronized solution. In two limit cases, the system can be reduced to
an "effective" topology: in the fast switching approximation, when the
network fluctuations are much faster than the internal time scale and
the coupling delay, the effective network topology is the arithmetic
mean over the different topologies. In the slow network limit, when the
network fluctuation time scale is equal to the coupling delay, the
effective adjacency matrix is the geometric mean over the adjacency
matrices of the different topologies. In the intermediate regime, the
system shows a sensitive dependence on the ratio of time scales, and on
the specific topologies, reproduced as well by numerical simulations.
Our results are shown to describe the synchronization properties of
fluctuating networks of delay-coupled chaotic maps.
U2 - 10.1140/epjst/e2018-800086-6
DO - 10.1140/epjst/e2018-800086-6
M3 - Article
SN - 1951-6401
VL - 227
SP - 1129
EP - 1150
JO - The European Physical Journal Special Topics
JF - The European Physical Journal Special Topics
IS - 10
ER -