Supplemental Material: Engineering chimera patterns in networks using heterogeneous delays.pdf (42.45 kB)
Supplemental Material: Engineering chimera patterns in networks using heterogeneous delays
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journal contribution
modified on 2018-07-31, 13:31 Supplemental Material for Symmetry
breaking spatial patterns, referred to as chimera states, have recently
been catapulted into the limelight due to their coexisting coherent and
incoherent hybrid dynamics. Here, we present a method to engineer a
chimera state by using an appropriate distribution of heterogeneous time
delays on the edges of a network. The time delays in interactions,
intrinsic to natural or artificial complex systems, are known to induce
various modifications in spatiotemporal behaviors of the coupled
dynamics on networks. Using a coupled chaotic map with the identical
coupling environment, we demonstrate that control over the spatial
location of the incoherent region of a chimera state in a network can be
achieved by appropriately introducing time delays. This method allows
for the engineering of tailor-made one cluster or multi-cluster chimera
patterns. Furthermore, borrowing a measure of eigenvector localization
from the spectral graph theory, we introduce a spatial inverse
participation ratio, which provides a robust way for the identification
of the chimera state. This report highlights the necessity to consider
the heterogeneous time delays to develop applications for the chimera
states in particular and understand coupled dynamical systems in
general.
The
study of time-delayed dynamics on a complex network is a field of high
interest for both its fundamental significance in the study of
non-linear systems and its applicability in understanding various
networks modeled after biological, chemical, and artificial or natural
systems, which intrinsically possess the information propagation delays
among their constituent entities. Both homogeneous and heterogeneous
propagation delays between the nodes can induce a significant change in
the dynamical properties of a complex system represented by networks.
Specifically, a massive amount of work has been done to investigate the
impact of delays on various types of synchronization. Among them,
partially synchronized chimera states received particular attention due
to the coexistence of coherent and incoherent dynamics. Since their
discovery, the hybrid spatial patterns of chimera states have become a
prime branch of complex systems research primarily due to fascinating
phenomena of symmetry breaking in identical systems along with many
other applications ranging from getting insight into the transition
between coherence to incoherence and neuroscience. Despite numerous
studies on chimeras, controlling chimera states has remained a tricky
problem due to the peculiar nature of chimera patterns. Here, we propose
a scheme to engineer the chimera patterns by suitable placement of
delayed edges in a network. Furthermore, inspired by the eigenvector
localization measures, we suggest a measure to identify chimera states.
