627 research outputs found
Excitation Waves on a Minimal Small-World Model
We examine traveling-wave solutions on a regular ring network with one
additional long-range link that spans a distance d. The nodes obey the
FitzHugh-Nagumo kinetics in the excitable regime. The additional shortcut
induces a plethora of spatio-temporal behavior that is not present without it.
We describe the underlying mechanisms for different types of patterns:
propagation failure, period decreasing, bistability, shortcut blocking and
period multiplication. For this purpose, we investigate the dependence on d,
the network size, the coupling range in the original ring and the global
coupling strength and present a phase diagram summarizing the different
scenarios. Furthermore, we discuss the scaling behavior of the critical
distance by analytical means and address the connection to spatially continuous
excitable media.Comment: 14 pages, 11 figure
Clustered Chimera States in Systems of Type-I Excitability
Chimera is a fascinating phenomenon of coexisting synchronized and
desynchronized behaviour that was discovered in networks of nonlocally coupled
identical phase oscillators over ten years ago. Since then, chimeras were found
in numerous theoretical and experimental studies and more recently in models of
neuronal dynamics as well. In this work, we consider a generic model for a
saddle-node bifurcation on a limit cycle representative for neural excitability
type I. We obtain chimera states with multiple coherent regions (clustered
chimeras/multi-chimeras) depending on the distance from the excitability
threshold, the range of nonlocal coupling as well as the coupling strength. A
detailed stability diagram for these chimera states as well as other
interesting coexisting patterns like traveling waves are presented
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