Synchronization of pulse-coupled biological oscillators
SIAM Journal on Applied Mathematics
Stable periodic solutions to discrete and continuum arrays of weakly coupled nonlinear oscillators
SIAM Journal on Applied Mathematics
Stable rotating waves in two-dimensional discrete active media
SIAM Journal on Applied Mathematics
The existence of spiral waves in an oscillatory reaction-diffusion system
SIAM Journal on Applied Mathematics
Synchrony in excitatory neural networks
Neural Computation
Weakly connected neural networks
Weakly connected neural networks
Mathematical Models in Biology
Mathematical Models in Biology
Dynamics of Strongly Coupled Spiking Neurons
Neural Computation
Type i membranes, phase resetting curves, and synchrony
Neural Computation
Low-Dimensional Maps Encoding Dynamics in Entorhinal Cortex and Hippocampus
Neural Computation
A traveling wave-based self-organizing communication mechanism for WSNs
Proceedings of the 5th international conference on Embedded networked sensor systems
Zero-lag long range synchronization of neurons is enhanced by dynamical relaying
ICANN'07 Proceedings of the 17th international conference on Artificial neural networks
Synchrony and asynchrony in neural networks
SODA '10 Proceedings of the twenty-first annual ACM-SIAM symposium on Discrete Algorithms
Synaptic and intrinsic determinants of the phase resetting curve for weak coupling
Journal of Computational Neuroscience
Stability of two cluster solutions in pulse coupled networks of neural oscillators
Journal of Computational Neuroscience
Future Generation Computer Systems
Functional identification of spike-processing neural circuits
Neural Computation
Review: Pulse coupled neural networks and its applications
Expert Systems with Applications: An International Journal
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We study non-trivial firing patterns in small assemblies of pulse-coupled oscillatory maps. We find conditions for the existence of waves in rings of coupled maps that are coupled bi-directionally. We also find conditions for stable synchrony in general all-to-all coupled oscillators. Surprisingly, we find that for maps that are derived from physiological data, the stability of synchrony depends on the number of oscillators. We describe rotating waves in two-dimensional lattices of maps and reduce their existence to a reduced system of algebraic equations which are solved numerically.