Networks

Group and Main topics

Dynamics, structural and combinatorial properties of networks of coupled dynamical systems with a view to applications in engineering. Asynchronous networks and event driven dynamics. STDP, adaptive networks and visualization schemes for network dynamics.

• Random, Deterministic and Discrete (RDD) networks, Visualization; intermingled basins and cycling chaos.
• Adaptive Networks
• Adaption using STDP and frequency detection
• Asynchronous Networks
• Phase Oscillator Networks, Chimera States

Research supported by NSF Grants DMS-0600927, DMS-0806321 and (current) DMS-1265253

Recent preprints and publications

• M Aguiar, P Ashwin, A Dias, and M J Field, Dynamics of coupled cell systems: synchrony, heteroclinic cycles and inflation.Journal of Nonlinear Science, 21(2) (2011), 271-323. (preprint 2010, version of August, 2010).
• N Agarwal and M J Field, Dynamical equivalence of networks of coupled dynamical systems I: Asymmetric inputs, preprint 2009, Nonlinearity 23 (2010), 1245-1268.
• N Agarwal and M J Field, Dynamical equivalence of networks of coupled dynamical systems II: general case, preprint 2009, Nonlinearity, 23 (2010), 1269-1289.
• N Agarwal, Inflation of strongly connected networks, Camb Phil Soc, 150 (2011). 367-384.
• M J Field, Notes on Networks and Dynamics. In preparation.
• C Bick and M J Field, Asynchronous Networks and Event Driven Dynamics. preprint, 2015.
• M J Field, Heteroclinic networks in homogeneous and heterogeneous identical cell systems, JNLS, 2015

Resources

• General articles on Networks.
• Articles on STDP .
• Articles on adaptation using STDP .
• Learning and computation.
• Dynamics and synchronization in neuronal networks.
• Papers on asynchronous dynamics and networks.
• Papers on synchronization and chimera states.
• Brian-Simulator