Networks

Group and Main topics

Dynamics, structural and combinatorial properties of networks of coupled dynamical systems with a view to applications in engineering and neuroscience. Asynchronous networks and event driven dynamics. Synaptic plasiticity (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 DMS-1265253

Selected recent 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.
• N Agarwal and M J Field, 'Dynamical equivalence of networks of coupled dynamical systems I: Asymmetric inputs', Nonlinearity 23 (2010), 1245-1268.
• N Agarwal and M J Field, 'Dynamical equivalence of networks of coupled dynamical systems II: general case', Nonlinearity, 23 (2010), 1269-1289.
• N Agarwal, 'Inflation of strongly connected networks', Camb Phil Soc, 150 (2011). 367-384.
• M J Field, 'Heteroclinic networks in homogeneous and heterogeneous identical cell systems', Journal of Nonlinear Science, 2015
• C Bick and M J Field, 'Functional Asynchronous Networks: Factorization of Dynamics and Function', MATEC Web of Conferences, 83 (2016).
• C Bick and M J Field, 'Asynchronous Networks and Event Driven Dynamics', Nolinearity 30(2) (2017), 558-594.
• C Bick and M J Field, 'Asynchronous Networks: Modularization of Dynamics Theorem', Nolinearity 30(2) (2017), 595-621.
• M J Field, 'Patterns of Desynchronization and Resychronization in Heteroclinic Networks', Nonlinearity 30(2) (2017), 516-557.

• M A D Aguiar, A P Dias, and M J Field, 'Feedforward Networks: Adaptation, Feedback, and Synchrony',J. Nonlinear Sci., November, 2018.

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