-- Dynamics of bursting behaviors in neuronal models and networks--

In collaboration with Gennady Cymbalyuk (Physics), Ronald Calabrese (Biology,Emory), and Igor Belykh (Math)

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Java applet showing bi-stability where tonic-sping co-exist with bursting in the leech neuron model.

Transition from tonic-spiking to burtsing through the blue sky catastrophe K2shift=-0.0244

Bi-stability: co-exising tonic spiking modes: periodic and chaotic via period doubling cascade

The goal of the project is to understand how single neuron dynamics contributes to network oscillations and spatio-temporal pattern formation. We envisage a neuron as a dynamic system and approach this goal through the analysis of its oscillatory and stationary behaviors. We suggest a few novel scenarios for routes to bursting that are detected in mathematical models of neurons and in experiments with living neurons of the medicinal leech. These scenarios are generic and can be detected in experiments with other neurons.

Grad Students
Paul Channell (MS), Tatyana Malashenko(PhD), Matt Brooks (MS), Konstantin Mokhov (PhD), Oleksiy Pochapinskyy (PhD)
Undergrads
James Bates, Jeremy Wojick (Physics).

Publications
° Shilnikov, A.L. and Turaev D., Blue Sky Catastrophe, Scholarpedia, 2006
° Channell P., Cymbalyuk, G. and Shilnikov, A. L., Origin of bursting through homoclinic spike adding in a neuron model, Phy Rev Letters, in review [pdf]
° Channell P., Cymbalyuk, G. and Shilnikov, A. L., Applications of the Poincare mapping technique to analysis of neuronal dynamics, Neurocomputing, 2006, doi:10.1016/j.neucom.2006.10.091 [pdf]
° Shilnikov, A. L. and Cymbaluyk, G. Transition between tonic-spiking and bursting in a neuron model via the blue-sky catastrophe, Phys Review Letters, 94, 048101 (2005). [pdf] [gzipped ps]
° Cymbaluyk, G. and Shilnikov, A. L. Co-existent tonic spiking modes in a leech neuron model, J. Computational Neuroscince 18 (3), 255-263, 2005 [pdf] [zip ps]
° Shilnikov, A. L., Calabrese R. and Cymbalyuk, G., How a neuron model can demonstrate coexistence of tonic spiking and bursting? Neurocomputing 65-66, 869-875, 2005 [pdf]
° Shilnikov, A. L., Calabrese R. and Cymbalyuk, G. Mechanism of bi-stability: tonic spiking and bursting in a neuron model, Phys Review E 71(5), 056214-046221, 2005, [pdf]
° Shilnikov, A. L. and Cymbaluyk, G. Homoclinic saddle-node orbit bifurcations en a route between tonic spiking and bursting in neuron models, Invited review, Regular & Chaotic Dynamics 9( 3), 281-297, 2004.
° Cymbalyuk G., Calabrese R. and Shilnikov A., Yin and Yang of leech heart central pattern generator: endogenously bursting neurons yoked together into a half-center oscillator. Proc. of the Annual Computational Neuroscince Meeting (CNS-2003) Alecante, Spain, July 5-9, 2003
° Shilnikov, A. L. Cymbalyuk G. and Calabrese R., Multistability and infinite cycles in a model fof the leech heart interneuron, Proc NDES 2003, Scuol, Switzerland [pdf]

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