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- Nikolai F Rulkov
- Physical review. E, Statistical, nonlinear, and…
- 2002

A simple model that replicates the dynamics of spiking and spiking-bursting activity of real biological neurons is proposed. The model is a two-dimensional map that contains one fast and one slow variable. The mechanisms behind generation of spikes, bursts of spikes, and restructuring of the map behavior are explained using phase portrait analysis. The… (More)

- N F Rulkov
- Physical review letters
- 2001

The onset of regular bursts in a group of irregularly bursting neurons with different individual properties is one of the most interesting dynamical properties found in neurobiological systems. In this paper we show how synchronization among chaotically bursting cells can lead to the onset of regular bursting. In order to clearly present the mechanism… (More)

Henry D. I. Abarbanel, 1,2 Nikolai F. Rulkov, 2 and Mikhail M. Sushchik 3 Department of Physics and Marine Physical Laboratory, Scripps Institution of Oceanography, University of California, San Diego, La Jolla, California 92093-0402 Institute for Nonlinear Science, University of California, San Diego, La Jolla, California 92093-0402 Department of Physics… (More)

- H D Abarbanel, R Huerta, M I Rabinovich, N F Rulkov, P F Rowat, A I Selverston
- Neural computation
- 1996

Experimental observations of the intracellular recorded electrical activity in individual neurons show that the temporal behavior is often chaotic. We discuss both our own observations on a cell from the stomatogastric central pattern generator of lobster and earlier observations in other cells. In this paper we work with models with chaotic neurons,… (More)

Robert C. Elson,1,2 Allen I. Selverston,1,2,3 Ramon Huerta,2,4 Nikolai F. Rulkov,2 Mikhail I. Rabinovich,2 and Henry D. I. Abarbanel2,5 1Department of Biology, University of California, San Diego, La Jolla, California 92093-0357 2Institute for Nonlinear Science, University of California, San Diego, La Jolla, California 92093-0402 3Instituto de… (More)

Synchronization of oscillations underlies organized dynamical behavior of many physical, biological and other systems. Recent studies of the dynamics of coupled systems with complex behavior indicate that synchronization can occur not only in case of periodic oscillations, but also in regimes of chaotic oscillations. Using experimental observations of… (More)

Self-sustained subthreshold oscillations in a discrete-time model of neuronal behavior are considered. We discuss bifurcation scenarios explaining the birth of these oscillations and their transformation into tonic spikes. Specific features of these transitions caused by the discrete-time dynamics of the model and the influence of external noise are… (More)

- Andrey Shilnikov, Nikolai F. Rulkov
- I. J. Bifurcation and Chaos
- 2003

Origin of chaos in a simple two-dimensional map model replicating the spiking and spikingbursting activity of real biological neurons is studied. The map contains one fast and one slow variable. Individual dynamics of a fast subsystem of the map is characterized by two types of possible attractors: stable fixed point (replicating silence) and superstable… (More)

Utilization of chaotic signals for covert communications remains a very promising practical application. Multiple studies indicate that the major shortcoming of recently proposed chaos-based communication schemes is their susceptibility to noise and distortions in communication channels. In this paper, we review a new approach to communication with chaotic… (More)

- V Afraimovich, A Cordonet, N F Rulkov
- Physical review. E, Statistical, nonlinear, and…
- 2002

The properties of functional relation between a noninvertible chaotic drive and a response map in the regime of generalized synchronization of chaos are studied. It is shown that despite a very fuzzy image of the relation between the current states of the maps, the functional relation becomes apparent when a sufficient interval of driving trajectory is… (More)