Selected and Recent Papers

Dynamics of biological neurons

Map-based models of neuron spiking:

M. Bazhenov, N.F. Rulkov, J.M. Fellous, and I. Timofeev, Role of Network Dynamics in Shaping Spike Timing Reliability. Phys. Rev. E , 72 (2005) 041903

N.F. Rulkov, I. Timofeev, M. Bazhenov, Oscillations in Large-Scale Cortical Networks: Map-Based Model. Journal of Computational Neuroscience , 17 (2004) 203-223

A.L. Shilnikov and N.F. Rulkov, Subthreshold oscillations in a map-based neuron model. Physics Letters , A 328 (2004) 177-184

A.L. Shilnikov and N.F. Rulkov, Origin of chaos in a Two-Dimensional Map Modeling Spiking-Bursting Neural Activity. Int. J. Bifurcation and Chaos, 13 (2003) 3325-40

N.F. Rulkov, Modeling of Spiking-Bursting Neural Behavior Using Two-Dimensional Map. Phys. Rev. E, 65 (2002) 041922

N.F. Rulkov, Regularization of Synchronized Chaotic Bursts. Phys. Rev. Lett. v.86, (2001) 183-186

Synchronization of chaos in PD neurons:

R. C. Elson, A. I. Selverston, R. Huerta, N. F. Rulkov, M. I. Rabinovich, and H. D. I. Abarbanel. Synchronous Behavior of Two Coupled Biological neurons. Phys. Rev. Lett. v.81, (1998) 5692-95

H. D. I. Abarbanel, R. Huerta, M. I. Rabinovich, N. F. Rulkov, P. F. Rovat, and A. I. Selverston. Synchronized action of synaptically coupled chaotic model neurons. Neural Computation, 15 Nov. 1996, vol.8, (no.8):1567-602


N.F.Rulkov, L.S. Tsimring, M.L.Larsen, M.Gabbay Synchronization and beam forming in an array of repulsively coupled oscillators, Phys. Rev. E 74 (2006) 056205.

L.S. Tsimring, N.F.Rulkov, M.L.Larsen, M.Gabbay Repulsive synchronization in an array of phase oscillators, Phys. Rev. Lett. 95 (2005) 014101.

Synchronization of chaotic oscillators

Generalized synchronization:

N.F. Rulkov and V.S. Afraimovich Detectability of nondifferentiable generalized synchrony. Physical Review E , 67 (2003) 066218.

V. Afraimovich, A. Cordonet and N.F. Rulkov, Generalized synchronization of chaos in non-invertible maps. Physical Review E , 66 (2002) 016208.

N.F. Rulkov, V.S. Afraimovich, C.T. Lewis, J.-R. Chazottes, A. Cordonet Multi-valued mappings in generalized chaos synchronization. Physical Review E , 64 (2001) 016217.

N.F. Rulkov and C.T. Lewis Subharmonic destruction of generalized chaos synchronization. Phys. Rev. E. v.63, (2001) 065204(4)

Henry D. I. Abarbanel, Nikolai F. Rulkov and M. M. Sushchik. Generalized synchronization of chaos: The auxiliary system approach. Phys. Rev. E, 53 (1996) 4528.

N.F. Rulkov, M. M. Sushchik, L. S. Tsimring, and H.D.I.Abarbanel. Generalized synchronization of chaos in directionally coupled chaotic systems, Phys. Rev. E, v.51, pp. 980-994 (1995).

H.D.I. Abarbanel, N.F. Rulkov and M. M. Sushchik. Blending chaotic attractors using the synchronization of chaos. Phys. Rev. E, 52 (1995) 214.


N.F.Rulkov. Images of synchronized chaos:Experiments with circuits, CHAOS, v.6, n.3, 262-279 (1996)

Identical synchronization of chaos:

R.Brown and N.F.Rulkov. Synchronization of chaotic systems: Transverse stability of trajectories in invariant manifolds, CHAOS, v.7, n.3, 395-413 (1997)

R.Brown and N.F.Rulkov. Designing coupling that guarantees synchronization between identical chaotic systems. Phys. Rev. Lett. v.78, (1997) 4189-92

Applications of Chaos Synchronization

Chaos-based communication:

A.R.Volkovskii, L.S.Tsimring, N.F.Rulkov, and I. Langmore, Spread Spectrum Communication System with Chaotic Frequency Modulation, CHAOS , 15 , (2005) 033101.

N.F. Rulkov, M.A. Vorontsov and L. Illing Chaotic Free-Space Laser Communication over Turbulent Channel. Phys. Rev. Lett. 89 , (2002) 277905

N.F. Rulkov, M.M. Sushchik, L.S. Tsimring, and A.R. Volkovskii Digital Communication Using Chaotic-Pulse-Position Modulation. IEEE Trans. Circuits Syst.- Part I 48 (2001) 1436.

G.M. Maggio, N. Rulkov, L.Reggiani Pseudo-Chaotic Time Hopping For UWD Impulse Radio. IEEE Trans. Circuits Syst.- Part I 48 (2001) 1424.

N.F.Rulkov and L.S.Tsimring. Synchronization Methods for Communication with Chaos over Band-Limited Channels. International Journal of Circuit Theory and Application. v.27, (1999) 555

N.F.Rulkov and L.S.Tsimring. Communication with Chaos over Band-Limited Channels. (Electronic NonLinear Science Preprint, chao-dyn/9705019)


N.F.Rulkov, L.S.Tsimring, H.D.I.Abarbanel. Tracking unstable orbits in chaos using dissipative feedback control, Phys. Rev. E, v.50, n.1, 314-324 (1994).

Data-based modeling:

R.Brown, N.F.Rulkov and E.R. Tracy. Modeling and synchronizing chaotic systems from time-series data. Phys. Rev. E. v.49, (1994) 3784.


N.F. Rulkov and A.R. Volkovskii Generation of Broad-Band Chaos Using Blocking Oscillator. IEEE Trans. Circuits Syst. 48 (2001) 673.

M.M. Sushchik and N.F. Rulkov, Hidden Chaos. (Electronic NonLinear Science Preprint, nlin.CD/0106008)

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