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1

[World Scientific Series on Nonlinear Science Series A] Methods of Qualitative Theory in Nonlinear Dynamics - Part I Volume 4 || CENTER MANIFOLD.: NON-LOCAL CASE

Shilnikov, Leonid P., Shilnikov, Andrey L., Turaev, Dmitry V., Chua, Leon O.

Year:

1998

Language:

english

File:

PDF, 1.34 MB

english, 1998

2

[World Scientific Series on Nonlinear Science Series A] Methods of Qualitative Theory in Nonlinear Dynamics - Part I Volume 4 || STRUCTURALLY STABLE EQUILIBRIUM STATES OF DYNAMICAL SYSTEMS

Shilnikov, Leonid P., Shilnikov, Andrey L., Turaev, Dmitry V., Chua, Leon O.

Year:

1998

Language:

english

File:

PDF, 3.32 MB

english, 1998

3

[World Scientific Series on Nonlinear Science Series A] Methods of Qualitative Theory in Nonlinear Dynamics - Part I Volume 4 || STRUCTURALLY STABLE PERIODIC TRAJECTORIES OF DYNAMICAL SYSTEMS

Shilnikov, Leonid P., Shilnikov, Andrey L., Turaev, Dmitry V., Chua, Leon O.

Year:

1998

Language:

english

File:

PDF, 4.46 MB

english, 1998

4

[World Scientific Series on Nonlinear Science Series A] Methods of Qualitative Theory in Nonlinear Dynamics - Part I Volume 4 || INVARIANT TORI

Shilnikov, Leonid P., Shilnikov, Andrey L., Turaev, Dmitry V., Chua, Leon O.

Year:

1998

Language:

english

File:

PDF, 1.12 MB

english, 1998

5

[World Scientific Series on Nonlinear Science Series A] Methods of Qualitative Theory in Nonlinear Dynamics - Part I Volume 4 || CENTER MANIFOLD.: LOCAL CASE

Shilnikov, Leonid P., Shilnikov, Andrey L., Turaev, Dmitry V., Chua, Leon O.

Year:

1998

Language:

english

File:

PDF, 2.06 MB

english, 1998

6

Polyrhythmic synchronization in bursting networking motifs

Shilnikov, Andrey, Gordon, René, Belykh, Igor

Journal:

Chaos An Interdisciplinary Journal of Nonlinear Science

Year:

2008

Language:

english

File:

PDF, 1.63 MB

english, 2008

7

[World Scientific Series on Nonlinear Science Series A] Methods of Qualitative Theory in Nonlinear Dynamics - Part I Volume 4 || BASIC CONCEPTS

Shilnikov, Leonid P., Shilnikov, Andrey L., Turaev, Dmitry V., Chua, Leon O.

Year:

1998

Language:

english

File:

PDF, 773 KB

english, 1998

8

Spontaneous voltage oscillations and response dynamics of a Hodgkin-Huxley type model of sensory hair cells

Alexander B Neiman, Kai Dierkes, Benjamin Lindner, Lijuan Han, Andrey L Shilnikov

Journal:

The Journal of Mathematical Neuroscience (JMN)

Year:

2011

Language:

english

File:

PDF, 2.20 MB

english, 2011

9

How a neuron model can demonstrate co-existence of tonic spiking and bursting

Gennady S. Cymbalyuk, Ronald L. Calabrese, Andrey L. Shilnikov

Journal:

Year:

2005

Language:

english

File:

PDF, 261 KB

english, 2005

10

Bistability of bursting and silence regimes in a model of a leech heart interneuron

Malashchenko, Tatiana, Shilnikov, Andrey, Cymbalyuk, Gennady

Journal:

Physical Review E

Year:

2011

Language:

english

File:

PDF, 482 KB

english, 2011

11

Mechanism of bistability: Tonic spiking and bursting in a neuron model

Shilnikov, Andrey, Calabrese, Ronald L., Cymbalyuk, Gennady

Journal:

Physical Review E

Year:

2005

Language:

english

File:

PDF, 1.72 MB

english, 2005

12

Order parameter for bursting polyrhythms in multifunctional central pattern generators

Wojcik, Jeremy, Clewley, Robert, Shilnikov, Andrey

Journal:

Physical Review E

Year:

2011

Language:

english

File:

PDF, 3.10 MB

english, 2011

13

Robust design of polyrhythmic neural circuits

Schwabedal, Justus T. C., Neiman, Alexander B., Shilnikov, Andrey L.

Journal:

Physical Review E

Year:

2014

Language:

english

File:

PDF, 794 KB

english, 2014

14

Global organization of spiral structures in biparameter space of dissipative systems with Shilnikov saddle-foci

Barrio, Roberto, Blesa, Fernando, Serrano, Sergio, Shilnikov, Andrey

Journal:

Physical Review E

Year:

2011

Language:

english

File:

PDF, 1008 KB

english, 2011

15

Origin of Bursting through Homoclinic Spike Adding in a Neuron Model

Channell, Paul, Cymbalyuk, Gennady, Shilnikov, Andrey

Journal:

Physical Review Letters

Year:

2007

Language:

english

File:

PDF, 6.62 MB

english, 2007

16

METHODS OF THE QUALITATIVE THEORY FOR THE HINDMARSH–ROSE MODEL: A CASE STUDY – A TUTORIAL

SHILNIKOV, ANDREY, KOLOMIETS, MARINA

Journal:

International Journal of Bifurcation and Chaos

Year:

2008

Language:

english

File:

PDF, 4.67 MB

english, 2008

17

[World Scientific Series on Nonlinear Science Series A] Methods of Qualitative Theory in Nonlinear Dynamics Volume 5 ((Part II)) || STRUCTURALLY STABLE SYSTEMS

Shilnikov, Leonid P, Shilnikov, Andrey L, Turaev, Dmitry V, Chua, Leon O

Year:

2001

Language:

english

File:

PDF, 1.39 MB

english, 2001

18

Symbolic Quest into Homoclinic Chaos

Xing, Tingli, Barrio, Roberto, Shilnikov, Andrey

Journal:

International Journal of Bifurcation and Chaos

Year:

2014

Language:

english

File:

PDF, 1.23 MB

english, 2014

19

Macro- and micro-chaotic structures in the Hindmarsh-Rose model of bursting neurons

Barrio, Roberto, Angeles Martínez, M., Serrano, Sergio, Shilnikov, Andrey

Journal:

Chaos An Interdisciplinary Journal of Nonlinear Science

Year:

2014

Language:

english

File:

PDF, 5.15 MB

english, 2014

20

[IEEE 2018 IEEE International Symposium on Circuits and Systems (ISCAS) - Florence, Italy (2018.5.27-2018.5.30)] 2018 IEEE International Symposium on Circuits and Systems (ISCAS) - Design of Minimal Synthetic Circuits with Sensory Feedback for Quadruped Locomotion

Lodi, Matteo, Shilnikov, Andrey, Storace, Marco

Year:

2018

Language:

english

File:

PDF, 827 KB

english, 2018

21

[IEEE 2017 IEEE International Symposium on Circuits and Systems (ISCAS) - Baltimore, MD, USA (2017.5.28-2017.5.31)] 2017 IEEE International Symposium on Circuits and Systems (ISCAS) - CEPAGE: A toolbox for Central Pattern Generator analysis

Lodi, Matteo, Shilnikov, Andrey, Storace, Marco

Year:

2017

Language:

english

File:

PDF, 635 KB

english, 2017

22

[IEEE 2019 IEEE International Symposium on Circuits and Systems (ISCAS) - Sapporo, Japan (2019.5.26-2019.5.29)] 2019 IEEE International Symposium on Circuits and Systems (ISCAS) - Digital Architecture to Realize Programmable Central Pattern Generators Producing Multiple Gaits

Lodi, Matteo, Shilnikov, Andrey, Storace, Marco

Year:

2019

Language:

english

File:

PDF, 289 KB

english, 2019

23

Models of Multifunctional Central Pattern Generators: Polyrhythmic Bursting

Shilnikov, Andrey

Journal:

Bioentrepreneur

Year:

2011

Language:

english

File:

PDF, 6.67 MB

english, 2011

24

Models of Multifunctional Central Pattern Generators: Polyrhythmic Bursting

Shilnikov, Andrey

Journal:

Bioentrepreneur

Year:

2011

File:

PDF, 6.67 MB

2011

25

Voltage interval mappings for activity transitions in neuron models for elliptic bursters

Jeremy Wojcik, Andrey Shilnikov

Journal:

Physica D: Nonlinear Phenomena

Year:

2011

Language:

english

File:

PDF, 4.34 MB

english, 2011

26

Subthreshold oscillations in a map-based neuron model

Andrey L Shilnikov, Nikolai F Rulkov

Journal:

Physics Letters A

Year:

2004

Language:

english

File:

PDF, 474 KB

english, 2004

27

Parameter-sweeping techniques for temporal dynamics of neuronal systems: case study of Hindmarsh-Rose model

Roberto Barrio, Andrey Shilnikov

Journal:

The Journal of Mathematical Neuroscience (JMN)

Year:

2011

Language:

english

File:

PDF, 2.11 MB

english, 2011

28

Coexistence of Tonic Spiking Oscillations in a Leech Neuron Model

Gennady Cymbalyuk, Andrey Shilnikov

Journal:

Journal of Computational Neuroscience

Year:

2005

Language:

english

File:

PDF, 2.74 MB

english, 2005

29

Variability of bursting patterns in a neuron model in the presence of noise

Paul Channell, Ibiyinka Fuwape, Alexander B. Neiman, Andrey L. Shilnikov

Journal:

Journal of Computational Neuroscience

Year:

2009

Language:

english

File:

PDF, 4.78 MB

english, 2009

30

Complete dynamical analysis of a neuron model

Andrey Shilnikov

Journal:

Nonlinear Dynamics

Year:

2012

Language:

english

File:

PDF, 762 KB

english, 2012

31

Spikes matter for phase-locked bursting in inhibitory neurons

Jalil, Sajiya, Belykh, Igor, Shilnikov, Andrey

Journal:

Physical Review E

Year:

2012

Language:

english

File:

PDF, 984 KB

english, 2012

32

Applications of the Poincaré mapping technique to analysis of neuronal dynamics

Paul Channell Jr., Gennady Cymbalyuk, Andrey Shilnikov

Journal:

Year:

2007

Language:

english

File:

PDF, 1.01 MB

english, 2007

33

Modeling study of a Central Pattern Generator in the Melibe seaslug

Sajiya Jalil,Dane Allen,Andrey Shilnikov

Journal:

BMC Neuroscience

Year:

2012

Language:

english

File:

PDF, 133 KB

english, 2012

34

Voltage oscillations and response dynamics in a model of sensory hair cells

Neiman, Alexander B, Dierkes, Kai, Lindner, Benjamin, Shilnikov, Andrey L

Journal:

BMC Neuroscience

Year:

2012

Language:

english

File:

PDF, 131 KB

english, 2012

35

Phase-lag return mappings for a 3 cell multifunctional central pattern generator

Jeremy Wojcik,Robert Clewley,Andrey Shilnikov

Journal:

BMC Neuroscience

Year:

2012

Language:

english

File:

PDF, 201 KB

english, 2012

36

The role of burst duration in inhibitory synchronization

Igor Belykh, Andrey Shilnikov

Journal:

BMC Neuroscience

Year:

2008

Language:

english

File:

PDF, 100 KB

english, 2008

37

Fast reciprocal inhibition can synchronize bursting neurons

Jalil, Sajiya, Belykh, Igor, Shilnikov, Andrey

Journal:

Physical Review E

Year:

2010

Language:

english

File:

PDF, 2.41 MB

english, 2010

38

Toward robust phase-locking in Melibe swim central pattern generator models

Jalil, Sajiya, Allen, Dane, Youker, Joseph, Shilnikov, Andrey

Journal:

Chaos An Interdisciplinary Journal of Nonlinear Science

Year:

2013

Language:

english

File:

PDF, 2.64 MB

english, 2013

39

Showcase of Blue Sky Catastrophes

Shilnikov, Leonid Pavlovich, Shilnikov, Andrey L., Turaev, Dmitry V.

Journal:

International Journal of Bifurcation and Chaos

Year:

2014

Language:

english

File:

PDF, 646 KB

english, 2014

40

When Weak Inhibition Synchronizes Strongly Desynchronizing Networks of Bursting Neurons

Belykh, Igor, Shilnikov, Andrey

Journal:

Physical Review Letters

Year:

2008

Language:

english

File:

PDF, 517 KB

english, 2008

41

Transition between Tonic Spiking and Bursting in a Neuron Model via the Blue-Sky Catastrophe

Shilnikov, Andrey, Cymbalyuk, Gennady

Journal:

Physical Review Letters

Year:

2005

Language:

english

File:

PDF, 2.26 MB

english, 2005

42

Electrogenic properties of the Na + /K + ATPase control transitions between normal and pathological brain states

Krishnan, Giri P., Filatov, Gregory, Shilnikov, Andrey, Bazhenov, Maxim

Journal:

Journal of Neurophysiology

Year:

2015

Language:

english

File:

PDF, 2.33 MB

english, 2015

43

ON SOME MATHEMATICAL TOPICS IN CLASSICAL SYNCHRONIZATION.: A TUTORIAL

SHILNIKOV, ANDREY, SHILNIKOV, LEONID, TURAEV, DMITRY

Journal:

International Journal of Bifurcation and Chaos

Year:

2004

Language:

english

File:

PDF, 1.74 MB

english, 2004

44

ORIGIN OF CHAOS IN A TWO-DIMENSIONAL MAP MODELING SPIKING-BURSTING NEURAL ACTIVITY

SHILNIKOV, ANDREY L., RULKOV, NIKOLAI F.

Journal:

International Journal of Bifurcation and Chaos

Year:

2003

Language:

english

File:

PDF, 2.51 MB

english, 2003

45

KNEADINGS, SYMBOLIC DYNAMICS AND PAINTING LORENZ CHAOS

BARRIO, ROBERTO, SHILNIKOV, ANDREY, SHILNIKOV, LEONID

Journal:

International Journal of Bifurcation and Chaos

Year:

2012

Language:

english

File:

PDF, 1.89 MB

english, 2012

46

SLOW–FAST DYNAMICS GENERATED BY NONINVERTIBLE PLANE MAPS

MIRA, CHRISTIAN, SHILNIKOV, ANDREY

Journal:

International Journal of Bifurcation and Chaos

Year:

2005

Language:

english

File:

PDF, 4.08 MB

english, 2005

47

[World Scientific Series on Nonlinear Science Series A] Methods of Qualitative Theory in Nonlinear Dynamics Volume 5 ((Part II)) || BACK MATTER

Shilnikov, Leonid P, Shilnikov, Andrey L, Turaev, Dmitry V, Chua, Leon O

Year:

2001

Language:

english

File:

PDF, 4.52 MB

english, 2001

48

[AIP WOMEN IN PHYSICS: Third IUPAP International Conference on Women in Physics - Seoul (South Korea) (8–10 October 2008)] AIP Conference Proceedings - The Effect of Noise on Spike-Adding Bifurcations in a Neuronal Burster (abstract)

Fuwape, Ibiyinka, Neiman, Alexander, Shilnikov, Andrey L., Hartline, Beverly Karplus, Horton, Renee K., Kaicher, Catherine M.

Year:

2009

Language:

english

File:

PDF, 98 KB

english, 2009

49

Mixed-mode synchronization between two inhibitory neurons with post-inhibitory rebound

Nagornov, Roman, Osipov, Grigory, Komarov, Maxim, Pikovsky, Arkady, Shilnikov, Andrey

Journal:

Communications in Nonlinear Science and Numerical Simulation

Year:

2015

Language:

english

File:

PDF, 11.70 MB

english, 2015

50

Mechanism of quasi-periodic lag jitter in bursting rhythms by a neuronal network

Barrio, R., Rodríguez, Marcos, Serrano, S., Shilnikov, Andrey

Journal:

EPL (Europhysics Letters)

Year:

2015

Language:

english

File:

PDF, 1.29 MB

english, 2015