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Andrey Shilnikov - Publications

Affiliations: 
Mathematics and Statistics Georgia State University, Atlanta, GA, United States 
Area:
Applied Mathematics, Neuroscience Biology, Bioinformatics Biology
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41 high-probability publications. We are testing a new system for linking publications to authors. You can help! If you notice any inaccuracies, please sign in and mark papers as correct or incorrect matches. If you identify any major omissions or other inaccuracies in the publication list, please let us know.

Year Citation  Score
2020 Pusuluri K, Basodi S, Shilnikov A. Computational exposition of multistable rhythms in 4-cell neural circuits Communications in Nonlinear Science and Numerical Simulation. 83: 105139. DOI: 10.1016/J.Cnsns.2019.105139  0.416
2019 Lodi M, Shilnikov AL, Storace M. Design Principles for Central Pattern Generators With Preset Rhythms. Ieee Transactions On Neural Networks and Learning Systems. PMID 31722491 DOI: 10.1109/TNNLS.2019.2945637  0.312
2018 Ju H, Neiman AB, Shilnikov AL. Bottom-up approach to torus bifurcation in neuron models. Chaos (Woodbury, N.Y.). 28: 106317. PMID 30384623 DOI: 10.1063/1.5042078  0.355
2018 Lodi M, Shilnikov A, Storace M. Design of Synthetic Central Pattern Generators Producing Desired Quadruped Gaits Ieee Transactions On Circuits and Systems I: Regular Papers. 65: 1028-1039. DOI: 10.1109/Tcsi.2017.2759320  0.399
2018 Pusuluri K, Shilnikov A. Homoclinic chaos and its organization in a nonlinear optics model Physical Review E. 98. DOI: 10.1103/Physreve.98.040202  0.375
2016 Shilnikov AL, Maurer AP. The Art of Grid Fields: Geometry of Neuronal Time. Frontiers in Neural Circuits. 10: 12. PMID 27013981 DOI: 10.3389/fncir.2016.00012  0.307
2016 Nagornov R, Osipov G, Komarov M, Pikovsky A, Shilnikov A. Mixed-mode synchronization between two inhibitory neurons with post-inhibitory rebound Communications in Nonlinear Science and Numerical Simulation. 36: 175-191. DOI: 10.1016/J.Cnsns.2015.11.024  0.429
2015 Barrio R, Rodríguez M, Serrano S, Shilnikov A. Mechanism of quasi-periodic lag jitter in bursting rhythms by a neuronal network Epl. 112: 38002. DOI: 10.1209/0295-5075/112/38002  0.5
2015 Alaçam D, Shilnikov A. Making a Swim Central Pattern Generator Out of Latent Parabolic Bursters International Journal of Bifurcation and Chaos. 25: 1540003. DOI: 10.1142/S0218127415400039  0.442
2014 Schwabedal JT, Neiman AB, Shilnikov AL. Robust design of polyrhythmic neural circuits. Physical Review. E, Statistical, Nonlinear, and Soft Matter Physics. 90: 022715. PMID 25215766 DOI: 10.1103/Physreve.90.022715  0.335
2014 Barrio R, Martínez MA, Serrano S, Shilnikov A. Macro- and micro-chaotic structures in the Hindmarsh-Rose model of bursting neurons. Chaos (Woodbury, N.Y.). 24: 023128. PMID 24985442 DOI: 10.1063/1.4882171  0.44
2014 Wojcik J, Schwabedal J, Clewley R, Shilnikov AL. Key bifurcations of bursting polyrhythms in 3-cell central pattern generators. Plos One. 9: e92918. PMID 24739943 DOI: 10.1371/Journal.Pone.0092918  0.624
2014 Xing T, Barrio R, Shilnikov A. Symbolic Quest into Homoclinic Chaos International Journal of Bifurcation and Chaos. 24: 1440004. DOI: 10.1142/S0218127414400045  0.383
2014 Xing T, Wojcik J, Zaks MA, Shilnikov A. Fractal Parameter Space of Lorenz-like Attractors: A Hierarchical Approach Chaos. 87. DOI: 10.1142/9789814602136_0005  0.525
2013 Jalil S, Allen D, Youker J, Shilnikov A. Toward robust phase-locking in Melibe swim central pattern generator models. Chaos (Woodbury, N.Y.). 23: 046105. PMID 24387584 DOI: 10.1063/1.4825389  0.455
2012 Jalil S, Belykh I, Shilnikov A. Spikes matter for phase-locked bursting in inhibitory neurons. Physical Review. E, Statistical, Nonlinear, and Soft Matter Physics. 85: 036214. PMID 22587168 DOI: 10.1103/Physreve.85.036214  0.466
2012 Wojcik J, Clewley R, Shilnikov A. Phase-lag return mappings for a 3 cell multifunctional central pattern generator Bmc Neuroscience. 13. DOI: 10.1186/1471-2202-13-S1-P188  0.654
2012 Jalil S, Allen D, Shilnikov A. Modeling study of a Central Pattern Generator in the Melibe seaslug Bmc Neuroscience. 13. DOI: 10.1186/1471-2202-13-S1-P187  0.505
2012 Barrio R, Shilnikov A, Shilnikov LP. Kneadings, Symbolic Dynamics And Painting Lorenz Chaos International Journal of Bifurcation and Chaos. 22: 1230016. DOI: 10.1142/S0218127412300169  0.324
2012 Shilnikov A. Complete dynamical analysis of a neuron model Nonlinear Dynamics. 68: 305-328. DOI: 10.1007/S11071-011-0046-Y  0.495
2011 Barrio R, Shilnikov A. Parameter-sweeping techniques for temporal dynamics of neuronal systems: case study of Hindmarsh-Rose model. Journal of Mathematical Neuroscience. 1: 6. PMID 22656867 DOI: 10.1186/2190-8567-1-6  0.348
2011 Malashchenko T, Shilnikov A, Cymbalyuk G. Bistability of bursting and silence regimes in a model of a leech heart interneuron. Physical Review. E, Statistical, Nonlinear, and Soft Matter Physics. 84: 041910. PMID 22181178 DOI: 10.1103/Physreve.84.041910  0.411
2011 Barrio R, Blesa F, Serrano S, Shilnikov A. Global organization of spiral structures in biparameter space of dissipative systems with Shilnikov saddle-foci. Physical Review. E, Statistical, Nonlinear, and Soft Matter Physics. 84: 035201. PMID 22060441 DOI: 10.1103/Physreve.84.035201  0.305
2011 Malashchenko T, Shilnikov A, Cymbalyuk G. Six types of multistability in a neuronal model based on slow calcium current. Plos One. 6: e21782. PMID 21814554 DOI: 10.1371/Journal.Pone.0021782  0.478
2011 Wojcik J, Clewley R, Shilnikov A. Order parameter for bursting polyrhythms in multifunctional central pattern generators. Physical Review. E, Statistical, Nonlinear, and Soft Matter Physics. 83: 056209. PMID 21728632 DOI: 10.1103/Physreve.83.056209  0.637
2011 Shilnikov A. Models of Multifunctional Central Pattern Generators: Polyrhythmic Bursting Nature Precedings. 6: 1-1. DOI: 10.1038/Npre.2011.5800.1  0.38
2011 Wojcik J, Shilnikov A. Voltage interval mappings for activity transitions in neuron models for elliptic bursters Physica D: Nonlinear Phenomena. 240: 1164-1180. DOI: 10.1016/J.Physd.2011.04.003  0.607
2010 Jalil S, Belykh I, Shilnikov A. Fast reciprocal inhibition can synchronize bursting neurons. Physical Review. E, Statistical, Nonlinear, and Soft Matter Physics. 81: 045201. PMID 20481777 DOI: 10.1103/Physreve.81.045201  0.434
2010 Belykh I, Jalil S, Shilnikov A. Burst-duration mechanism of in-phase bursting in inhibitory networks Regular and Chaotic Dynamics. 15: 146-158. DOI: 10.1134/S1560354710020048  0.479
2009 Channell P, Fuwape I, Neiman AB, Shilnikov AL. Variability of bursting patterns in a neuron model in the presence of noise. Journal of Computational Neuroscience. 27: 527-42. PMID 19543963 DOI: 10.1007/S10827-009-0167-1  0.321
2008 Shilnikov A, Gordon R, Belykh I. Polyrhythmic synchronization in bursting networking motifs. Chaos (Woodbury, N.Y.). 18: 037120. PMID 19045494 DOI: 10.1063/1.2959850  0.471
2008 Belykh I, Shilnikov A. When weak inhibition synchronizes strongly desynchronizing networks of bursting neurons. Physical Review Letters. 101: 078102. PMID 18764581 DOI: 10.1103/Physrevlett.101.078102  0.424
2008 Belykh I, Shilnikov A. The role of burst duration in inhibitory synchronization Bmc Neuroscience. 9: 151. DOI: 10.1186/1471-2202-9-S1-P151  0.316
2008 Shilnikov A, Kolomiets M. Methods Of The Qualitative Theory For The Hindmarsh–Rose Model: A Case Study – A Tutorial International Journal of Bifurcation and Chaos. 18: 2141-2168. DOI: 10.1142/S0218127408021634  0.452
2007 Channell P, Cymbalyuk G, Shilnikov A. Origin of bursting through homoclinic spike adding in a neuron model. Physical Review Letters. 98: 134101. PMID 17501202 DOI: 10.1103/Physrevlett.98.134101  0.412
2007 Channell P, Cymbalyuk G, Shilnikov A. Applications of the Poincaré mapping technique to analysis of neuronal dynamics Neurocomputing. 70: 2107-2111. DOI: 10.1016/J.Neucom.2006.10.091  0.479
2005 Shilnikov A, Calabrese RL, Cymbalyuk G. Mechanism of bistability: tonic spiking and bursting in a neuron model. Physical Review. E, Statistical, Nonlinear, and Soft Matter Physics. 71: 056214. PMID 16089641 DOI: 10.1103/Physreve.71.056214  0.459
2005 Cymbalyuk G, Shilnikov A. Coexistence of tonic spiking oscillations in a leech neuron model Journal of Computational Neuroscience. 18: 255-263. PMID 15830162 DOI: 10.1007/s10827-005-0354-7  0.399
2005 Shilnikov A, Cymbalyuk G. Transition between tonic spiking and bursting in a neuron model via the blue-sky catastrophe Physical Review Letters. 94. PMID 15783604 DOI: 10.1103/Physrevlett.94.048101  0.355
2005 Mira C, Shilnikov A. Slow–Fast Dynamics Generated By Noninvertible Plane Maps International Journal of Bifurcation and Chaos. 15: 3509-3534. DOI: 10.1142/S0218127405014192  0.368
2004 Shilnikov AL, Rulkov NF. Subthreshold oscillations in a map-based neuron model Physics Letters, Section a: General, Atomic and Solid State Physics. 328: 177-184. DOI: 10.1016/j.physleta.2004.05.062  0.345
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