Бурилко Олександр Андрійович
Публікації
1. O. Burylko, M. Wolfrum, S. Yanchuk. Reversible saddle-node separatrix-loop bifurcation, WIAS Preprint, 3133 (2024)
https://www.wias-berlin.de/publications/wias-publ/run.jsp?template=abstract&type=Preprint&year=2024&number=3133
pdf
2. M Wei, A Amann, O Burylko, X Han, S Yanchuk, J Kurths. Synchronization cluster bursting in adaptive oscillators networks (2024)
https://arxiv.org/pdf/2409.08348
pdf
3. O. Burylko, M. Wolfrum, S. Yanchuk, J. Kurths. Time-reversible dynamics in a system of two coupled active rotators. Proceedings of the Royal Society A, 479, 20230401 (2023)
https://doi.org/10.1098/rspa.2023.0401
pdf
4. O. Burylko, E. Martens, and C. Bick. Symmetry breaking yields chimeras in two small populations of kuramoto-type oscillators, Chaos, 32, 093109 (2022)
https://doi.org/10.1063/5.0088465
pdf
5. O. Burylko, Collective dynamics and bifurcations in symmetric networks of phase oscillators. II, Journal of Mathematical Sciences, 253(2), 204-229 (2021)
pdf
6. O. Burylko, Collective dynamics and bifurcations in symmetric networks of phase oscillators. I, Journal of Mathematical Sciences, 249(4), 573-600 (2020)
pdf
7. О. Бурилко, Колективна динаміка та біфуркації у симетричних мережах фазових осциляторів. II, Нелінійні Коливання, 22(3), 312-340 (2019)
pdf
8. О. Бурилко, Колективна динаміка та біфуркації у симетричних мережах фазових осциляторів. I, Нелінійні Коливання, 22(2), 165-195 (2019)
pdf
9. O. Burylko, A. Mielke, M. Wolfrum, and S. Yanchuk, Coexistence of Hamiltonian-like and dissipative dynamics in rings of coupled phase oscillators with skew-symmetric coupling, SIAM J. Appl. Dyn. Syst. 17 (3), 2076–2105 (2018)
https://epubs.siam.org/doi/abs/10.1137/17M1155685
pdf
10. O. Burylko, Y. Kazanovich, and R. Borisyuk, Winner-take-all in a phase oscillator system with adaptation, Scientific Reports, 8, 416 (2018)
https://epubs.siam.org/doi/abs/10.1137/17M1155685
pdf
11. P. Ashwin, C. Bick, and O. Burylko, Identical phase oscillator networks: bifurcations, symmetry and reversibility for generalized coupling, Frontiers in Applied Mathematics and Statistics, 2(7), (2016)
https://doi.org/10.3389/fams.2016.00007
pdf
12. P. Ashwin, and O. Burylko, Weak chimeras in minimal networks of coupled phase oscillators, Chaos, 25, 013106 (2015) pdf
13. O. Burylko, Y. Kazanovich, and R. Borisyuk, Bifurcation study of phase oscillator systems with attractive and repulsive interaction, Phys. Rev. E, 90, 022911 (2014) pdf
14. Y. Kazanovich, O. Burylko, and R. Borisyuk, Competition for Synchronization in a Phase Oscillator System, Physica D, 261, 114-124 (2013) pdf
15. R. Merrison, N. Yousif, F. Njap, U. Hofmann, O. Burylko, and R. Borisyuk, An interactive channel model of the Basal Ganglia: bifurcation analysis under healthy and parkinsonian conditions, The Journal of Mathematical Neuroscience, 3(1): 14, Doi:10.1186/2190-8567-3-14 (2013) pdf
16. O. Burylko, Y. Kazanovich, and R. Borisyuk, Bifurcations in phase oscillator networks with a central element, Physica D, 241, 1072-1089 (2012) pdf
17. O. Burylko, and A. Pikovsky, Desynchronization transitions in nonlinearly coupled phase oscillators, Physica D, 240, 1352-1361 (2011) pdf
18. P.Ashwin, O.Burylko, and Yu.Maistrenko, Bifurcation to heteroclinic cycles and sensitivity in three and four phase coupled oscillators. Physica D, 237, 454-466 (2008) pdf
19. Yu. Maistrenko, B. Lysyansky, C. Hauptmann, O. Burylko, and P.A. Tass, Multistability in the Kuramoto model with synaptic plasticity, Phys. Rev. E, 75, 066207 (2007) pdf
20. P.Ashwin, O.Burylko, Yu.Maistrenko, and O.Popovych, Extreme sensitivity to detuning for globally coupled phase oscillators, Phys. Rev. Lett., 96, 054102 (2006) pdf
21. Yu. Maistrenko, O. Popovych, O. Burylko, and P.A. Tass, Mechanism of Desynchronization in the Finite-Dimensional Kuramoto Model, Phys. Rev. Lett., 93, 084102 (2004) pdf
22. O. Burylko, and A. Davydenko, To the problem of complementability of periodic frame to a periodic basis, Nonlinear Oscillations, 4, 458-470 (2001)
pdf
23. O. Burylko, and A. Davydenko, To the problem of introduction of local coordinates in the neighbourhood of an invariant toroidal set, Nonlinear Oscillations, 4, 171-190 (2001)
24. O. Burylko, Green function of weakly regular systems of linear differential equations, Nonlinear Oscillations, 3, 315-322 (2000).
25. А. М. Самойленко, О. Бурилко, И. Грод. Модули непрерывности производных инвариантных торов линейных расширений динамических систем, Дифференциальные уравнения, 36, 103-113 (2000) pdf
26. A.M. Samoilenko, and O. Burylko, The problem of smoothness of the Green function of the problem about bounded invariant manifold, Ukrainian Mathematical Journal, 51, 570-584 (1998) pdf
27. O. Burylko, Separation of variables in linear extensions of dynamical systems on the torus, Ukrainian Mathematical Journal, 48, 146-150 (1996) pdf
https://www.wias-berlin.de/publications/wias-publ/run.jsp?template=abstract&type=Preprint&year=2024&number=3133
2. M Wei, A Amann, O Burylko, X Han, S Yanchuk, J Kurths. Synchronization cluster bursting in adaptive oscillators networks (2024)
https://arxiv.org/pdf/2409.08348
3. O. Burylko, M. Wolfrum, S. Yanchuk, J. Kurths. Time-reversible dynamics in a system of two coupled active rotators. Proceedings of the Royal Society A, 479, 20230401 (2023)
https://doi.org/10.1098/rspa.2023.0401
4. O. Burylko, E. Martens, and C. Bick. Symmetry breaking yields chimeras in two small populations of kuramoto-type oscillators, Chaos, 32, 093109 (2022)
https://doi.org/10.1063/5.0088465
5. O. Burylko, Collective dynamics and bifurcations in symmetric networks of phase oscillators. II, Journal of Mathematical Sciences, 253(2), 204-229 (2021)
6. O. Burylko, Collective dynamics and bifurcations in symmetric networks of phase oscillators. I, Journal of Mathematical Sciences, 249(4), 573-600 (2020)
7. О. Бурилко, Колективна динаміка та біфуркації у симетричних мережах фазових осциляторів. II, Нелінійні Коливання, 22(3), 312-340 (2019)
8. О. Бурилко, Колективна динаміка та біфуркації у симетричних мережах фазових осциляторів. I, Нелінійні Коливання, 22(2), 165-195 (2019)
9. O. Burylko, A. Mielke, M. Wolfrum, and S. Yanchuk, Coexistence of Hamiltonian-like and dissipative dynamics in rings of coupled phase oscillators with skew-symmetric coupling, SIAM J. Appl. Dyn. Syst. 17 (3), 2076–2105 (2018)
https://epubs.siam.org/doi/abs/10.1137/17M1155685
10. O. Burylko, Y. Kazanovich, and R. Borisyuk, Winner-take-all in a phase oscillator system with adaptation, Scientific Reports, 8, 416 (2018)
https://epubs.siam.org/doi/abs/10.1137/17M1155685
11. P. Ashwin, C. Bick, and O. Burylko, Identical phase oscillator networks: bifurcations, symmetry and reversibility for generalized coupling, Frontiers in Applied Mathematics and Statistics, 2(7), (2016)
https://doi.org/10.3389/fams.2016.00007
12. P. Ashwin, and O. Burylko, Weak chimeras in minimal networks of coupled phase oscillators, Chaos, 25, 013106 (2015) pdf
13. O. Burylko, Y. Kazanovich, and R. Borisyuk, Bifurcation study of phase oscillator systems with attractive and repulsive interaction, Phys. Rev. E, 90, 022911 (2014) pdf
14. Y. Kazanovich, O. Burylko, and R. Borisyuk, Competition for Synchronization in a Phase Oscillator System, Physica D, 261, 114-124 (2013) pdf
15. R. Merrison, N. Yousif, F. Njap, U. Hofmann, O. Burylko, and R. Borisyuk, An interactive channel model of the Basal Ganglia: bifurcation analysis under healthy and parkinsonian conditions, The Journal of Mathematical Neuroscience, 3(1): 14, Doi:10.1186/2190-8567-3-14 (2013) pdf
16. O. Burylko, Y. Kazanovich, and R. Borisyuk, Bifurcations in phase oscillator networks with a central element, Physica D, 241, 1072-1089 (2012) pdf
17. O. Burylko, and A. Pikovsky, Desynchronization transitions in nonlinearly coupled phase oscillators, Physica D, 240, 1352-1361 (2011) pdf
18. P.Ashwin, O.Burylko, and Yu.Maistrenko, Bifurcation to heteroclinic cycles and sensitivity in three and four phase coupled oscillators. Physica D, 237, 454-466 (2008) pdf
19. Yu. Maistrenko, B. Lysyansky, C. Hauptmann, O. Burylko, and P.A. Tass, Multistability in the Kuramoto model with synaptic plasticity, Phys. Rev. E, 75, 066207 (2007) pdf
20. P.Ashwin, O.Burylko, Yu.Maistrenko, and O.Popovych, Extreme sensitivity to detuning for globally coupled phase oscillators, Phys. Rev. Lett., 96, 054102 (2006) pdf
21. Yu. Maistrenko, O. Popovych, O. Burylko, and P.A. Tass, Mechanism of Desynchronization in the Finite-Dimensional Kuramoto Model, Phys. Rev. Lett., 93, 084102 (2004) pdf
22. O. Burylko, and A. Davydenko, To the problem of complementability of periodic frame to a periodic basis, Nonlinear Oscillations, 4, 458-470 (2001)
23. O. Burylko, and A. Davydenko, To the problem of introduction of local coordinates in the neighbourhood of an invariant toroidal set, Nonlinear Oscillations, 4, 171-190 (2001)
24. O. Burylko, Green function of weakly regular systems of linear differential equations, Nonlinear Oscillations, 3, 315-322 (2000).
25. А. М. Самойленко, О. Бурилко, И. Грод. Модули непрерывности производных инвариантных торов линейных расширений динамических систем, Дифференциальные уравнения, 36, 103-113 (2000) pdf
26. A.M. Samoilenko, and O. Burylko, The problem of smoothness of the Green function of the problem about bounded invariant manifold, Ukrainian Mathematical Journal, 51, 570-584 (1998) pdf
27. O. Burylko, Separation of variables in linear extensions of dynamical systems on the torus, Ukrainian Mathematical Journal, 48, 146-150 (1996) pdf