Burylko Oleksandr A.
Publications
1. 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
2. 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
3. O. Burylko, Collective dynamics and bifurcations in symmetric networks of phase oscillators. II, Journal of Mathematical Sciences, 253(2), 204-229 (2021)
https://doi.org/10.1007/s10958-021-05223-7
pdf
4. O. Burylko, Collective dynamics and bifurcations in symmetric networks of phase oscillators. I, Journal of Mathematical Sciences, 249(4), 573-600 (2020)
https://doi.org/10.1007/s10958-020-04959-y
pdf
5. 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
6. 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
7. 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
8. P. Ashwin, and O. Burylko, Weak chimeras in minimal networks of coupled phase oscillators, Chaos, 25, 013106 (2015) pdf
9. 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
10. Y. Kazanovich, O. Burylko, and R. Borisyuk, Competition for synchronization in a phase oscillator system, Physica D, 261, 114-124 (2013) pdf
11. 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
12. O. Burylko, Y. Kazanovich, and R. Borisyuk, Bifurcations in phase oscillator networks with a central element, Physica D, 241, 1072-1089 (2012) pdf
13. O. Burylko, and A. Pikovsky, Desynchronization transitions in nonlinearly coupled phase oscillators, Physica D, 240, 1352-1361 (2011) pdf
14. 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
15. 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
16. 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
17. 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
18. O. Burylko, and A. Davydenko, To the problem of complementability of periodic frame to a periodic basis, Nonlinear Oscillations, 4, 458-470 (2001)
pdf
19. 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)
20. O. Burylko, Green function of weakly regular systems of linear differential equations, Nonlinear Oscillations, 3, 315-322 (2000).
21. A.M. Samoilenko, O. Burylko, and I.N. Grod, Modules of continuity of derivative invariant tori of linear extensions of dynamical systems, Differential Equations, 36(1), 120-131 (2000) pdf
22. 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
23. O. Burylko, Separation of variables in linear extensions of dynamical systems on the torus, Ukrainian Mathematical Journal, 48, 146-150 (1996) pdf
https://doi.org/10.1098/rspa.2023.0401
2. 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
3. O. Burylko, Collective dynamics and bifurcations in symmetric networks of phase oscillators. II, Journal of Mathematical Sciences, 253(2), 204-229 (2021)
https://doi.org/10.1007/s10958-021-05223-7
4. O. Burylko, Collective dynamics and bifurcations in symmetric networks of phase oscillators. I, Journal of Mathematical Sciences, 249(4), 573-600 (2020)
https://doi.org/10.1007/s10958-020-04959-y
5. 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
6. 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
7. 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
8. P. Ashwin, and O. Burylko, Weak chimeras in minimal networks of coupled phase oscillators, Chaos, 25, 013106 (2015) pdf
9. 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
10. Y. Kazanovich, O. Burylko, and R. Borisyuk, Competition for synchronization in a phase oscillator system, Physica D, 261, 114-124 (2013) pdf
11. 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
12. O. Burylko, Y. Kazanovich, and R. Borisyuk, Bifurcations in phase oscillator networks with a central element, Physica D, 241, 1072-1089 (2012) pdf
13. O. Burylko, and A. Pikovsky, Desynchronization transitions in nonlinearly coupled phase oscillators, Physica D, 240, 1352-1361 (2011) pdf
14. 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
15. 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
16. 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
17. 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
18. O. Burylko, and A. Davydenko, To the problem of complementability of periodic frame to a periodic basis, Nonlinear Oscillations, 4, 458-470 (2001)
19. 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)
20. O. Burylko, Green function of weakly regular systems of linear differential equations, Nonlinear Oscillations, 3, 315-322 (2000).
21. A.M. Samoilenko, O. Burylko, and I.N. Grod, Modules of continuity of derivative invariant tori of linear extensions of dynamical systems, Differential Equations, 36(1), 120-131 (2000) pdf
22. 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
23. O. Burylko, Separation of variables in linear extensions of dynamical systems on the torus, Ukrainian Mathematical Journal, 48, 146-150 (1996) pdf