preprints
A. N. Busch*, R. C. Budzinski*, F. W. Pasini, J. Mináč, J. A. Michaels, M. Roussy, R. A. Gulli, B. Corrigan, J. A. Pruszynski, J. Martinez-Trujillo, L. E. Muller, "A mathematical language for linking fine-scale structure in spikes from hundreds to thousands of neurons with behaviour", arXiv:2412.03804. (link)
R. C. Budzinski, J. W. C. Graham, J. Mináč, L. E. Muller, "Theory of transient chimeras in finite Sakaguchi-Kuramoto networks", arXiv:2311.01382. (link)
2025
A. Mihara, C. M. Kuwana, R. C. Budzinski, L. E. Muller, R. O. Medrano-T, "Bifurcations and collective states of Kuramoto oscillators with higher-order interactions and rotational symmetry breaking", Chaos 35 (3), 033133, 2025. (link)
M. Jacobs, R. C. Budzinski, L. Muller, D. Ba, T. A. Keller, "Traveling Waves Integrate Spatial Information Into Spectral Representations", ICLR 2025 Re-Align Workshop. (link)
K. L. Rossi, R. C. Budzinski, E. S. Ribeiro, B. R. R. Boaretto, L. E. Muller, U. Feudel, “Dynamical properties and mechanisms of metastability: a perspective in neuroscience”, (perspective paper) Physical Review E 111, 021001. (link)
L. H. B. Liboni*, R. C. Budzinski*, A. N. Busch*, S. Löwe, T. A. Keller, M. Welling, L. E. Muller, "Image segmentation with traveling waves in an exactly solvable recurrent neural network", PNAS 122 (1) e2321319121, 2025. (link)
2024
R. C. Budzinski*, A. N. Busch*, S. Mestern, E. Martin, L. H. B. Liboni, F. Pasini, J. Mináč, T. Coleman, W. Inoue, L. E. Muller, "An exact mathematical description of computation with transient spatiotemporal dynamics in a complex-valued neural network", Communications Physics 7 (1), 239, 2024. (link)
2023
P. B. Jain*, T. T. Nguyen*, J. Minàč, L. E. Muller, R. C. Budzinski, "Composed solutions of synchronized patterns in multiplex networks of Kuramoto oscillators", Chaos (Editor's pick), 33 (10), 103128, 2023. (link)
G. Benigno, R. C. Budzinski, Z. Davis, J. Reynolds, L. E. Muller, “Waves traveling over a map of visual space can ignite short-term predictions of sensory input”, Nature Communications 14 (1), 3409, 2023. (link)
R. C. Budzinski*, T. T. Nguyen*, G. Benigno*, J. Doàn, J. Mináč, T. J. Sejnowski, L. E. Muller, “Analytical prediction of specific spatiotemporal patterns in nonlinear oscillator networks with distance-dependent time delays”, Physical Review Research 5 (1), 013159, 2023. (link)
B. R. R. Boaretto, R. C. Budzinski, K. L. Rossi, C. Masoller, E. E. N. Macau, “Spatial permutation entropy distinguishes resting brain states”, Chaos, Solitons & Fractals 171, 113453, 2023. (link)
K. L. Rossi, R. C. Budzinski, B. R. R. Boaretto, L. E. Muller, U. Feudel, “Small changes at single nodes can shift global network dynamics”, Physical Review Research 5 (1), 013220, 2023. (link)
T. T. Nguyen, R. C. Budzinski, J. Đoàn, F. Pasini, J. Mináč, L. Muller, “Equilibria in Kuramoto oscillator networks: An algebraic approach”, accepted in SIAM Applied Dynamical Systems 22 (2), 802-824, 2023. (link)
T. T. Nguyen*, R. C. Budzinski*, F. Pasini, R. Delabays, J. Mináč, L. Muller, “Broadcasting solutions on networked systems of phase oscillators”, Chaos, Solutions & Fractals, 168, 113166, 2023. (link)
2022
R. C. Budzinski*, T. T. Nguyen*, J. Đoàn, J. Mináč, T. J. Sejnowski, L. E. Muller, “Geometry unites synchrony, chimeras, and waves in nonlinear oscillator networks”, Chaos (Fast Track) 32 (3), 031104, 2022. (link)
2021
R. C. Budzinski, S. R. Lopes, C. Masoller, “Symbolic analysis of bursting dynamical regimes of Rulkov neural networks”, Neurocomputing 441, 44–51, 2021. (link)
B. R. R. Boaretto, R. C. Budzinski, K. L. Rossi, T. L. Prado, S. R. Lopes, C. Masoller. “Discriminating chaotic and stochastic time series using permutation entropy and artificial neural networks”, Scientific Reports 11, 15789, 2021. (link)
K. L. Rossi, R. C. Budzinski, B. R. R. Boaretto, T. L. Prado, U. Feudel, S. R. Lopes. “Phase-locking intermittency induced by dynamical heterogeneity in networks of thermosensitive neurons”, Chaos 31 (8), 083121, 2021. (link)
B. R. R. Boaretto, R. C. Budzinski, K. L. Rossi, C. Manchein, T. L. Prado, U. Feudel, S. R. Lopes. “Bistability in the synchronization of identical neurons”, Physical Review E 104, 024204, 2021. (link)
B. R. R. Boaretto, R. C. Budzinski, K. L. Rossi, T. L. Prado, S. R. Lopes, C. Masoller. “Evaluating temporal correlations in time series using permutation entropy, ordinal probabilities and machine learning”, Entropy 23 (8), 1025, 2021. (link)
K. L. Rossi, B. R. R. Boaretto, R. C. Budzinski, “The role of synchronization in neural systems and their consequence to the neural behavior” (invited comment), Physics of Life Reviews 36, 68–70, 2021. (link)
2020
R. C. Budzinski*, K. L. Rossi*, B. R. R. Boaretto, T. L. Prado, S. R. Lopes, “Synchronization malleability in neural networks under a distance-dependent coupling”, Physical Review Research 2 (4), 043309, 2020. (link)
T. L. Prado, G. Corso, G. Z. dos Santos Lima, R. C. Budzinski, B. R. R. Boaretto, F. A. S. Ferrari, E. E. N. Macau, S. R. Lopes, “Maximum entropy principle in recurrence plot analysis on stochastic and chaotic systems”, Chaos 30 (4), 043123, 2020. (link)
2019
R. C. Budzinski, B. R. R. Boaretto, T. L. Prado, R. L. Viana, S. R. Lopes, “Synchronous patterns and intermittency in a network induced by the rewiring of connections and coupling”, Chaos 29 (12), 123132, 2019. (link)
R. C. Budzinski, B. R. R. Boaretto, T. L. Prado, S. R. Lopes. “Temperature dependence of phase and spike synchronization of neural networks”, Chaos, Solitons & Fractals 123, 35–42, 2019. (link)
B. R. R. Boaretto, R. C. Budzinski, T. L. Prado, S. R. Lopes. “Mechanism for explosive synchronization of neural networks”, Physical Review E 100 (5), 052301, 2019. (link)
R. C. Budzinski, B. R. R. Boaretto, T. L. Prado, S. R. Lopes. “Synchronization domains in two coupled neural networks”, Communications in Nonlinear Science and Numerical Simulation 75, 140–151, 2019. (link)
R. C. Budzinski, B. R. R. Boaretto, T. L. Prado, S. R. Lopes. “Phase synchronization and intermittent behavior in healthy and Alzheimer-affected human-brain-based neural network”, Physical Review E 99 (2), 022402, 2019. (link)
B. R. R. Boaretto, R. C. Budzinski, T. L. Prado, S. R. Lopes. “Protocol for suppression of phase synchronization in Hodgkin-Huxley-type networks”, Physica A 528, 121388, 2019. (link)
R. C. Budzinski, B. R. R. Boaretto, T. L. Prado, S. R. Lopes. “Investigation of details in the transition to synchronization in complex networks by using recurrence analysis”, Mathematical and Computational Applications 24 (2), 42, 2019. (link)
B. R. R. Boaretto, R. C. Budzinski, T. L. Prado, S. R. Lopes. “Suppression of phase synchronization in scale-free neural networks using external pulsed current protocols”, Mathematical and Computational Applications 24 (2), 46, 2019. (link)
2018
R. C. Budzinski, B. R. R. Boaretto, K. L. Rossi, T. L. Prado, J. Kurths, S. R. Lopes. “Nonstationary transition to phase synchronization of neural networks induced by the coupling architecture”, Physica A 507, 321–334, 2018. (link)
B. R. R. Boaretto, R. C. Budzinski, T. L. Prado, J. Kurths, S. R. Lopes. “Neuron dynamics variability and anomalous phase synchronization of neural networks”, Chaos 28 (10), 106304, 2018. (link)
2017
R. C. Budzinski, B. R. R. Boaretto, T. L. Prado, S. R. Lopes. “Detection of nonstationary transition to synchronized states of a neural network using recurrence analyses”, Physical Review E 96 (1), 012320, 2017. (link)
* equal contribution (co-first author)