TY - JOUR AU - Sykora, Henrik Tamás AU - Beregi, Sándor TI - From deterministic to stochastic: limits of extracting bifurcation diagrams for noisy bistable oscillators with the control-based continuation method JF - NONLINEAR DYNAMICS J2 - NONLINEAR DYNAM VL - 113 PY - 2025 IS - 8 SP - 8249 EP - 8263 PG - 15 SN - 0924-090X DO - 10.1007/s11071-024-10522-0 UR - https://m2.mtmt.hu/api/publication/35600391 ID - 35600391 N1 - First published online: 11 November 2024 Correspondence Address: Beregi, S.; Department of Infectious Disease Epidemiology, United Kingdom; email: s.beregi@imperial.ac.uk Funding details: Nemzeti Kutatási Fejlesztési és Innovációs Hivatal, NKFIH, NKFIH-PD-146459 Funding details: Nemzeti Kutatási Fejlesztési és Innovációs Hivatal, NKFIH Funding details: Medical Research Council, MRC, MR/X020258/1 Funding details: Medical Research Council, MRC Funding text 1: This work was supported by the Hungarian National Research, Development and Innovation Office (Henrik T Sykora: NKFIH-PD-146459) and the MRC Centre for Global Infectious Disease Analysis funded by the UK Medical Research Council (MRC) (Sandor Beregi: MR/X020258/1). AB - Noise limits the information that can be experimentally extracted from dynamical systems. In this study, we review the Control-based Continuation (CBC) approach, which is commonly used for experimental characterisation of nonlinear systems with coexisting stable and unstable steady states. The CBC technique, however, uses a deterministic framework, whereas in practice, almost all measurements are subject to some level of random perturbation, and the underlying dynamical system is inherently noisy. In order to discover what the CBC is capable of extracting from inherently noisy experiments, we study the Hopf normal form with quintic terms with additive noise. The bifurcation diagram of the deterministic core of this system is well-known, therefore the discrepancies introduced by noise can be easily assessed. First, we utilise the Step-Matrix Multiplication based Path Integral (SMM-PI) method to approximate the system’s steady state probability density function (PDF) for different intensity noise perturbations. We associate the local extrema of the resulting PDFs with limit cycles, and compare the resulting bifurcation diagram to those captured by CBC. We show that CBC estimates the bifurcation diagram of the noisy system well for noise intensities varying from small to moderate, and in practice, the amplitudes provided by CBC may be accepted as a ’best guess’ proxy for the vibration amplitudes characteristic to the near periodic solutions in a wide range of experiments. © The Author(s) 2024. LA - English DB - MTMT ER - TY - CHAP AU - Köpeczi-Bócz, Ákos Tamás AU - Sykora, Henrik Tamás AU - Takács, Dénes ED - Lacarbonara, Walter TI - Data-driven delay identification with SINDy T2 - Advances in Nonlinear Dynamics, Volume III PB - Springer CY - Cham SN - 9783031506352 T3 - NODYCON Conference Proceedings Series, ISSN 2730-7689 PY - 2024 SP - 481 EP - 491 PG - 11 DO - 10.1007/978-3-031-50635-2_45 UR - https://m2.mtmt.hu/api/publication/33755058 ID - 33755058 LA - English DB - MTMT ER - TY - GEN AU - Köpeczi-Bócz, Ákos Tamás AU - Sykora, Henrik Tamás AU - Takács, Dénes TI - Identifying driver models with reaction time from heavy urban traffic data PY - 2024 SP - 1 EP - 10 PG - 10 UR - https://m2.mtmt.hu/api/publication/34774873 ID - 34774873 LA - English DB - MTMT ER - TY - JOUR AU - Sykora, Henrik Tamás AU - Kuske, Rachel AU - Yurchenko, Daniil TI - Stochastic dynamics of mechanical systems with impacts via the Step Matrix multiplication based Path Integration method JF - NONLINEAR DYNAMICS J2 - NONLINEAR DYNAM VL - 112 PY - 2024 IS - 11 SP - 9095 EP - 9116 PG - 22 SN - 0924-090X DO - 10.1007/s11071-024-09513-y UR - https://m2.mtmt.hu/api/publication/34855016 ID - 34855016 AB - In this work we propose the Step Matrix Multiplication based Path Integration method (SMM-PI) for nonlinear vibro-impact oscillator systems. This method allows the efficient and accurate deterministic computation of the time-dependent response probability density function by transforming the corresponding Chapman–Kolmogorov equation to a matrix–vector multiplication using high-order numerical time-stepping and interpolation methods. Additionally, the SMM-PI approach yields the computation of the joint probability distribution for response and impact velocity, as well as the time between impacts and other important characteristics. The method is applied to a nonlinear oscillator with a pair of impact barriers, and to a linear oscillator with a single barrier, providing relevant densities and analysing energy accumulation and absorption properties. We validate the results with the help of stochastic Monte-Carlo simulations and show the superior ability of the introduced formulation to compute accurate response statistics. LA - English DB - MTMT ER - TY - CONF AU - Köpeczi-Bócz, Ákos Tamás AU - Takács, Dénes AU - Sykora, Henrik Tamás ED - Metrikine, Andrei ED - Alijani, Farbod TI - Investigating optimal velocity model in urban traffic environment T2 - Online Book of Abstracts of the 11th European Nonlinear Dynamics Conference (ENOC 2024) PY - 2024 UR - https://m2.mtmt.hu/api/publication/35322424 ID - 35322424 LA - English DB - MTMT ER - TY - CONF AU - Köpeczi-Bócz, Ákos Tamás AU - Sykora, Henrik Tamás AU - Takács, Dénes TI - System Identification with SINDy in Presence of Time-Delay T2 - 18th IFAC TDS - Time Delay Systems - Program & Book of abstracts PY - 2024 PG - 2 UR - https://m2.mtmt.hu/api/publication/35667156 ID - 35667156 LA - English DB - MTMT ER - TY - CONF AU - Sykora, Henrik Tamás ED - Metrikine, Andrei ED - Alijani, Farbod TI - A transition likelihood maximisation approach to identify nonlinear stochastic dynamics T2 - Online Book of Abstracts of the 11th European Nonlinear Dynamics Conference (ENOC 2024) PY - 2024 UR - https://m2.mtmt.hu/api/publication/35690868 ID - 35690868 LA - English DB - MTMT ER - TY - CONF AU - Sykora, Henrik Tamás AU - Rachel, Kuske AU - Daniil, Yurchenko ED - Metrikine, Andrei ED - Alijani, Farbod TI - Stochastic characterisation of vibro-impact oscillators with frictional impacts T2 - Online Book of Abstracts of the 11th European Nonlinear Dynamics Conference (ENOC 2024) PY - 2024 UR - https://m2.mtmt.hu/api/publication/35690922 ID - 35690922 LA - English DB - MTMT ER - TY - JOUR AU - Fodor, Gergő AU - Sykora, Henrik Tamás AU - Bachrathy, Dániel TI - Collocation method for stochastic delay differential equations JF - PROBABILISTIC ENGINEERING MECHANICS J2 - PROBABILIST ENG MECH VL - 74 PY - 2023 PG - 8 SN - 0266-8920 DO - 10.1016/j.probengmech.2023.103515 UR - https://m2.mtmt.hu/api/publication/34124575 ID - 34124575 N1 - Funding Agency and Grant Number: Hungar-ian Scientific Research Fund [OTKA FK-138500] Funding text: The research leading to these results was supported by the Hungar-ian Scientific Research Fund (OTKA FK-138500) . AB - In this work, we present a collocation-based numerical approach for handling stochastic delay differential equations. We approximate the solution function, and after that, we carry out integrations between the predefined collocation points to achieve a mapping from the delayed state to the present state. We build the first and second moment mapping matrices based on the mapping, and we utilize the matrices to approximate the stationary first and second moments and their stability. Numerical studies of a first and second-order stochastic delay differential equation show the convergence and time complexity of the stochastic collocation method. The last section covers the issues and possible further improvements of the method. LA - English DB - MTMT ER - TY - CONF AU - Köpeczi-Bócz, Ákos Tamás AU - Sykora, Henrik Tamás AU - Takács, Dénes ED - Baksa, Attila ED - Bertóti, Edgár ED - Kiss, László Péter TI - Időkésés adatalapú identifikációja SINDy algoritmus segı́tségével T2 - XIV. Magyar Mechanikai Konferencia, Az előadások összefoglalói PB - Miskolci Egyetem, Gépészmérnöki és Informatikai Kar C1 - Miskolc-Egyetemváros SN - 9789633583012 PY - 2023 SP - 1 PG - 1 UR - https://m2.mtmt.hu/api/publication/34137422 ID - 34137422 LA - Hungarian DB - MTMT ER -