@article{MTMT:35600391,
	title = {From deterministic to stochastic: limits of extracting bifurcation diagrams for noisy bistable oscillators with the control-based continuation method},
	url = {https://m2.mtmt.hu/api/publication/35600391},
	author = {Sykora, Henrik Tamás and Beregi, Sándor},
	doi = {10.1007/s11071-024-10522-0},
	journal-iso = {NONLINEAR DYNAM},
	journal = {NONLINEAR DYNAMICS},
	volume = {113},
	unique-id = {35600391},
	issn = {0924-090X},
	abstract = {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.},
	keywords = {Probability density function; Matrix algebra; Perturbation techniques; nonlinear dynamical systems; stochastic systems; Bifurcation diagram; Bifurcation diagram; Stochastic control systems; Vibration analysis; Hopf bifurcation; Subcritical Hopf bifurcation; Subcritical Hopf bifurcation; MATRIX MULTIPLICATION; Deterministics; path integral method; Control-based continuation; stochastics; Control-based continuation (CBC); Noisy systems; Step-matrix multiplication path integral (SMM-PI) method; Bi-stable oscillators; Noisy system; Step-matrix multiplication path integral method},
	year = {2025},
	eissn = {1573-269X},
	pages = {8249-8263},
	orcid-numbers = {Sykora, Henrik Tamás/0000-0003-1034-4387; Beregi, Sándor/0000-0002-3167-9250}
}

@inproceedings{MTMT:33755058,
	title = {Data-driven delay identification with SINDy},
	url = {https://m2.mtmt.hu/api/publication/33755058},
	author = {Köpeczi-Bócz, Ákos Tamás and Sykora, Henrik Tamás and Takács, Dénes},
	booktitle = {Advances in Nonlinear Dynamics, Volume III},
	doi = {10.1007/978-3-031-50635-2_45},
	unique-id = {33755058},
	year = {2024},
	pages = {481-491},
	orcid-numbers = {Sykora, Henrik Tamás/0000-0003-1034-4387; Takács, Dénes/0000-0003-1226-8613}
}

@misc{MTMT:34774873,
	title = {Identifying driver models with reaction time from heavy urban traffic data},
	url = {https://m2.mtmt.hu/api/publication/34774873},
	author = {Köpeczi-Bócz, Ákos Tamás and Sykora, Henrik Tamás and Takács, Dénes},
	unique-id = {34774873},
	year = {2024},
	pages = {1-10},
	orcid-numbers = {Sykora, Henrik Tamás/0000-0003-1034-4387; Takács, Dénes/0000-0003-1226-8613}
}

@article{MTMT:34855016,
	title = {Stochastic dynamics of mechanical systems with impacts via the Step Matrix multiplication based Path Integration method},
	url = {https://m2.mtmt.hu/api/publication/34855016},
	author = {Sykora, Henrik Tamás and Kuske, Rachel and Yurchenko, Daniil},
	doi = {10.1007/s11071-024-09513-y},
	journal-iso = {NONLINEAR DYNAM},
	journal = {NONLINEAR DYNAMICS},
	volume = {112},
	unique-id = {34855016},
	issn = {0924-090X},
	abstract = {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.},
	keywords = {Probability density function; Stochastic differential equations; Nonsmooth dynamics; random dynamical system; Vibroimpact systems; Path integration method; Chapman Kolmogorov equation},
	year = {2024},
	eissn = {1573-269X},
	pages = {9095-9116},
	orcid-numbers = {Sykora, Henrik Tamás/0000-0003-1034-4387}
}

@CONFERENCE{MTMT:35322424,
	title = {Investigating optimal velocity model in urban traffic environment},
	url = {https://m2.mtmt.hu/api/publication/35322424},
	author = {Köpeczi-Bócz, Ákos Tamás and Takács, Dénes and Sykora, Henrik Tamás},
	booktitle = {Online Book of Abstracts of the 11th European Nonlinear Dynamics Conference (ENOC 2024)},
	unique-id = {35322424},
	year = {2024},
	orcid-numbers = {Takács, Dénes/0000-0003-1226-8613; Sykora, Henrik Tamás/0000-0003-1034-4387}
}

@CONFERENCE{MTMT:35667156,
	title = {System Identification with SINDy in Presence of Time-Delay},
	url = {https://m2.mtmt.hu/api/publication/35667156},
	author = {Köpeczi-Bócz, Ákos Tamás and Sykora, Henrik Tamás and Takács, Dénes},
	booktitle = {18th IFAC TDS - Time Delay Systems - Program & Book of abstracts},
	unique-id = {35667156},
	year = {2024},
	orcid-numbers = {Sykora, Henrik Tamás/0000-0003-1034-4387; Takács, Dénes/0000-0003-1226-8613}
}

@CONFERENCE{MTMT:35690868,
	title = {A transition likelihood maximisation approach to identify nonlinear stochastic dynamics},
	url = {https://m2.mtmt.hu/api/publication/35690868},
	author = {Sykora, Henrik Tamás},
	booktitle = {Online Book of Abstracts of the 11th European Nonlinear Dynamics Conference (ENOC 2024)},
	unique-id = {35690868},
	year = {2024},
	orcid-numbers = {Sykora, Henrik Tamás/0000-0003-1034-4387}
}

@CONFERENCE{MTMT:35690922,
	title = {Stochastic characterisation of vibro-impact oscillators with frictional impacts},
	url = {https://m2.mtmt.hu/api/publication/35690922},
	author = {Sykora, Henrik Tamás and Rachel, Kuske and Daniil, Yurchenko},
	booktitle = {Online Book of Abstracts of the 11th European Nonlinear Dynamics Conference (ENOC 2024)},
	unique-id = {35690922},
	year = {2024},
	orcid-numbers = {Sykora, Henrik Tamás/0000-0003-1034-4387}
}

@article{MTMT:34124575,
	title = {Collocation method for stochastic delay differential equations},
	url = {https://m2.mtmt.hu/api/publication/34124575},
	author = {Fodor, Gergő and Sykora, Henrik Tamás and Bachrathy, Dániel},
	doi = {10.1016/j.probengmech.2023.103515},
	journal-iso = {PROBABILIST ENG MECH},
	journal = {PROBABILISTIC ENGINEERING MECHANICS},
	volume = {74},
	unique-id = {34124575},
	issn = {0266-8920},
	abstract = {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.},
	year = {2023},
	eissn = {1878-4275},
	orcid-numbers = {Fodor, Gergő/0009-0003-5095-489X; Sykora, Henrik Tamás/0000-0003-1034-4387; Bachrathy, Dániel/0000-0003-1491-1852}
}

@CONFERENCE{MTMT:34137422,
	title = {Időkésés adatalapú identifikációja SINDy algoritmus segı́tségével},
	url = {https://m2.mtmt.hu/api/publication/34137422},
	author = {Köpeczi-Bócz, Ákos Tamás and Sykora, Henrik Tamás and Takács, Dénes},
	booktitle = {XIV. Magyar Mechanikai Konferencia, Az előadások összefoglalói},
	unique-id = {34137422},
	year = {2023},
	pages = {1-2},
	orcid-numbers = {Sykora, Henrik Tamás/0000-0003-1034-4387; Takács, Dénes/0000-0003-1226-8613}
}