Publications | Siyuan (Simon) Xing

2026

Data-driven discovery of high-dimensional dynamical systems with sparse interpretable neural networks

S. Xing, Q. Han^*, E. G. Charalampidis, and Y.-C. Lai

PRX Intelligence, vol. 1, no. 1, Art. 013024 (2026).

Featured on the official APS X account

@article{Xing2026DataDriven,
  author = {Xing, Siyuan and Han, Qingyu and Charalampidis, Efstathios G. and Lai, Ying-Cheng},
  title = {Data-driven discovery of high-dimensional dynamical systems with sparse interpretable neural networks},
  journal = {PRX Intelligence},
  year = {2026},
  month = sep,
  volume = {1},
  pages = {013024},
  doi = {10.1103/pdkf-98zb},
  number = {1}
}

Sparse semi-interpretable networks for discovering nonlinear dynamics with time-varying parameters and switching structures

B. Xiao^*, J. Huang, and S. Xing

Chaos, Solitons & Fractals, vol. 212, Art. 119017 (2026).

DOI Bib PDF

@article{Xiao2026Sparse,
  author = {Xiao, Binghang and Huang, Jianzhe and Xing, Siyuan},
  title = {Sparse semi-interpretable networks for discovering nonlinear dynamics with time-varying parameters and switching structures},
  journal = {Chaos, Solitons {&} Fractals},
  year = {2026},
  volume = {212},
  pages = {119017},
  doi = {10.1016/j.chaos.2026.119017},
}

2025

Sparse separable Gaussian neural network for interpretable learning of stationary solutions of Fokker–Planck–Kolmogorov equations

W. Yu^*, Y. Xu, X. Wang, L. Hong, J. Jiang, and S. Xing

Nonlinear Dynamics, vol. 113, no. 21, pp. 28961–28982 (2025).

DOI Bib

@article{Yu2025Sparse,
  author = {Yu, W. and Xu, Y. and Wang, X. and Hong, L. and Jiang, J. and Xing, S.},
  title = {Sparse separable Gaussian neural network for interpretable learning of stationary solutions of Fokker--Planck--Kolmogorov equations},
  journal = {Nonlinear Dynamics},
  year = {2025},
  doi = {10.1007/s11071-025-11602-5},
  volume = {113},
  pages = {28961--28982},
  number = {21}
}

CombOpNet: a Neural-network Accelerator for SINDy

S. Xing, Q. Han^*, and E. Charalampidis

Journal of Vibration Testing and System Dynamics, vol. 9, no. 1, pp. 1–20 (2025).

DOI Bib PDF

@article{CombOpNetVTSD2025,
  author = {Xing, Siyuan and Han, Qingyu and Charalampidis, Efstathios},
  title = {CombOpNet: a Neural-network Accelerator for SINDy},
  journal = {Journal of Vibration Testing and System Dynamics},
  year = {2025},
  volume = {9},
  pages = {1--20},
  doi = {10.5890/JVTSD.2025.03.001},
  number = {1}
}

2024

Time-Embedding GRBFNN: Learning Transient Response of Stochastic Dynamical Systems

S. Xing and J. Sun

In ASME International Design Engineering Technical Conferences and Computers and Information in Engineering Conference, vol. 9, Paper V009T09A002, Washington, D.C., USA (2024).

DOI Bib

@inproceedings{IDETC2024,
  title = {Time-Embedding GRBFNN: Learning Transient Response of Stochastic Dynamical Systems},
  author = {Xing, Siyuan and Sun, Jianqiao},
  booktitle = {ASME International Design Engineering Technical Conferences and Computers and Information in Engineering Conference},
  year = {2024},
  month = aug,
  address = {Washington, D.C., USA},
  doi = {10.1115/DETC2024-143365},
  publisher = {ASME},
  pages = {V009T09A002},
  volume = {9}
}

Radial Basis Function Neural Networks for Optimal Control with Model Reduction and Transfer Learning

A. Zhao^*, S. Xing, X. Wang, and J.-Q. Sun

Engineering Applications of Artificial Intelligence, vol. 136, Art. 108899 (2024).

DOI Bib

@article{ZHAO2024108899,
  title = {Radial Basis Function Neural Networks for Optimal Control with Model Reduction and Transfer Learning},
  journal = {Engineering Applications of Artificial Intelligence},
  volume = {136},
  pages = {108899},
  year = {2024},
  author = {Zhao, Anni and Xing, Siyuan and Wang, Xi and Sun, Jian-Qiao},
  doi = {10.1016/j.engappai.2024.108899}
}

Separable Gaussian Neural Networks for High-dimensional Nonlinear Stochastic Systems

X. Wang^*, S. Xing, J. Jiang, L. Hong, and J.-Q. Sun

Probabilistic Engineering Mechanics, vol. 76, Art. 103594 (2024).

DOI Bib PDF

@article{WangSGNNFPK2024,
  title = {Separable Gaussian Neural Networks for High-dimensional Nonlinear Stochastic Systems},
  author = {Wang, Xi and Xing, Siyuan and Jiang, Jun and Hong, Ling and Sun, Jian-Qiao},
  year = {2024},
  volume = {76},
  pages = {103594},
  journal = {Probabilistic Engineering Mechanics},
  doi = {10.1016/j.probengmech.2024.103594},
}

Learning Traveling Solitary Waves Using Separable Gaussian Neural Networks

S. Xing and E. G. Charalampidis

Entropy, vol. 26, no. 5, Art. 396 (2024).

DOI Bib

@article{XINGTravelingSoliton2024,
  title = {Learning Traveling Solitary Waves Using Separable Gaussian Neural Networks},
  author = {Xing, Siyuan and Charalampidis, Efstathios G},
  year = {2024},
  journal = {Entropy},
  volume = {26},
  doi = {10.3390/e26050396},
  number = {5},
  pages = {396}
}

2023

Spikes Adding to Infinity on Period-1 Orbits to Chaos in the Rössler System

S. Xing and A. C. J. Luo

International Journal of Bifurcation and Chaos, vol. 33, no. 13, Art. 2330033 (2023).

DOI Bib

@article{XingandXINGSpikeAdding2023,
  title = {Spikes Adding to Infinity on Period-1 Orbits to Chaos in the R\"ossler System},
  author = {Xing, Siyuan and Luo, Albert C. J.},
  year = {2023},
  volume = {33},
  pages = {2330033},
  journal = {International Journal of Bifurcation and Chaos},
  doi = {10.1142/S0218127423300331},
  url = {https://www.worldscientific.com/doi/abs/10.1142/S0218127423300331},
  number = {13}
}

Separable Gaussian Neural Networks: Structure, Analysis, and Function Approximations

S. Xing and J. Sun

Algorithms, vol. 16, no. 10, Art. 453 (2023).

DOI Bib PDF

@article{XingandSunSGNN2023,
  title = {Separable Gaussian Neural Networks: Structure, Analysis, and Function Approximations},
  author = {Xing, Siyuan and Sun, Jianqiao},
  year = {2023},
  volume = {16},
  pages = {453},
  journal = {Algorithms},
  doi = {10.3390/a16100453},
  url = {https://doi.org/10.3390/a16100453},
  number = {10}
}

Period-1 Motions to Twin Spiral Homoclinic Orbits in the Rössler System

S. Xing and A. C. J. Luo

Journal of Computational and Nonlinear Dynamics, vol. 18, no. 8, Art. 081008 (2023).

DOI Bib

@article{XingandLuoJCND2023,
  title = {Period-1 Motions to Twin Spiral Homoclinic Orbits in the R\"ossler System},
  author = {Xing, Siyuan and Luo, Albert C. J.},
  year = {2023},
  volume = {18},
  pages = {081008},
  journal = {Journal of Computational and Nonlinear Dynamics},
  doi = {10.1115/1.4062201},
  url = {https://doi.org/10.1115/1.4062201},
  number = {8}
}

Breathers in Lattices with Alternating Strain-hardening and Strain-softening Interactions

M. M. Lee^*, E. G. Charalampidis, S. Xing, C. Chong, and P. Kevrekidis

Physical Review E, vol. 107, no. 5, Art. 054208 (2023).

DOI Bib

@article{PRLLeeLattice2023,
  title = {Breathers in Lattices with Alternating Strain-hardening and Strain-softening Interactions},
  author = {Lee, Marisa M. and Charalampidis, Efstathios G. and Xing, Siyuan and Chong, Chris and Kevrekidis, Panayotis},
  year = {2023},
  volume = {107},
  pages = {054208},
  numpages = {18},
  journal = {Physical Review E},
  doi = {10.1103/PhysRevE.107.054208},
  url = {https://doi.org/10.1103/PhysRevE.107.054208},
  number = {5}
}

Impulse Response of an Elastic Rod with a Mass-damper-spring Termination

S. Xing and J. Sun

Journal of Vibration Testing and System Dynamics, vol. 7, no. 2, pp. 169–186 (2023).

DOI Bib

@article{JVSTD2023XingandSun,
  title = {Impulse Response of an Elastic Rod with a Mass-damper-spring Termination},
  author = {Xing, Siyuan and Sun, Jianqiao},
  year = {2023},
  volume = {7},
  pages = {169--186},
  journal = {Journal of Vibration Testing and System Dynamics},
  doi = {10.5890/JVTSD.2023.06.005},
  url = {https://www.lhscientificpublishing.com/Journals/articles/DOI-10.5890-JVTSD.2023.06.005.aspx},
  number = {2}
}

Mathematical Modeling and System Identification of a Piezo-actuated, Cantilever Beam with Interferometric Measurement

J. Kochavi^* and S. Xing

Journal of Vibration Testing and System Dynamics, vol. 7, no. 4, pp. 447–461 (2023).

DOI Bib

@article{JVSTD2023XingandKochavi,
  title = {Mathematical Modeling and System Identification of a Piezo-actuated, Cantilever Beam with Interferometric Measurement},
  author = {Kochavi, Jordan and Xing, Siyuan},
  year = {2023},
  volume = {7},
  pages = {447--461},
  journal = {Journal of Vibration Testing and System Dynamics},
  doi = {10.5890/JVTSD.2023.12.004},
  url = {https://www.lhscientificpublishing.com/Journals/articles/DOI-10.5890-JVTSD.2023.12.004.aspx},
  number = {4}
}

2022

Coexisting Unstable Periodic Motions in the Rössler System

S. Xing and A. C. J. Luo

In ASME International Mechanical Engineering Congress and Exposition, vol. 5, Paper V005T07A101, Columbus, OH, USA (2022).

DOI Bib

@inproceedings{IMECE2022-1,
  title = {Coexisting Unstable Periodic Motions in the R\"ossler System},
  author = {Xing, Siyuan and Luo, Albert C. J.},
  booktitle = {ASME International Mechanical Engineering Congress and Exposition},
  year = {2022},
  month = oct,
  address = {Columbus, OH, USA},
  doi = {10.1115/IMECE2022-95826},
  publisher = {ASME},
  pages = {V005T07A101},
  volume = {5}
}

Mathematical Modelling of a Piezo-Actuated Cantilever Beam with Interferometer Feedback

J. Kochavi and S. Xing

In ASME International Mechanical Engineering Congress and Exposition, vol. 5, Paper V005T07A100, Columbus, OH, USA (2022).

DOI Bib

@inproceedings{IMECE2022-2,
  title = {Mathematical Modelling of a Piezo-Actuated Cantilever Beam with Interferometer Feedback},
  author = {Kochavi, Jordan and Xing, Siyuan},
  booktitle = {ASME International Mechanical Engineering Congress and Exposition},
  year = {2022},
  month = oct,
  address = {Columbus, OH, USA},
  doi = {10.1115/IMECE2022-95819},
  publisher = {ASME},
  pages = {V005T07A100},
  volume = {5}
}

Period-1 Motions to Homoclinic Orbits in the Rössler System

S. Xing and A. C. J. Luo

In ASME International Design Engineering Technical Conferences and Computers and Information in Engineering Conference, vol. 9, Paper V009T09A021, St. Louis, MO, USA (2022).

DOI Bib

@inproceedings{IDETC2022-1,
  title = {Period-1 Motions to Homoclinic Orbits in the R\"ossler System},
  author = {Xing, Siyuan and Luo, Albert C. J.},
  booktitle = {ASME International Design Engineering Technical Conferences and Computers and Information in Engineering Conference},
  year = {2022},
  month = aug,
  address = {St. Louis, MO, USA},
  doi = {10.1115/DETC2022-91029},
  publisher = {ASME},
  pages = {V009T09A021},
  volume = {9}
}

Multi-objective Optimization of an Elastic Rod with Viscous Termination

S. Xing and J. Sun

Mathematical and Computational Applications, vol. 27, no. 6, Art. 94 (2022).

DOI Bib

@article{MCJ2022XingandSun,
  title = {Multi-objective Optimization of an Elastic Rod with Viscous Termination},
  author = {Xing, Siyuan and Sun, Jianqiao},
  year = {2022},
  journal = {Mathematical and Computational Applications},
  volume = {27},
  pages = {94},
  doi = {10.3390/mca27060094},
  url = {https://doi.org/10.3390/mca27060094},
  number = {6}
}

On an Origami Structure of Period-1 Motions to Homoclinic Orbits in the Rössler System

S. Xing and A. C. J. Luo

Chaos: An Interdisciplinary Journal of Nonlinear Science, vol. 32, no. 12, Art. 123121 (2022).

DOI Bib PDF

@article{XingandLuoChaos2022,
  title = {On an Origami Structure of Period-1 Motions to Homoclinic Orbits in the R\"ossler System},
  author = {Xing, Siyuan and Luo, Albert C. J.},
  year = {2022},
  journal = {Chaos: An Interdisciplinary Journal of Nonlinear Science},
  volume = {32},
  pages = {123121},
  doi = {10.1063/5.0131970},
  url = {https://doi.org/10.1063/5.0131970},
  number = {12}
}

Modeling and Control of the Locomotion of a Monopod Robot Mounted to a Vertical Slider

S. Xing, B. Kwan^*, and P. Duan

Journal of Vibration Testing and System Dynamics, vol. 6, no. 4, pp. 413–430 (2022).

DOI Bib

@article{JVTSD2022,
  title = {Modeling and Control of the Locomotion of a Monopod Robot Mounted to a Vertical Slider},
  author = {Xing, Siyuan and Kwan, Bradley and Duan, Pengji},
  year = {2022},
  volume = {6},
  pages = {413--430},
  journal = {Journal of Vibration Testing and System Dynamics},
  doi = {10.5890/JVTSD.2022.12.005},
  url = {https://www.lhscientificpublishing.com/Journals/articles/DOI-10.5890-JVTSD.2022.12.005.aspx},
  number = {4}
}

Periodic Cutting Motions in a Vibration-Assisted, Regenerative, Nonlinear Orthogonal Turning System

S. Xing and A. C. J. Luo

International Journal of Dynamics and Control, vol. 10, no. 1, pp. 1–12 (2022).

DOI Bib

@article{IJDC2021,
  title = {Periodic Cutting Motions in a Vibration-Assisted, Regenerative, Nonlinear Orthogonal Turning System},
  author = {Xing, Siyuan and Luo, Albert C. J.},
  year = {2022},
  volume = {10},
  pages = {1--12},
  journal = {International Journal of Dynamics and Control},
  doi = {10.1007/s40435-021-00779-3},
  url = {https://doi.org/10.1007/s40435-021-00779-3},
  number = {1}
}

2021

A Sequential Order of Periodic Motions in a 1-Dimensional, Time-Delay, Dynamical System

S. Xing and A. C. J. Luo

In Nonlinear Dynamics, Chaos, and Complexity: In Memory of Valentin Afraimovich (1945–2018), edited by Volchenkov, Dimitri, Nonlinear Physical Science, pp. 95–112, Springer, Cham (2021).

DOI Bib

@inbook{ValentinChapter,
  title = {A Sequential Order of Periodic Motions in a 1-Dimensional, Time-Delay, Dynamical System},
  author = {Xing, Siyuan and Luo, Albert C. J.},
  booktitle = {Nonlinear Dynamics, Chaos, and Complexity: In Memory of Valentin Afraimovich (1945--2018)},
  year = {2021},
  pages = {95--112},
  editor = {Volchenkov, Dimitri},
  series = {Nonlinear Physical Science},
  publisher = {Springer, Cham},
  doi = {10.1007/978-981-15-9034-4_7},
}

Controlling the Dynamics of a Quadratic Oscillator Using Infinite-Equilibrium

S. Xing and A. C. J. Luo

In ASME International Mechanical Engineering Congress and Exposition, vol. 7B, Paper V07BT07A049, Online, USA (2021).

DOI Bib

@inproceedings{IMECE2021-1,
  title = {Controlling the Dynamics of a Quadratic Oscillator Using Infinite-Equilibrium},
  author = {Xing, Siyuan and Luo, Albert C. J.},
  booktitle = {ASME International Mechanical Engineering Congress and Exposition},
  year = {2021},
  month = nov,
  address = {Online, USA},
  doi = {10.1115/IMECE2021-71998},
  publisher = {ASME},
  pages = {V07BT07A049},
  volume = {7B}
}

Understanding Dynamics of Infinite-Equilibrium Systems via a Quadratic Nonlinear System

S. Xing and A. C. J. Luo

Journal of Vibration Testing and System Dynamics, vol. 5, no. 2, pp. 131–147 (2021).

DOI Bib

@article{JVTSD2021,
  title = {Understanding Dynamics of Infinite-Equilibrium Systems via a Quadratic Nonlinear System},
  author = {Xing, Siyuan and Luo, Albert C. J.},
  year = {2021},
  volume = {5},
  pages = {131--147},
  journal = {Journal of Vibration Testing and System Dynamics},
  doi = {10.5890/JVTSD.2021.06.003},
  url = {https://www.lhscientificpublishing.com/Journals/articles/DOI-10.5890-JVTSD.2021.06.003.aspx},
  number = {2}
}

Sequential Periodic Motions in a Vibration-Assisted, Regenerative, Nonlinear Turning-Tool System

S. Xing and A. C. J. Luo

International Journal of Bifurcation and Chaos, vol. 31, no. 12, Art. 2150186 (2021).

DOI Bib

@article{IJBC2021,
  title = {Sequential Periodic Motions in a Vibration-Assisted, Regenerative, Nonlinear Turning-Tool System},
  author = {Xing, Siyuan and Luo, Albert C. J.},
  year = {2021},
  volume = {31},
  pages = {2150186},
  journal = {International Journal of Bifurcation and Chaos},
  doi = {10.1142/S0218127421501868},
  url = {https://doi.org/10.1142/S0218127421501868},
  number = {12}
}

2020

Sequential Bifurcation Trees to Chaos in Nonlinear Time-delay Systems

S. Xing and A. C. J. Luo

Springer, Cham (2020).

DOI Bib

@book{SBTCINTSbook,
  author = {Xing, Siyuan and Luo, Albert C. J.},
  title = {Sequential Bifurcation Trees to Chaos in Nonlinear Time-delay Systems},
  publisher = {Springer, Cham},
  year = {2020},
  doi = {10.1007/978-3-031-79669-2},
}

On the Dynamics of a Quadratic-oscillator-based, Infinite-equilibrium System

S. Xing, A. C. J. Luo, and J. Huang

In ASME International Design Engineering Technical Conferences and Computers and Information in Engineering Conference, vol. 2, Paper V002T02A040, Online, USA (2020).

DOI Bib

@inproceedings{IDETC2020-1,
  title = {On the Dynamics of a Quadratic-oscillator-based, Infinite-equilibrium System},
  author = {Xing, Siyuan and Luo, Albert C. J. and Huang, Jianzhe},
  booktitle = {ASME International Design Engineering Technical Conferences and Computers and Information in Engineering Conference},
  year = {2020},
  month = aug,
  address = {Online, USA},
  doi = {10.1115/DETC2020-22233},
  publisher = {ASME},
  pages = {V002T02A040},
  volume = {2}
}

Discontinuous Dynamics and Bifurcation for Morphing Aircraft Switching on the Velocity Boundary

J. Huang, X. Fu, Z. Jing, and S. Xing

In ASME International Design Engineering Technical Conferences and Computers and Information in Engineering Conference, vol. 7, Paper V007T07A028, Online, USA (2020).

DOI Bib

@inproceedings{IDETC2020-2,
  title = {Discontinuous Dynamics and Bifurcation for Morphing Aircraft Switching on the Velocity Boundary},
  author = {Huang, Jianzhe and Fu, Xilin and Jing, Zhongliang and Xing, Siyuan},
  booktitle = {ASME International Design Engineering Technical Conferences and Computers and Information in Engineering Conference},
  year = {2020},
  month = aug,
  address = {Online, USA},
  doi = {10.1115/DETC2020-22008},
  publisher = {ASME},
  pages = {V007T07A028},
  volume = {7}
}

On the Analytical Modeling of a Resonant Fatigue Testing Rig

L. Chen^*, S. Xing, and X. Xiong

Journal of Vibration Testing and System Dynamics, vol. 4, no. 4, pp. 389–399 (2020).

DOI Bib

@article{JVSTDFATIGUE2020,
  title = {On the Analytical Modeling of a Resonant Fatigue Testing Rig},
  author = {Chen, Leilei and Xing, Siyuan and Xiong, Xingzhong},
  year = {2020},
  pages = {389--399},
  volume = {4},
  journal = {Journal of Vibration Testing and System Dynamics},
  doi = {10.5890/JVTSD.2020.12.007},
  url = {https://www.lhscientificpublishing.com/journals/articles/DOI-10.5890-JVTSD.2020.12.007.aspx},
  number = {4}
}

On Period-1 Motions to Chaos in a 1-dimensional, Time-delay, Nonlinear System

S. Xing and A. C. J. Luo

International Journal of Dynamics and Control, vol. 8, no. 1, pp. 44–50 (2020).

DOI Bib

@article{IJDC1DTIMEDELAY2019,
  title = {On Period-1 Motions to Chaos in a 1-dimensional, Time-delay, Nonlinear System},
  author = {Xing, Siyuan and Luo, Albert C. J.},
  year = {2020},
  pages = {44--50},
  journal = {International Journal of Dynamics and Control},
  doi = {10.1007/s40435-019-00546-5},
  url = {https://doi.org/10.1007/s40435-019-00546-5},
  number = {1},
  volume = {8}
}

2019

Period-1 Motions in a Periodically Forced, Nonlinear, Machine-tool System

S. Xing and A. C. J. Luo

In ASME International Mechanical Engineering Congress and Exposition, vol. 4, Paper V004T05A092, Salt Lake City, Utah, USA (2019).

DOI Bib

@inproceedings{IMECE2019,
  title = {Period-1 Motions in a Periodically Forced, Nonlinear, Machine-tool System},
  author = {Xing, Siyuan and Luo, Albert C. J.},
  booktitle = {ASME International Mechanical Engineering Congress and Exposition},
  year = {2019},
  month = nov,
  address = {Salt Lake City, Utah, USA},
  doi = {10.1115/IMECE2019-10771},
  publisher = {ASME},
  pages = {V004T05A092},
  volume = {4}
}

Regenerative Cutting Dynamics for a Periodically Forced Machine-tool System

S. Xing and A. C. J. Luo

In ASME International Design Engineering Technical Conferences and Computers and Information in Engineering Conference, vol. 8, Paper V008T10A031, Anaheim, California, USA (2019).

DOI Bib

@inproceedings{IDETC2019,
  title = {Regenerative Cutting Dynamics for a Periodically Forced Machine-tool System},
  author = {Xing, Siyuan and Luo, Albert C. J.},
  booktitle = {ASME International Design Engineering Technical Conferences and Computers and Information in Engineering Conference},
  year = {2019},
  month = aug,
  address = {Anaheim, California, USA},
  doi = {10.1115/DETC2019-97262},
  publisher = {ASME},
  pages = {V008T10A031},
  volume = {8}
}

Periodic Motions to Chaos in a 1-dimensional, Time-delay, Nonlinear System

S. Xing and A. C. J. Luo

The European Physical Journal Special Topics, vol. 228, no. 9, pp. 1747–1765 (2019).

DOI Bib

@article{PM1DEUROJOUR2019,
  title = {Periodic Motions to Chaos in a 1-dimensional, Time-delay, Nonlinear System},
  author = {Xing, Siyuan and Luo, Albert C. J.},
  year = {2019},
  pages = {1747--1765},
  volume = {228},
  journal = {The European Physical Journal Special Topics},
  doi = {10.1140/epjst/e2019-800243-y},
  url = {https://doi.org/10.1140/epjst/e2019-800243-y},
  number = {9}
}

On a Global Sequential Scenario of Bifurcation Trees to Chaos in a First-Order, Periodically Excited, Time-Delayed System

S. Xing and A. C. J. Luo

International Journal of Bifurcation and Chaos, vol. 29, no. 10, Art. 1950141 (2019).

DOI Bib

@article{JOURNALOFBIFURCATION2019,
  title = {On a Global Sequential Scenario of Bifurcation Trees to Chaos in a First-Order, Periodically Excited, Time-Delayed System},
  author = {Xing, Siyuan and Luo, Albert C. J.},
  year = {2019},
  pages = {1950141},
  volume = {29},
  journal = {International Journal of Bifurcation and Chaos},
  doi = {10.1142/S0218127419501414},
  url = {https://doi.org/10.1142/S0218127419501414},
  number = {10}
}

Bifurcation Trees of Period-1 Motions in a Periodically Excited, Softening Duffing Oscillator with Time-delay

S. Xing and A. C. J. Luo

International Journal of Dynamics and Control, vol. 7, no. 3, pp. 842–855 (2019).

DOI Bib

@article{SOFTNONDYNC2018,
  title = {Bifurcation Trees of Period-1 Motions in a Periodically Excited, Softening Duffing Oscillator with Time-delay},
  author = {Xing, Siyuan and Luo, Albert C. J.},
  year = {2019},
  pages = {842--855},
  volume = {7},
  journal = {International Journal of Dynamics and Control},
  doi = {10.1007/s40435-019-00520-1},
  url = {https://doi.org/10.1007/s40435-019-00520-1},
  number = {3}
}

2018

Bifurcation Trees of Period-3 Motions to Chaos in a Time-delayed Duffing Oscillator

A. C. J. Luo and S. Xing

In Regularity and Stochasticity of Nonlinear Dynamical Systems, edited by Volchenkov, Dimitri and Leoncini, Xavier, vol. 21, pp. 247–262, Springer, Cham (2018).

DOI Bib

@inbook{RSNDSChapter,
  title = {Bifurcation Trees of Period-3 Motions to Chaos in a Time-delayed Duffing Oscillator},
  author = {Luo, Albert C. J. and Xing, Siyuan},
  booktitle = {Regularity and Stochasticity of Nonlinear Dynamical Systems},
  year = {2018},
  editor = {Volchenkov, Dimitri and Leoncini, Xavier},
  volume = {21},
  pages = {247--262},
  publisher = {Springer, Cham},
  doi = {10.1007/978-3-319-58062-3_10},
}

Time-delay Effects on Periodic Motions in a Duffing Oscillator

A. C. J. Luo and S. Xing

In Chaotic, Fractional, and Complex Dynamics: New Insights and Perspectives, edited by Edelman, Mark and Macau, Elbert E. N. and Sanjuan, Miguel A. F, Understanding Complex Systems, pp. 77–100, Springer, Cham (2018).

DOI Bib

@inbook{CFCDChapter,
  title = {Time-delay Effects on Periodic Motions in a Duffing Oscillator},
  author = {Luo, Albert C. J. and Xing, Siyuan},
  booktitle = {Chaotic, Fractional, and Complex Dynamics: New Insights and Perspectives},
  year = {2018},
  editor = {Edelman, Mark and Macau, Elbert E. N. and Sanjuan, Miguel A. F},
  pages = {77--100},
  series = {Understanding Complex Systems},
  publisher = {Springer, Cham},
  doi = {10.1007/978-3-319-68109-2_5},
}

Periodic Motions in a First-Order, Time-Delayed, Nonlinear System

S. Xing and A. C. J. Luo

In ASME International Mechanical Engineering Congress and Exposition, vol. 4B, Paper V04BT06A026, Pittsburgh, Pennsylvania, USA (2018).

DOI Bib

@inproceedings{IMECE2018,
  title = {Periodic Motions in a First-Order, Time-Delayed, Nonlinear System},
  author = {Xing, Siyuan and Luo, Albert C. J.},
  booktitle = {ASME International Mechanical Engineering Congress and Exposition},
  year = {2018},
  month = nov,
  address = {Pittsburgh, Pennsylvania, USA},
  doi = {10.1115/IMECE2018-86824},
  volume = {4B},
  pages = {V04BT06A026},
  publisher = {ASME}
}

On Possible Infinite Bifurcation Trees of Period-3 Motions to Chaos in a Time-delayed, Twin-well Duffing Oscillator

S. Xing and A. C. J. Luo

International Journal of Dynamics and Control, vol. 6, no. 4, pp. 1429–1464 (2018).

DOI Bib

@article{IJDC2018,
  title = {On Possible Infinite Bifurcation Trees of Period-3 Motions to Chaos in a Time-delayed, Twin-well Duffing Oscillator},
  author = {Xing, Siyuan and Luo, Albert C. J.},
  year = {2018},
  url = {https://doi.org/10.1007/s40435-018-0418-y},
  pages = {1429--1464},
  volume = {6},
  journal = {International Journal of Dynamics and Control},
  doi = {10.1007/s40435-018-0418-y},
  number = {4}
}

2017

Analytical Prediction of Period-1 Motions in a Time-delayed, Softening Duffing Oscillator

A. C. J. Luo and S. Xing

In ASME International Mechanical Engineering Congress and Exposition, vol. 4B, Paper V04BT05A029, Tampa, Florida, USA (2017).

DOI Bib

@inproceedings{IMECE2017,
  title = {Analytical Prediction of Period-1 Motions in a Time-delayed, Softening Duffing Oscillator},
  author = {Luo, Albert C. J. and Xing, Siyuan},
  booktitle = {ASME International Mechanical Engineering Congress and Exposition},
  year = {2017},
  month = nov,
  address = {Tampa, Florida, USA},
  doi = {10.1115/IMECE2017-70824},
  publisher = {ASME},
  pages = {V04BT05A029},
  volume = {4B}
}

Period-3 Motions in a Periodically Forced, Damped, Double-well Duffing Oscillator with Time-delay

A. C. J. Luo and S. Xing

In ASME International Design Engineering Technical Conferences and Computers and Information in Engineering Conference, vol. 6, Paper V006T10A062, Cleveland, Ohio, USA (2017).

DOI Bib

@inproceedings{IDETC2017,
  title = {Period-3 Motions in a Periodically Forced, Damped, Double-well Duffing Oscillator with Time-delay},
  author = {Luo, Albert C. J. and Xing, Siyuan},
  booktitle = {ASME International Design Engineering Technical Conferences and Computers and Information in Engineering Conference},
  year = {2017},
  month = aug,
  address = {Cleveland, Ohio, USA},
  doi = {10.1115/DETC2017-67210},
  publisher = {ASME},
  pages = {V006T10A062},
  volume = {6}
}

Towards Infinite Bifurcation Trees of Period-1 Motions to Chaos in a Time-Delayed, Twin-Well Duffing Oscillator

S. Xing and A. C. J. Luo

Journal of Vibration Testing and System Dynamics, vol. 1, no. 4, pp. 353–392 (2017).

DOI Bib

@article{TIBTP1MTTD,
  title = {Towards Infinite Bifurcation Trees of Period-1 Motions to Chaos in a Time-Delayed, Twin-Well Duffing Oscillator},
  author = {Xing, Siyuan and Luo, Albert C. J.},
  year = {2017},
  pages = {353--392},
  volume = {1},
  journal = {Journal of Vibration Testing and System Dynamics},
  doi = {10.5890/JVTSD.2017.12.006},
  url = {https://www.lhscientificpublishing.com/journals/articles/DOI-10.5890-JVTSD.2017.12.006.aspx},
  number = {4}
}

Bifurcation Trees of Period-3 Motions to Chaos in a Time-Delayed Duffing Oscillator

A. C. J. Luo and S. Xing

Nonlinear Dynamics, vol. 88, no. 4, pp. 2831–2862 (2017).

DOI Bib

@article{BTP3CTDFO,
  title = {Bifurcation Trees of Period-3 Motions to Chaos in a Time-Delayed Duffing Oscillator},
  author = {Luo, Albert C. J. and Xing, Siyuan},
  year = {2017},
  pages = {2831--2862},
  volume = {88},
  journal = {Nonlinear Dynamics},
  doi = {10.1007/s11071-017-3415-3},
  url = {https://doi.org/10.1007/s11071-017-3415-3},
  number = {4}
}

Time-Delay Effects on Periodic Motions in a Periodically Forced, Time-Delayed, Hardening Duffing Oscillator

A. C. J. Luo and S. Xing

Journal of Vibration Testing and System Dynamics, vol. 1, no. 1, pp. 73–91 (2017).

DOI Bib

@article{TDEPMPFTHDO,
  title = {Time-Delay Effects on Periodic Motions in a Periodically Forced, Time-Delayed, Hardening Duffing Oscillator},
  author = {Luo, Albert C. J. and Xing, Siyuan},
  year = {2017},
  pages = {73--91},
  volume = {1},
  journal = {Journal of Vibration Testing and System Dynamics},
  doi = {10.5890/JVTSD.2017.03.006},
  url = {https://www.lhscientificpublishing.com/Journals/articles/DOI-10.5890-JVTSD.2017.03.006.aspx},
  number = {1}
}

On Frequency Responses of Period-1 Motions to Chaos in a Periodically Forced, Time-Delayed Quadratic Nonlinear System

A. C. J. Luo and S. Xing

International Journal of Dynamics and Control, vol. 5, no. 3, pp. 466–476 (2017).

DOI Bib

@article{FRP1PTQNS,
  title = {On Frequency Responses of Period-1 Motions to Chaos in a Periodically Forced, Time-Delayed Quadratic Nonlinear System},
  author = {Luo, Albert C. J. and Xing, Siyuan},
  year = {2017},
  pages = {466--476},
  volume = {5},
  journal = {International Journal of Dynamics and Control},
  doi = {10.1007/s40435-015-0222-x},
  url = {https://doi.org/10.1007/s40435-015-0222-x},
  number = {3}
}

2016

On Time-Delay Effects on Period-1 Motions in a Periodically Forced, Time-Delayed, Duffing Oscillator

A. C. J. Luo and S. Xing

In ASME International Mechanical Engineering Congress and Exposition, vol. 4B, Paper V04BT05A020, Phoenix, AZ, USA (2016).

DOI Bib

@inproceedings{IMECE2016,
  title = {On Time-Delay Effects on Period-1 Motions in a Periodically Forced, Time-Delayed, Duffing Oscillator},
  author = {Luo, Albert C. J. and Xing, Siyuan},
  booktitle = {ASME International Mechanical Engineering Congress and Exposition},
  year = {2016},
  month = nov,
  address = {Phoenix, AZ, USA},
  doi = {10.1115/IMECE2016-66198},
  publisher = {ASME},
  pages = {V04BT05A020},
  volume = {4B}
}

On Complex Periodic Motions in a Time-delayed, Double-well Duffing Oscillator with Strong Excitation

A. C. J. Luo and S. Xing

In ASME International Design Engineering Technical Conferences and Computers and Information in Engineering Conference, vol. 6, Paper V006T09A068, Charlotte, NC, USA (2016).

DOI Bib

@inproceedings{IDETC2016,
  title = {On Complex Periodic Motions in a Time-delayed, Double-well Duffing Oscillator with Strong Excitation},
  author = {Luo, Albert C. J. and Xing, Siyuan},
  booktitle = {ASME International Design Engineering Technical Conferences and Computers and Information in Engineering Conference},
  year = {2016},
  month = aug,
  address = {Charlotte, NC, USA},
  doi = {10.1115/DETC2016-59343},
  publisher = {ASME},
  pages = {V006T09A068},
  volume = {6}
}

Symmetric and Asymmetric Period-1 Motions in a Periodically Forced, Time-Delayed, Hardening Duffing Oscillator

A. C. J. Luo and S. Xing

Nonlinear Dynamics, vol. 85, no. 2, pp. 1141–1166 (2016).

DOI Bib

@article{SASP1PTHDO,
  title = {Symmetric and Asymmetric Period-1 Motions in a Periodically Forced, Time-Delayed, Hardening Duffing Oscillator},
  author = {Luo, Albert C. J. and Xing, Siyuan},
  year = {2016},
  pages = {1141--1166},
  volume = {85},
  journal = {Nonlinear Dynamics},
  doi = {10.1007/s11071-016-2750-0},
  url = {https://doi.org/10.1007/s11071-016-2750-0},
  number = {2}
}

Multiple Bifurcation Trees of Period-1 Motions to Chaos in a Periodically Forced, Time-Delayed, Hardening Duffing Oscillator

A. C. J. Luo and S. Xing

Chaos, Solitons & Fractals, vol. 89, pp. 405–434 (2016).

DOI Bib

@article{MBTP1PHDO,
  title = {Multiple Bifurcation Trees of Period-1 Motions to Chaos in a Periodically Forced, Time-Delayed, Hardening Duffing Oscillator},
  author = {Luo, Albert C. J. and Xing, Siyuan},
  year = {2016},
  pages = {405--434},
  volume = {89},
  journal = {Chaos, Solitons {&} Fractals},
  doi = {10.1016/j.chaos.2016.02.005},
  url = {https://doi.org/10.1016/j.chaos.2016.02.005},
}

Analytical Predictions of Period-1 Motions to Chaos in a Periodically Driven Quadratic Nonlinear Oscillator with a Time-Delay

A. C. J. Luo and S. Xing

Mathematical Modelling of Natural Phenomena, vol. 11, no. 2, pp. 75–88 (2016).

DOI Bib

@article{AP1PDQNOT,
  title = {Analytical Predictions of Period-1 Motions to Chaos in a Periodically Driven Quadratic Nonlinear Oscillator with a Time-Delay},
  author = {Luo, Albert C. J. and Xing, Siyuan},
  year = {2016},
  pages = {75--88},
  volume = {11},
  journal = {Mathematical Modelling of Natural Phenomena},
  doi = {10.1051/mmnp/201611206},
  url = {https://doi.org/10.1051/mmnp/201611206},
  number = {2}
}

2015

Bifurcation Trees of Period-1 Motions to Chaos in a Quadratic Nonlinear Oscillator with Time-Delayed Displacement

A. C. J. Luo and S. Xing

In ASME International Mechanical Engineering Congress and Exposition, vol. 4B, Paper V04BT04A011, Houston, TX, USA (2015).

DOI Bib

@inproceedings{IMECE2015,
  title = {Bifurcation Trees of Period-1 Motions to Chaos in a Quadratic Nonlinear Oscillator with Time-Delayed Displacement},
  author = {Luo, Albert C. J. and Xing, Siyuan},
  booktitle = {ASME International Mechanical Engineering Congress and Exposition},
  year = {2015},
  month = nov,
  address = {Houston, TX, USA},
  doi = {10.1115/IMECE2015-50029},
  publisher = {ASME},
  pages = {V04BT04A011},
  volume = {4B}
}