HBSS_Cont is a Matlab toolbox for nonlinear frequency response analysis based on Harmonic Balance in extended state space combined with pseudo-arc-length continuation.
The toolbox supports continuous and discrete-time state-space models, created analytically or identified experimentally with methods such as NSI (Nonlinear Subspace Identification) or NFR-ID.
Stability analysis of periodic solutions is also performed through Floquet multipliers, with automatic detection of Fold, Period-Doubling, and Neimark–Sacker bifurcations.
- Harmonic Balance formulation in extended state space
- Pseudo-arc-length continuation of nonlinear frequency response curves
- Support for theoretical and experimentally identified models
- Stability analysis via monodromy matrix and Floquet multipliers
- Automatic detection of bifurcation events
A detailed description of the theory, algorithms, and examples is provided in User Guide.
Tested on Matlab R2024b, R2025b.
Run any script in the examples/ folder.
Each example automatically adds the src/ directory to the MATLAB path.
This software is intended for research purposes and is released under the GNU General Public License v3 (GPLv3). See the LICENSE file for details.
Disclaimer: this software is provided "as is", without warranty of any kind. The authors shall not be held liable for any inaccuracies in the results or damages resulting from the use of the code.
If you use HBSS_Cont in academic work, please cite the following paper, which provides methodological description of the method:
D. Anastasio, S. Marchesiello, Nonlinear frequency response curves estimation and stability analysis of randomly excited systems in the subspace framework. Nonlinear Dynamics, 2023. DOI: 10.1007/s11071-023-08280-6
The methodology implemented in this toolbox has been adopted and discussed in:
[1] D. Anastasio, S. Marchesiello, Nonlinear frequency response curves estimation and stability analysis of randomly excited systems in the subspace framework, Nonlinear Dynamics, 2023. DOI: 10.1007/s11071-023-08280-6
[2] D. Anastasio, S. Marchesiello, G. Kerschen, Estimation of the periodic solutions of geometrically nonlinear structures by broadband excitation, Proceedings of ISMA2024. Link
[3] D. Anastasio, G. Raze, G. Kerschen, Frequency-domain system identification of nonlinear structures using experimental continuation data, Journal of Vibration and Control, 2025. DOI: 10.1177/10775463251405337
[4] D. Anastasio, G. Raze, S. Marchesiello, G. Kerschen, Identification of primary and secondary resonances: experimental continuation and broadband data-based modeling, Nonlinear Dynamics, 2026.DOI: 10.1007/s11071-025-11940-4