[1] Yan, Z., Sun, W., Tan, T., Huang, W., Nonlinear analysis of galloping piezoelectric energy harvesters with inductive-resistive circuits for boundaries of analytical solutions, Communications in Nonlinear Science and Numerical Simulation, 62, 2018, 90–116.
[2] duToit, N., Wardle, B., Experimental verification of models for microfabricated piezoelectric vibration energy harvesters, AIAA Journal, 45, 2007, 1126–1137.
[3] Abohamer, M., Amer, T., Arab, A., Galal, A., Analyzing the chaotic and stability behavior of a Duffing oscillator excited by a sinusoidal external force, Journal of Low Frequency Noise, Vibration and Active Control, 44(2), 2025, 969–986.
[4] Amer, T.S., Bek, M.A., Hassan, S.S., The dynamical analysis for the motion of a harmonically two degrees of freedom damped spring pendulum in an elliptic trajectory, Alexandria Engineering Journal, 61(2), 2022, 1715–1733.
[5] Hamdi, M., Belhaq, M., Quasiperiodic Birhythmicity in a Multicycle van der Pol Oscillator, In: Belhaq, M. (ed.), Advances in Nonlinear Dynamics and Control of Mechanical and Physical Systems, Springer Proceedings in Physics, Vol. 301, Springer, Singapore, 2024.
[6] Butcher, J.C., Wanner, G., Runge-Kutta methods: some historical notes, Applied Numerical Mathematics, 22(1–3), 1996, 113–151.
[7] Amer, T.S., Starosta, R., Almahalawy, A., Elameer, A.S., The stability analysis of a vibrating auto-parametric dynamical system near resonance, Applied Sciences, 12(3), 2022, 1737.
[8] Moatimid, G.M., Amer, T.S., Analytical approximate solutions of a magnetic spherical pendulum: stability analysis, Journal of Vibration Engineering & Technologies, 11, 2023, 2155–2165.
[9] Zhao, H., Ma, X., Bi, Q., Chaotic bursting patterns induced by transient chaos in a smooth three-dimensional dynamic model, International Journal of Non-Linear Mechanics, 159, 2024, 104592.
[10] Zhang, Z., Ma, X., Zhang, Z., Different vibration-switching modes induced by pulse-shaped explosion in a hybrid van der Pol-Rayleigh-Duffing system, Chinese Journal of Physics, 96, 2025, 891–905.
[11] Zhang, Z., Ma, X., Zhang, Z., Bursting oscillations induced by pulse-shaped explosion in a Duffing-Rayleigh-van der Pol system, Chinese Journal of Physics, 103, 2026, 1346–1372.
[12] Nayfeh, A.H., Mook, D.T., Nonlinear Oscillations, John Wiley & Sons, 1979.
[13] Guckenheimer, J., Holmes, P., Nonlinear Oscillations, Dynamical Systems and Bifurcations of Vector Fields, Springer-Verlag, 1983.
[14] Strogatz, S.H., Nonlinear Dynamics and Chaos, 2nd ed., Westview Press, 2015.
[15] Warminski, J., Nonlinear dynamics of self-, parametric and externally excited oscillator with time delay, van der Pol versus Rayleigh models, Nonlinear Dynamics, 99(1), 2020, 35–56.
[16] Domany, E., Gendelman, O.V., Dynamic responses and mitigation of limit cycle oscillations in Van der Pol–Duffing oscillator with nonlinear energy sink, Journal of Sound and Vibration, 332, 2013, 5489–5507.
[17] Cartwright, M.L., Littlewood, J.E., On non-linear differential equations of the second order, Journal of the London Mathematical Society, 20, 1945, 180–189.
[18] Pikovsky, A., Rosenblum, M., Kurths, J., Synchronization: A Universal Concept in Nonlinear Sciences, Cambridge University Press, 2001.
[19] Balanov, A., Janson, N., Postnov, D., Sosnovtseva, O., Synchronization: From Simple to Complex, Springer, 2009.
[20] Ma, X., Zhou, S., A review of flow-induced vibration energy harvesters, Energy Conversion and Management, 254, 2022, 115223.
[21] Dunnmon, J.A., Stanton, S.C., Mann, B.P., Dowell, E.H., Power extraction from aeroelastic limit cycle oscillations, Journal of Fluids and Structures, 27(8), 2011, 1182–1198.
[22] Den Hartog, J.P., Mechanical Vibrations, McGraw-Hill Book Company, 1985.
[23] Parkinson, G.V., Smith, J.D., The square prism as an aeroelastic nonlinear oscillator, Quarterly Journal of Mechanics and Applied Mathematics, 17, 1964, 225–239.
[24] Barrero-Gil, A., Alonso, G., Sanz-Andres, A., Energy harvesting from transverse galloping, Journal of Sound and Vibration, 329, 2010, 2873–2883.
[25] Zhao, L., Tang, L., Yang, Y., Comparison of modeling methods and parametric study for a piezoelectric wind energy harvester, Smart Materials and Structures, 22(12), 2013, 125003.
[26] Abdelkefi, A., Hajj, M.R., Nayfeh, A.H., Power harvesting from transverse galloping of square cylinder, Nonlinear Dynamics, 70, 2012, 1355–1363.
[27] Bibo, A., Daqaq, M.F., Energy harvesting under combined aerodynamic and base excitations, Journal of Sound and Vibration, 332, 2013, 5086–5102.
[28] Dai, H.L., Abdelkefi, A., Javed, U., Wang, L., Modeling and performance of electromagnetic energy harvesting from galloping oscillations, Smart Materials and Structures, 24, 2015, 045012.
[29] Dash, R.C., Maiti, D.K., Singh, B.N., Dynamic stability analysis of inclined galloping based piezoelectric energy harvester employing finite element method, Mechanics Based Design of Structures and Machines, 51(8), 2023, 4588–4603.
[30] Wang, J., Zhou, S., Zhang, Z., Yurchenko, D., High-performance piezoelectric wind energy harvester with Y-shaped attachment, Energy Conversion and Management, 181, 2019, 645–652.
[31] El Moussati, Y., Hamdi, M., Belhaq, M., Energy harvesting from simultaneous galloping and vortex-induced vibrations in a 2DOF system, Journal of Vibration Testing and System Dynamics, 9(2), 2025, 147–158.
[32] Bichri, A., Kirrou, I., Belhaq, M., Energy harvesting from quasiperiodic vibrations in a delayed Rayleigh-Duffing harvester device, Journal of Vibration Testing and System Dynamics, 4(2), 2020, 191–200.
[33] Kirrou, I., Bichri, A., Belhaq, M., Quasiperiodic energy harvesting in a delayed Rayleigh-Duffing oscillator near the 3-subharmonic resonance, Journal of Vibration Testing and System Dynamics, 7(3), 2023, 265–273.
[34] Belhaq, M., Hamdi, M., Energy harvesting from quasi-periodic vibrations, Nonlinear Dynamics, 86, 2016, 2193–2205.
[35] Ghouli, Z., Hamdi, M., Lakrad, F., Belhaq, M., Quasiperiodic energy harvesting in a forced and delayed Duffing harvester device, Journal of Sound and Vibration, 407, 2017, 271–285.
[36] Hayashi, C., Nonlinear Oscillations in Physical Systems, McGraw-Hill, 1964.
[37] Jordan, D.W., Smith, P., Nonlinear Ordinary Differential Equations, 4th ed., Oxford University Press, 2007.
[38] Erturk, A., Hoffmann, J., Inman, D.J., A piezomagnetoelastic structure for broadband vibration energy harvesting, Applied Physics Letters, 94, 2009, 254102.
[39] El Moussati, Y., Hamdi, M., Performance enhancement energy harvesting from aeroelastic vibrations using a van der Pol circuit, Mechanics Based Design of Structures and Machines, 53(3), 2025, 2390–2402.
[40] El Moussati, Y., Hamdi, M., Belhaq, M., Energy harvesting using a van der Pol resonant circuit, Nonlinear Dynamics, 113, 2025, 30825–30840.
[41] Barrero-Gil, A., Pindado, S., Avila, S., Extracting energy from vortex-induced vibrations: A parametric study, Applied Mathematical Modelling, 36, 2012, 3153–3160.
[42] Alhadidi, A.H., Daqaq, M.F., A broadband bi-stable flow energy harvester based on the wake-galloping phenomenon, Applied Physics Letters, 109, 2016, 033904.
[43] Dai, H.L., Abdelkefi, A., Wang, L., Piezoelectric energy harvesting from concurrent vortex-induced vibrations and base excitations, Nonlinear Dynamics, 77, 2014, 967–981.
[44] Hafizh, M., Muthalif, A.G.A., Renno, J., et al., Vortex induced vibration energy harvesting using magnetically coupled broadband circular-array piezoelectric patch: Modelling, parametric study, and experiments, Energy Conversion and Management, 276, 2023, 116559.
[45] Belhaq, M., Houssni, M., Quasi-periodic oscillations, chaos and suppression of chaos in a nonlinear oscillator driven by parametric and external excitations, Nonlinear Dynamics, 18, 1999, 1–24.