[
Abdullah, S., Ismail, M., Ahmed, A.N. and Abdullah, A.M. (2019). Forecasting particulate matter concentration using linear and non-linear approaches for air quality decision support, Atmosphere 10(11): 667.10.3390/atmos10110667
]Search in Google Scholar
[
Azar, A.T. and Vaidyanathan, S. (2015). Chaos Modeling and Control Systems Design, Springer, Cham.10.1007/978-3-319-13132-0
]Search in Google Scholar
[
Bingi, K., Ibrahim, R., Karsiti, M.N., Hassam, S.M. and Harindran, V.R. (2019a). Frequency response based curve fitting approximation of fractional-order PID controllers, International Journal of Applied Mathematics and Computer Science 29(2): 311–326, DOI: 10.2478/amcs-2019-0023.10.2478/amcs-2019-0023
]Search in Google Scholar
[
Bingi, K., Ibrahim, R., Karsiti, M.N., Hassan, S.M., Elamvazuthi, I. and Devan, A.M. (2019b). Design and analysis of fractional-order oscillators using SCILAB, 2019 IEEE Student Conference on Research and Development (SCOReD), Bandar Seri Iskandar, Malaysia, pp. 311–316.10.1109/SCORED.2019.8896260
]Search in Google Scholar
[
Bingi, K., Ibrahim, R., Karsiti, M.N., Hassan, S.M. and Harindran, V.R. (2020). Fractional-order Systems and PID Controllers, Springer, Cham.10.1007/978-3-030-33934-0
]Search in Google Scholar
[
Bingi, K., Prusty, B.R., Kumra, A. and Chawla, A. (2021). Torque and temperature prediction for permanent magnet synchronous motor using neural networks, 3rd International Conference on Energy, Power and Environment: Towards Clean Energy Technologies, Shillong, Meghalaya, India, pp. 1–6.
]Search in Google Scholar
[
Cao, J., Ma, C., Xie, H. and Jiang, Z. (2010). Nonlinear dynamics of Duffing system with fractional order damping, Journal of Computational and Nonlinear Dynamics 5(4), Article ID: 041012, DOI: 10.1115/1.4002092.10.1115/1.4002092
]Search in Google Scholar
[
Cattani, C., Srivastava, H.M. and Yang, X.-J. (2015). Fractional Dynamics, De Gruyter, Warsaw.10.1515/9783110472097
]Search in Google Scholar
[
Corinto, F., Forti, M. and Chua, L.O. (2021). Nonlinear Circuits and Systems with Memristors: Nonlinear Dynamics and Analogue Computing via the Flux-Charge Analysis Method, Springer, Cham.10.1007/978-3-030-55651-8
]Search in Google Scholar
[
De Oliveira, E.C. and Tenreiro Machado, J.A. (2014). A review of definitions for fractional derivatives and integral, Mathematical Problems in Engineering 2014, Article ID: 238459, DOI: 10.1155/2014/238459.10.1155/2014/238459
]Search in Google Scholar
[
Giresse, T.A. and Crépin, K.T. (2017). Chaos generalized synchronization of coupled Mathieu–Van der Pol and coupled Duffing–Van der Pol systems using fractional order-derivative, Chaos, Solitons & Fractals 98: 88–100, DOI: 10.1016/j.chaos.2017.03.012.10.1016/j.chaos.2017.03.012
]Search in Google Scholar
[
Huang, W., Li, Y. and Huang, Y. (2020). Deep hybrid neural network and improved differential neuroevolution for chaotic time series prediction, IEEE Access 8: 159552–159565, DOI: 10.1109/ACCESS.2020.3020801.10.1109/ACCESS.2020.3020801
]Search in Google Scholar
[
Kabziński, J. (2018). Synchronization of an uncertain Duffing oscillator with higher order chaotic systems, International Journal of Applied Mathematics and Computer Science 28(4): 625–634, DOI: 10.2478/amcs-2018-0048.10.2478/amcs-2018-0048
]Search in Google Scholar
[
Kaczorek, T. and Sajewski, Ł. (2020). Pointwise completeness and pointwise degeneracy of fractional standard and descriptor linear continuous-time systems with different fractional orders, International Journal of Applied Mathematics and Computer Science 30(4): 641–647, DOI: 10.34768/amcs-2020-0047.
]Search in Google Scholar
[
Kanchana, C., Siddheshwar, P. and Yi, Z. (2020). The effect of boundary conditions on the onset of chaos in Rayleigh–Bénard convection using energy-conserving Lorenz models, Applied Mathematical Modelling 88: 349–366, DOI: 10.1016/j.apm.2020.06.062.10.1016/j.apm.2020.06.062
]Search in Google Scholar
[
Kuiate, G.F., Kingni, S.T., Tamba, V.K. and Talla, P.K. (2018). Three-dimensional chaotic autonomous Van der Pol–Duffing type oscillator and its fractional-order form, Chinese Journal of Physics 56(5): 2560–2573.10.1016/j.cjph.2018.08.003
]Search in Google Scholar
[
Li, Q. and Lin, R.-C. (2016). A new approach for chaotic time series prediction using recurrent neural network, Mathematical Problems in Engineering 2016, Article ID: 3542898, DOI: 10.1155/2016/3542898.10.1155/2016/3542898
]Search in Google Scholar
[
Liang, Y., Wang, G., Chen, G., Dong, Y., Yu, D. and Iu, H.H.-C. (2020). S-type locally active memristor-based periodic and chaotic oscillators, IEEE Transactions on Circuits and Systems I: Regular Papers 67(12): 5139–5152.10.1109/TCSI.2020.3017286
]Search in Google Scholar
[
Lu, Z., Hunt, B.R. and Ott, E. (2018). Attractor reconstruction by machine learning, Chaos: An Interdisciplinary Journal of Nonlinear Science 28(6): 061104.10.1063/1.503950829960382
]Search in Google Scholar
[
Lu, Z., Pathak, J., Hunt, B., Girvan, M., Brockett, R. and Ott, E. (2017). Reservoir observers: Model-free inference of unmeasured variables in chaotic systems, Chaos: An Interdisciplinary Journal of Nonlinear Science 27(4): 041102.10.1063/1.497966528456169
]Search in Google Scholar
[
Luo, W. and Cui, Y. (2020). Signal denoising based on Duffing oscillators system, IEEE Access 8: 86554–86563, DOI: 10.1109/ACCESS.2020.2992503.10.1109/ACCESS.2020.2992503
]Search in Google Scholar
[
Mainardi, F. (2018). Fractional Calculus: Theory and Applications, Multidisciplinary Digital Publishing Institute, Basel.10.3390/math6090145
]Search in Google Scholar
[
Miwadinou, C., Monwanou, A. and Chabi Orou, J. (2015). Effect of nonlinear dissipation on the basin boundaries of a driven two-well modified Rayleigh–Duffing oscillator, International Journal of Bifurcation and Chaos 25(02): 1550024.10.1142/S0218127415500248
]Search in Google Scholar
[
Pan, I. and Das, S. (2018). Evolving chaos: Identifying new attractors of the generalised Lorenz family, Applied Mathematical Modelling 57: 391–405, DOI: 10.1016/j.apm.2018.01.015.10.1016/j.apm.2018.01.015
]Search in Google Scholar
[
Petras, I. (2010). Fractional-order memristor-based Chua’s circuit, IEEE Transactions on Circuits and Systems II: Express Briefs 57(12): 975–979.10.1109/TCSII.2010.2083150
]Search in Google Scholar
[
Petráš, I. (2011). Fractional-Order Nonlinear Systems: Modeling, Analysis and Simulation, Springer Science & Business Media, Berlin.10.1007/978-3-642-18101-6
]Search in Google Scholar
[
Salas, A.H. and El-Tantawy, S.A.E.-H. (2021). Analytical Solutions of Some Strong Nonlinear Oscillators, IntechOpen, London, DOI: 10.5772/intechopen.97677.10.5772/intechopen.97677
]Search in Google Scholar
[
Shaik, N.B., Pedapati, S.R., Othman, A., Bingi, K. and Abd Dzubir, F.A. (2021). An intelligent model to predict the life condition of crude oil pipelines using artificial neural networks, Neural Computing and Applications, DOI: 10.1007/s00521-021-06116-1.10.1007/s00521-021-06116-1
]Search in Google Scholar
[
Sheela, K.G. and Deepa, S.N. (2013). Review on methods to fix number of hidden neurons in neural networks, Mathematical Problems in Engineering 2013, Article ID: 425740, DOI: 10.1155/2013/425740.10.1155/2013/425740
]Search in Google Scholar
[
Shen, Y.-J., Wei, P. and Yang, S.-P. (2014). Primary resonance of fractional-order Van der Pol oscillator, Nonlinear Dynamics 77(4): 1629–1642.10.1007/s11071-014-1405-2
]Search in Google Scholar
[
Smith, J.S., Wu, B. and Wilamowski, B.M. (2018). Neural network training with Levenberg–Marquardt and adaptable weight compression, IEEE Transactions on Neural Networks and Learning Systems 30(2): 580–587.10.1109/TNNLS.2018.284677529994621
]Search in Google Scholar
[
Sun, Z., Xu, W., Yang, X. and Fang, T. (2006). Inducing or suppressing chaos in a double-well Duffing oscillator by time delay feedback, Chaos, Solitons & Fractals 27(3): 705–714.10.1016/j.chaos.2005.04.041
]Search in Google Scholar
[
Ueta, T. and Tamura, A. (2012). Bifurcation analysis of a simple 3D oscillator and chaos synchronization of its coupled systems, Chaos, Solitons & Fractals 45(12): 1460–1468.10.1016/j.chaos.2012.08.007
]Search in Google Scholar
[
Vaidyanathan, S. and Azar, A.T. (2020). Backstepping Control of Nonlinear Dynamical Systems, Academic Press, Cambridge.
]Search in Google Scholar
[
Vlachas, P.R., Byeon, W., Wan, Z.Y., Sapsis, T.P. and Koumoutsakos, P. (2018). Data-driven forecasting of high-dimensional chaotic systems with long short-term memory networks, Proceedings of the Royal Society A: Mathematical, Physical and Engineering Sciences 474(2213): 20170844.10.1098/rspa.2017.0844599070229887750
]Search in Google Scholar
[
Wang, X., Jin, C., Min, X., Yu, D. and Iu, H.H.C. (2020). An exponential chaotic oscillator design and its dynamic analysis, IEEE/CAA Journal of Automatica Sinica 7(4): 1081–1086.10.1109/JAS.2020.1003252
]Search in Google Scholar
[
Wu, J.-L., Kashinath, K., Albert, A., Chirila, D., Prabhat and Xiao, H. (2020). Enforcing statistical constraints in generative adversarial networks for modeling chaotic dynamical systems, Journal of Computational Physics 406, Article ID: 109209, DOI: 10.1016/j.jcp.2019.109209.10.1016/j.jcp.2019.109209
]Search in Google Scholar
[
Yang, Q., Sing-Long, C. and Reed, E. (2020). Rapid data-driven model reduction of nonlinear dynamical systems including chemical reaction networks using l1-regularization, Chaos: An Interdisciplinary Journal of Nonlinear Science 30(5): 053122.10.1063/1.513946332491878
]Search in Google Scholar
[
Zang, X., Iqbal, S., Zhu, Y., Liu, X. and Zhao, J. (2016). Applications of chaotic dynamics in robotics, International Journal of Advanced Robotic Systems 13(2): 60.10.5772/62796
]Search in Google Scholar