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Fractional-order dynamical models of love

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  • Ahmad, Wajdi M.
  • El-Khazali, Reyad

Abstract

This paper examines fractional-order dynamical models of love. It offers a generalization of a dynamical model recently reported in the literature. The generalization is obtained by permitting the state dynamics of the model to assume fractional orders. The fact that fractional systems possess memory justifies this generalization, as the time evolution of romantic relationships is naturally impacted by memory. We show that with appropriate model parameters, strange chaotic attractors may be obtained under different fractional orders, thus confirming previously reported results obtained from integer-order models, yet at an advantage of reduced system order. Furthermore, this work opens a new direction of research whereby fractional derivative applications might offer more insight into the modeling of dynamical systems in psychology and life sciences. Our results are validated by numerical simulations.

Suggested Citation

  • Ahmad, Wajdi M. & El-Khazali, Reyad, 2007. "Fractional-order dynamical models of love," Chaos, Solitons & Fractals, Elsevier, vol. 33(4), pages 1367-1375.
  • Handle: RePEc:eee:chsofr:v:33:y:2007:i:4:p:1367-1375
    DOI: 10.1016/j.chaos.2006.01.098
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    Cited by:

    1. Mekoth, Chitra & George, Santhosh & Jidesh, P., 2021. "Fractional Tikhonov regularization method in Hilbert scales," Applied Mathematics and Computation, Elsevier, vol. 392(C).
    2. Samer S. Ezz-Eldien & Ramy M. Hafez & Ali H. Bhrawy & Dumitru Baleanu & Ahmed A. El-Kalaawy, 2017. "New Numerical Approach for Fractional Variational Problems Using Shifted Legendre Orthonormal Polynomials," Journal of Optimization Theory and Applications, Springer, vol. 174(1), pages 295-320, July.
    3. Pirkhedri, A. & Javadi, H.H.S., 2015. "Solving the time-fractional diffusion equation via Sinc–Haar collocation method," Applied Mathematics and Computation, Elsevier, vol. 257(C), pages 317-326.
    4. Fang, Qingxiang & Peng, Jigen, 2018. "Synchronization of fractional-order linear complex networks with directed coupling topology," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 490(C), pages 542-553.
    5. Kumar, Pushpendra & Erturk, Vedat Suat & Murillo-Arcila, Marina, 2021. "A complex fractional mathematical modeling for the love story of Layla and Majnun," Chaos, Solitons & Fractals, Elsevier, vol. 150(C).
    6. Kumar, Surendra & Sharma, Abhishek & Pal Singh, Harendra, 2021. "Convergence and global stability analysis of fractional delay block boundary value methods for fractional differential equations with delay," Chaos, Solitons & Fractals, Elsevier, vol. 144(C).
    7. Al-Mdallal, Qasem M., 2009. "An efficient method for solving fractional Sturm–Liouville problems," Chaos, Solitons & Fractals, Elsevier, vol. 40(1), pages 183-189.
    8. Liu, Yifan & Cai, Jiazhi & Xu, Haowen & Shan, Minghe & Gao, Qingbin, 2023. "Stability and Hopf bifurcation of a love model with two delays," Mathematics and Computers in Simulation (MATCOM), Elsevier, vol. 205(C), pages 558-580.
    9. Yang, Yongge & Xu, Wei & Gu, Xudong & Sun, Yahui, 2015. "Stochastic response of a class of self-excited systems with Caputo-type fractional derivative driven by Gaussian white noise," Chaos, Solitons & Fractals, Elsevier, vol. 77(C), pages 190-204.
    10. Daniele Mortari & Roberto Garrappa & Luigi Nicolò, 2023. "Theory of Functional Connections Extended to Fractional Operators," Mathematics, MDPI, vol. 11(7), pages 1-18, April.
    11. Agarwal, Ritu & Kritika, & Purohit, Sunil Dutt, 2021. "Mathematical model pertaining to the effect of buffer over cytosolic calcium concentration distribution," Chaos, Solitons & Fractals, Elsevier, vol. 143(C).

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