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Hopf bifurcation in love dynamical models with nonlinear couples and time delays

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  • Liao, Xiaofeng
  • Ran, Jiouhong

Abstract

A love dynamical models with nonlinear couples and two delays is considered. Local stability of this model is studied by analyzing the associated characteristic transcendental equation. We find that the Hopf bifurcation occurs when the sum of the two delays varies and passes a sequence of critical values. The stability and direction of the Hopf bifurcation are determined by applying the normal form theory and the center manifold theorem. Numerical example is given to illustrate our results.

Suggested Citation

  • Liao, Xiaofeng & Ran, Jiouhong, 2007. "Hopf bifurcation in love dynamical models with nonlinear couples and time delays," Chaos, Solitons & Fractals, Elsevier, vol. 31(4), pages 853-865.
    • Handle: RePEc:eee:chsofr:v:31:y:2007:i:4:p:853-865
    DOI: 10.1016/j.chaos.2005.10.037
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    References listed on IDEAS

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    1. Liao, Xiaofeng & Li, Chuandong & Zhou, Shangbo, 2005. "Hopf bifurcation and chaos in macroeconomic models with policy lag," Chaos, Solitons & Fractals, Elsevier, vol. 25(1), pages 91-108.
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    Cited by:

    1. Hu, H.Y. & Wang, Z.H., 2009. "Singular perturbation methods for nonlinear dynamic systems with time delays," Chaos, Solitons & Fractals, Elsevier, vol. 40(1), pages 13-27.
    2. Pei, Xin & Zhan, Xiu-Xiu & Jin, Zhen, 2017. "Application of pair approximation method to modeling and analysis of a marriage network," Applied Mathematics and Computation, Elsevier, vol. 294(C), pages 280-293.
    3. Zulqurnain Sabir & Juan L. G. Guirao, 2023. "A Soft Computing Scaled Conjugate Gradient Procedure for the Fractional Order Majnun and Layla Romantic Story," Mathematics, MDPI, vol. 11(4), pages 1-14, February.
    4. Zulqurnain Sabir & Atef F. Hashem & Adnène Arbi & Mohamed A. Abdelkawy, 2023. "Designing a Bayesian Regularization Approach to Solve the Fractional Layla and Majnun System," Mathematics, MDPI, vol. 11(17), pages 1-13, September.
    5. Niu, Ben & Wei, Junjie, 2008. "Stability and bifurcation analysis in an amplitude equation with delayed feedback," Chaos, Solitons & Fractals, Elsevier, vol. 37(5), pages 1362-1371.
    6. Xu, Yong & Gu, Rencai & Zhang, Huiqing, 2011. "Effects of random noise in a dynamical model of love," Chaos, Solitons & Fractals, Elsevier, vol. 44(7), pages 490-497.
    7. JI, Conghuan & QIAO, Yuanhua & MIAO, Jun & DUAN, Lijuan, 2018. "Stability and Hopf bifurcation analysis of a complex-valued Wilson–Cowan neural network with time delay," Chaos, Solitons & Fractals, Elsevier, vol. 115(C), pages 45-61.
    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. Liu, Yang & Gao, Jian & Wang, Haiying & Semba, Sherehe & Gu, Changgui & Yang, Huijie, 2022. "Families’ influence on romantic relationship and its reconstruction," Chaos, Solitons & Fractals, Elsevier, vol. 155(C).
    10. Russu, Paolo, 2009. "Hopf bifurcation in a environmental defensive expenditures model with time delay," Chaos, Solitons & Fractals, Elsevier, vol. 42(5), pages 3147-3159.

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