Skip to main content
SpringerLink
Log in

Nonlinear Behavior in Romeo and Juliet’s Love Model Influenced by External Force with Fuzzy Membership Function

  • Published:
International Journal of Fuzzy Systems Aims and scope Submit manuscript

Abstract

Recently, the study of chaotic behaviors in the social sciences includes the habit and the mind of human can be represented using models which include addiction, happiness, family relationship, and love. Within this field, various forms of love model have widely been studied. One of the most famous love models is the Romeo and Juliet model. To generate chaotic behaviors in the love model of Romeo and Juliet, it is necessary to apply an external force that is organized by a periodic function such as sine or cosine wave, which we assume as an ideal external force. However, because this ideal external force cannot possibly represent the real mind of a human, we need to find a reasonable function that allows us to closely describe the mind of human. In this paper, we propose a function that can describe the mind of human by using fuzzy membership function. To do this, we use Gaussian, sigmoid, and triangular fuzzy membership function as external forces. In order to get nonlinear behaviors by using computer simulation, we fix three parameters (a, c, and d) and vary parameter (b) for love model of Romeo and Juliet with the external forces of Gaussian, sigmoid, and triangular fuzzy membership function. Finally, we find that the external force that represents the nonlinear behaviors in love model of Romeo and Juliet through time series and phase portraits most excellent manner is the triangular fuzzy membership function.

This is a preview of subscription content, log in via an institution to check access.

Access this article

Log in via an institution

Price excludes VAT (USA)
Tax calculation will be finalised during checkout.

Instant access to the full article PDF.

Institutional subscriptions

Fig. 1
Fig. 2
Fig. 3
Fig. 4
Fig. 5
Fig. 6
Fig. 7
Fig. 8
Fig. 9
Fig. 10
Fig. 11
Fig. 12
Fig. 13
Fig. 14
Fig. 15
Fig. 16
Fig. 17
Fig. 18
Fig. 19
Fig. 20
Fig. 21
Fig. 22
Fig. 23

Similar content being viewed by others

References

  1. Wang, C., Chen, C.: Intelligent chaos synchronization of fractional order systems via mean-based slide mode controller. Int. J. Fuzzy Syst. 17(2), 144–157 (2015). doi:10.1007/s40815-015-0030-7

    Article  MathSciNet  Google Scholar 

  2. Bae, Y.: Chaotic phenomena in addiction model for digital leisure. Int. J. Fuzzy Log. Intell. Syst. 13(4), 291–297 (2013). doi:10.5391/IJFIS.2013.13.4.291

    Article  Google Scholar 

  3. Kim, M., Bae, Y.: Mathematical modeling and chaotic behavior analysis of cyber addiction. J. Korean Inst. Intell. Syst. 24(3), 245–250 (2014). doi:10.5391/JKIIS.2014.24.3.245

    Article  Google Scholar 

  4. Bae, Y.: Chaotic dynamics in tobacco’s addiction model. Int. J. Fuzzy Log. Intell. Syst. 14(4), 322–331 (2014). doi:10.5391/IJFIS.2014.14.4.322

    Article  Google Scholar 

  5. Bae, Y.: Mathematical modeling and behavior analysis of addiction of physical exercise. J. Korean Inst. Intell. Syst. 24(6), 615–621 (2014). doi:10.5391/JKIIS.2014.24.6.615

    Article  Google Scholar 

  6. Sprott, J.C.: Dynamical models of happiness. Nonlinear Dyn. Psychol. Life Sci. 9(1), 23–34 (2005)

    Google Scholar 

  7. Sprott, J.C.: Dynamics of Love and Happiness. Chaos and Complex Systems Seminar, Madison (2001)

    Google Scholar 

  8. Kim, S., Choi, S., Bae, Y., Park, Y.: Mathematical modeling of happiness and its nonlinear analysis. J. Korea Inst. Electr. Commun. Sci. 9(6), 711–717 (2013). doi:10.13067/JKIECS.2014.9.6.711

    Article  Google Scholar 

  9. Bae, Y.: Synchronization of dynamical happiness model. Int. J. Fuzzy Log. Intell. Syst. 14(2), 91–97 (2014). doi:10.5391/IJFIS.2014.14.2.91

    Article  Google Scholar 

  10. Huang, L.Y., Bae, Y.: Analysis of nonlinear dynamics in family model. J. Korean Inst. Intell. Syst. 25(4), 313–318 (2015). doi:10.5391/JKIIS.2015.25.4.313

    Article  Google Scholar 

  11. Huang, L.Y., Bae, Y.: Analysis of nonlinear dynamics in family model including parent-in law. J. Korean Inst. Intell. Syst. 26(1), 37–43 (2016). doi:10.5391/JKIIS.2016.26.1.037

    Article  Google Scholar 

  12. Strogatz, S.H.: Love affairs and differential equations. Math. Mag. 61, 35 (1988). doi:10.2307/2690328

    Article  MathSciNet  Google Scholar 

  13. Strogatz, S.H.: Nonlinear Dynamics and Chaos: With Application to Physics, Biology, Chemistry and Engineering. Addison-Wesley, Reading (1994)

    Google Scholar 

  14. Kim, S., Shon, Y., Bae, Y.: Mathematical modeling of love and its nonlinear analysis. J. Korea Inst. Electr. Commun. Sci. 9(11), 1297–1303 (2014). doi:10.13067/JKIECS.2014.9.11.1297

    Article  Google Scholar 

  15. Bae, Y.: Behavior analysis of dynamic love model with time delay. J. Korea Inst. Electr. Commun. Sci. 10(2), 253–260 (2015). doi:10.13067/JKIECS.2015.10.2.253

    Article  Google Scholar 

  16. Bae, Y.: Modified mathematical modeling of love and its behavior analysis. J. Korea Inst. Electr. Commun. Sci. 9(12), 1441–1446 (2014). doi:10.13067/JKIECS.2014.9.12.1441

    Article  Google Scholar 

  17. Huang, L.Y., Bae, Y.: Behavior analysis in love model of Romeo and Juliet with time delay. J. Korean Inst. Intell. Syst. 25(2), 155–160 (2015). doi:10.5391/JKIIS.2015.25.2.155

    Article  Google Scholar 

  18. Huang, L.Y., Bae, Y.: Comparative behavior analysis in love model with same and different time delay. J. Korean Inst. Intell. Syst. 25(3), 210–216 (2015). doi:10.5391/JKIIS.2015.25.3.210

    Article  Google Scholar 

  19. Bae, Y.: Nonlinear behavior in love model with discontinuous external force. Int. J. Fuzzy Log. Intell. Syst. 16(1), 64–71 (2016). doi:10.5391/IJFIS.2016.16.1.64

    Article  Google Scholar 

  20. Bae, Y.: Chaotic behavior in dynamic love model with different external force. Int. J. Fuzzy Log. Intell. Syst. 15(4), 283–288 (2015). doi:10.5391/IJFIS.2015.15.4.283

    Article  Google Scholar 

  21. Hyang, L., Bae, Y.: Analysis of nonlinear behavior in love model with external force. J. Korea Inst. Electr. Commun. Sci. 10(7), 845–850 (2015). doi:10.13067/JKIECS.2015.10.7.845

    Article  Google Scholar 

  22. Rinaldi, S.: Laura and Patriarch: an intriguing case of cyclical love dynamics. SIAM J. Appl. Math. 58, 1205–1221 (1998). doi:10.1137/S003613999630592X

    Article  MathSciNet  MATH  Google Scholar 

  23. Breitenecker, F., Judex, F., Popper, N., Breitenecker, A.: Love emotions between Laura and Petrarch: an approach by mathematics and system dynamics. J. Comput. Inf. Technol. 16(4), 255–269 (2008). doi:10.2498/cit.1001393

    Article  Google Scholar 

  24. Wauer, J., Schwarzer, D., Cai, G.Q., Lin, Y.K.: Dynamical models of love with time-varying fluctuations. Appl. Math. Comput. 188(2), 1535–1548 (2007). doi:10.1016/j.amc.2006.11.026

    MathSciNet  MATH  Google Scholar 

  25. Rinaldi, S.: Love dynamics: the case of linear couples. Appl. Math. Comput. 95(2–3), 181–192 (1998). doi:10.1016/S0096-3003(97)10081-9

    MathSciNet  MATH  Google Scholar 

  26. Liao, X., Ran, J.: Hopf bifurcation in love dynamical models with nonlinear couples and time delays. Chaos Solitons Fractals 31(4), 853–865 (2007). doi:10.1016/j.chaos.2005.10.037

    Article  MathSciNet  MATH  Google Scholar 

  27. Ahmad, W.M., E-Khazali, R.: Fractional-order dynamical model of love. Chaos Solitons Fractals 33(4), 1367–1375 (2007). doi:10.1016/j.chaos.2006.01.098

    Article  MathSciNet  MATH  Google Scholar 

  28. Ahmad, W.L., Chen, K.: Chaotic behavior in a new fractional-order love triangle system with competition. Appl. Anal. Comput. 5(1), 103–113 (2015)

    MathSciNet  MATH  Google Scholar 

  29. Cresswell, C.: Mathematics and Sex. Griffin Press, Syndey (2003)

    Google Scholar 

  30. Huang, L., Hwang, S., Bae, Y.: Chaotic behavior in model with a Gaussian function as external force. Int. J. Fuzzy Log. Intell. Syst. 16(4), 262–269 (2016). doi:10.5391/IJFIS.2016.16.4.262

    Article  Google Scholar 

Download references

Author information

Authors and Affiliations

  1. Department of Biomedical and Electronic Engineering, Chonnam National University, Yeosu, 59626, Korea

    Linyun Huang

  2. Division of Electrical, Electronic Communication and Computer Engineering, Chonnam National University, Yeosu, 59626, Korea

    Youngchul Bae

Authors
  1. Linyun Huang
    View author publications

    You can also search for this author in PubMed Google Scholar

  2. Youngchul Bae
    View author publications

    You can also search for this author in PubMed Google Scholar

Corresponding author

Correspondence to Youngchul Bae.

Rights and permissions

Reprints and permissions

About this article

Check for updates. Verify currency and authenticity via CrossMark

Cite this article

Huang, L., Bae, Y. Nonlinear Behavior in Romeo and Juliet’s Love Model Influenced by External Force with Fuzzy Membership Function. Int. J. Fuzzy Syst. 19, 1670–1682 (2017). https://doi.org/10.1007/s40815-017-0346-6

Download citation

  • Received:

  • Revised:

  • Accepted:

  • Published:

  • Issue Date:

  • DOI: https://doi.org/10.1007/s40815-017-0346-6

Keywords

Search

Navigation