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Layla and Majnun: a complex love story

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Abstract

Following previous work, this paper introduces a new dynamical model involving two differential equations describing the time variation of behavior displayed by a couple in a romantic relationship. This model is different from previous ones because it uses complex variables. Since complex variables have both magnitude and phase, they are better able to represent love and can represent more complex emotions such as coexisting love and hate. The model treats feelings as a two-dimensional vector rather than a scalar, which is a step closer to reality. Another interesting characteristic of the new model is its ability to show transiently chaotic behavior between only two individuals, which in previous models appeared only in love triangles. The sensitive dependence on initial conditions represents the unpredictable dynamics of love affairs.

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References

  1. Luce, R.D.: Readings in Mathematical Psychology, vol. 2. Wiley, London (1965)

    MATH  Google Scholar 

  2. Xiao-ping, L.: Nonlinear science and its application in psychology. J. Nanjing Norm. Univ. (Soc. Sci. Ed.) 2 (2005)

  3. Sprott, J.: Dynamical models of happiness. Nonlinear Dynamics Psychol. Life Sci. 9(1), 23–36 (2005)

    Google Scholar 

  4. Baghdadi, G., Jafari, S., Sprott, J., Towhidkhah, F., Golpayegani, M.H.: A chaotic model of sustaining attention problem in attention deficit disorder. Commun. Nonlinear Sci. Numer. Simul. 20(1), 174–185 (2015)

    Article  MathSciNet  MATH  Google Scholar 

  5. Jafari, S., Ansari, Z., Golpayegani, S., Gharibzadeh, S.: Is attention a ”period window” in the chaotic brain? J. Neuropsychiatry Clin. Neurosci. 25(1), E05 (2013)

    Article  Google Scholar 

  6. Jafari, S., Baghdadi, G., Golpayegani, S., Towhidkhah, F., Gharibzadeh, S.: Is attention deficit hyperactivity disorder a kind of intermittent chaos? J. Neuropsychiatry Clin. Neurosci. 25(2), E2 (2013)

    Article  Google Scholar 

  7. Tabatabaei, S.S., Yazdanpanah, M.J., Jafari, S., Sprott, J.C.: Extensions in dynamic models of happiness: effect of memory. Int. J. Happiness Dev. 1(4), 344–356 (2014)

    Article  Google Scholar 

  8. Perc, M., Szolnoki, A.: Coevolutionary games—a mini review. BioSystems 99(2), 109–125 (2010)

    Article  Google Scholar 

  9. Szolnoki, A., Xie, N.-G., Wang, C., Perc, M.: Imitating emotions instead of strategies in spatial games elevates social welfare. EPL (Europhys. Lett.) 96(3), 38002 (2011)

  10. Szolnoki, A., Xie, N.-G., Ye, Y., Perc, M.: Evolution of emotions on networks leads to the evolution of cooperation in social dilemmas. Phys. Rev. E 87(4), 042805 (2013)

    Article  Google Scholar 

  11. Dercole, F., Rinaldi, S.: Love stories can be unpredictable: Jules et Jim in the vortex of life. Chaos Interdiscip. J. Nonlinear Sci. 24(2), 023134 (2014)

    Article  MathSciNet  Google Scholar 

  12. Gottman, J.M., Murray, J.D., Swanson, C.C., Tyson, R., Swanson, K.R.: The Mathematics of Marriage. Dynamic Nonlinear Models. The MIT Press, Cambridge (2002)

    MATH  Google Scholar 

  13. Gragnani, A., Rinaldi, S., Feichtinger, G.: Cyclic dynamics in romantic relationships. Int. J. Bifurcat. Chaos 7(11), 2611–2619 (1997)

    Article  MATH  Google Scholar 

  14. Liao, X., Ran, J.: Hopf bifurcation in love dynamical models with nonlinear couples and time delays. Chaos Solitons Fractals 31(4), 853–865 (2007)

    Article  MathSciNet  MATH  Google Scholar 

  15. Padula, J.: The Kama Sutra, Romeo and Juliet, and mathematics: studying mathematics for pleasure. Aust. Sr. Math. J. 19(2), 43 (2005)

    Google Scholar 

  16. Popper, N., Breitenecker, K., Mathe, A., Mathe, A., Judex, F., Breitenecker, F.: Love emotions between Laura and Petrarch—an approach by mathematics and system dynamics. CIT J. Comput. Inf. Technol. 16(4), 255–269 (2008)

    Google Scholar 

  17. Rinaldi, S.: Laura and Petrarch: an intriguing case of cyclical love dynamics. SIAM J. Appl. Math. 58(4), 1205–1221 (1998)

    Article  MathSciNet  MATH  Google Scholar 

  18. Rinaldi, S.: Love dynamics: the case of linear couples. Appl. Math. Comput. 95(2), 181–192 (1998)

    Article  MathSciNet  MATH  Google Scholar 

  19. Rinaldi, S., Della Rossa, F., Landi, P.: A mathematical model of “Gone with the Wind”. Phys. A Stat. Mech. Appl. 392(15), 3231–3239 (2013)

    Article  MathSciNet  Google Scholar 

  20. Rinaldi, S., Della Rossa, F., Landi, P.: A mathematical model of ‘Pride and Prejudice’. Nonlinear Dynamics Psychol. Life Sci. 18(2), 199–211 (2014)

    MathSciNet  Google Scholar 

  21. Rinaldi, S., Gragnani, A.: Love dynamics between secure individuals: a modeling approach. Nonlinear Dynamics Psychol. Life Sci. 2(4), 283–301 (1998)

    Article  MATH  Google Scholar 

  22. Rinaldi, S., Landi, P., Rossa, F.D.: Small discoveries can have great consequences in love affairs: the case of Beauty and the Beast. Int. J. Bifurc. Chaos 23(11), 1330038 (2013)

    Article  MATH  MathSciNet  Google Scholar 

  23. Rinaldi, S., Rossa, F.D., Dercole, F.: Love and appeal in standard couples. Int. J. Bifurc. Chaos 20(08), 2443–2451 (2010)

    Article  MATH  Google Scholar 

  24. Satsangi, D., Sinha, A.K.: Dynamics of love and happiness: a mathematical analysis. Int. J. Mod. Educ. Comput. Sci. (IJMECS) 4(5), 31 (2012)

    Article  Google Scholar 

  25. Son, W.-S., Park, Y.-J.: Time delay effect on the love dynamical model. arXiv preprint arXiv:1108.5786 (2011)

  26. Sprott, J.: Dynamical models of love. Nonlinear Dynamics Psychol. Life Sci. 8(3), 303–314 (2004)

    MathSciNet  Google Scholar 

  27. Sternberg, R.J., Barnes, M.L.: The Psychology of Love. Yale University Press, New Haven (1988)

    Google Scholar 

  28. Strogatz, S.H.: Love affairs and differential equations. Math. Mag. 61(1), 35 (1988)

    Article  MathSciNet  Google Scholar 

  29. Ahmad, W.M., El-Khazali, R.: Fractional-order dynamical models of love. Chaos Solitons Fractals 33(4), 1367–1375 (2007)

    Article  MathSciNet  MATH  Google Scholar 

  30. Cveticanin, L.: Resonant vibrations of nonlinear rotors. Mech. Mach. Theory 30(4), 581–588 (1995)

    Article  MathSciNet  Google Scholar 

  31. Rozhansky, V.A., Tsendin, L.D.: Transport Phenomena in Partially Ionized Plasma. CRC Press, Boca Raton (2001)

    Google Scholar 

  32. Newell, A.C., Moloney, J.V.: Nonlinear Optics. Addison-Wesley, Reading (1992)

    MATH  Google Scholar 

  33. Dilão, R., Alves-Pires, R.: Nonlinear Dynamics in Particle Accelerators, vol. 23. World Scientific, Singapore (1996)

    MATH  Google Scholar 

  34. Cveticanin, L.: Approximate analytical solutions to a class of non-linear equations with complex functions. J. Sound Vib. 157(2), 289–302 (1992)

    Article  MathSciNet  MATH  Google Scholar 

  35. Mahmoud, G.M., Aly, S.A.: On periodic solutions of parametrically excited complex non-linear dynamical systems. Phys. A Stat. Mech. Appl. 278(3), 390–404 (2000)

    Article  Google Scholar 

  36. Wu, X., Xu, Y., Zhang, H.: Random impacts of a complex damped system. Int. J. Non-Linear Mech. 46(5), 800–806 (2011)

    Article  Google Scholar 

  37. Xu, Y., Mahmoud, G.M., Xu, W., Lei, Y.: Suppressing chaos of a complex Duffing’s system using a random phase. Chaos Solitons Fractals 23(1), 265–273 (2005)

    Article  MATH  Google Scholar 

  38. Xu, Y., Xu, W., Mahmoud, G.M.: On a complex beam–beam interaction model with random forcing. Phys. A Stat. Mech. Appl. 336(3), 347–360 (2004)

    Article  Google Scholar 

  39. Xu, Y., Xu, W., Mahmoud, G.M.: Generating chaotic limit cycles for a complex Duffing-Van der Pol system using a random phase. Int. J. Mod. Phys. C 16(09), 1437–1447 (2005)

    Article  MathSciNet  MATH  Google Scholar 

  40. Xu, Y., Zhang, H., Xu, W.: On stochastic complex beam–beam interaction models with Gaussian colored noise. Phys. A Stat. Mech. Appl. 384(2), 259–272 (2007)

    Article  Google Scholar 

  41. Marshall, D., Sprott, J.: Simple driven chaotic oscillators with complex variables. Chaos Interdiscip. J. Nonlinear Sci. 19(1), 013124 (2009)

    Article  MathSciNet  MATH  Google Scholar 

  42. Marshall, D., Sprott, J.C.: Simple conservative, autonomous, second-order chaotic complex variable systems. Int. J. Bifurc. Chaos 20(03), 697–702 (2010)

    Article  MATH  Google Scholar 

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Correspondence to Sajad Jafari.

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Jafari, S., Sprott, J.C. & Golpayegani, S.M.R.H. Layla and Majnun: a complex love story. Nonlinear Dyn 83, 615–622 (2016). https://doi.org/10.1007/s11071-015-2351-3

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  • DOI: https://doi.org/10.1007/s11071-015-2351-3

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