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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Luce, R.D.: Readings in Mathematical Psychology, vol. 2. Wiley, London (1965)
Xiao-ping, L.: Nonlinear science and its application in psychology. J. Nanjing Norm. Univ. (Soc. Sci. Ed.) 2 (2005)
Sprott, J.: Dynamical models of happiness. Nonlinear Dynamics Psychol. Life Sci. 9(1), 23–36 (2005)
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)
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)
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)
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)
Perc, M., Szolnoki, A.: Coevolutionary games—a mini review. BioSystems 99(2), 109–125 (2010)
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)
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)
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)
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)
Gragnani, A., Rinaldi, S., Feichtinger, G.: Cyclic dynamics in romantic relationships. Int. J. Bifurcat. Chaos 7(11), 2611–2619 (1997)
Liao, X., Ran, J.: Hopf bifurcation in love dynamical models with nonlinear couples and time delays. Chaos Solitons Fractals 31(4), 853–865 (2007)
Padula, J.: The Kama Sutra, Romeo and Juliet, and mathematics: studying mathematics for pleasure. Aust. Sr. Math. J. 19(2), 43 (2005)
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)
Rinaldi, S.: Laura and Petrarch: an intriguing case of cyclical love dynamics. SIAM J. Appl. Math. 58(4), 1205–1221 (1998)
Rinaldi, S.: Love dynamics: the case of linear couples. Appl. Math. Comput. 95(2), 181–192 (1998)
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)
Rinaldi, S., Della Rossa, F., Landi, P.: A mathematical model of ‘Pride and Prejudice’. Nonlinear Dynamics Psychol. Life Sci. 18(2), 199–211 (2014)
Rinaldi, S., Gragnani, A.: Love dynamics between secure individuals: a modeling approach. Nonlinear Dynamics Psychol. Life Sci. 2(4), 283–301 (1998)
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)
Rinaldi, S., Rossa, F.D., Dercole, F.: Love and appeal in standard couples. Int. J. Bifurc. Chaos 20(08), 2443–2451 (2010)
Satsangi, D., Sinha, A.K.: Dynamics of love and happiness: a mathematical analysis. Int. J. Mod. Educ. Comput. Sci. (IJMECS) 4(5), 31 (2012)
Son, W.-S., Park, Y.-J.: Time delay effect on the love dynamical model. arXiv preprint arXiv:1108.5786 (2011)
Sprott, J.: Dynamical models of love. Nonlinear Dynamics Psychol. Life Sci. 8(3), 303–314 (2004)
Sternberg, R.J., Barnes, M.L.: The Psychology of Love. Yale University Press, New Haven (1988)
Strogatz, S.H.: Love affairs and differential equations. Math. Mag. 61(1), 35 (1988)
Ahmad, W.M., El-Khazali, R.: Fractional-order dynamical models of love. Chaos Solitons Fractals 33(4), 1367–1375 (2007)
Cveticanin, L.: Resonant vibrations of nonlinear rotors. Mech. Mach. Theory 30(4), 581–588 (1995)
Rozhansky, V.A., Tsendin, L.D.: Transport Phenomena in Partially Ionized Plasma. CRC Press, Boca Raton (2001)
Newell, A.C., Moloney, J.V.: Nonlinear Optics. Addison-Wesley, Reading (1992)
Dilão, R., Alves-Pires, R.: Nonlinear Dynamics in Particle Accelerators, vol. 23. World Scientific, Singapore (1996)
Cveticanin, L.: Approximate analytical solutions to a class of non-linear equations with complex functions. J. Sound Vib. 157(2), 289–302 (1992)
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)
Wu, X., Xu, Y., Zhang, H.: Random impacts of a complex damped system. Int. J. Non-Linear Mech. 46(5), 800–806 (2011)
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)
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)
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)
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)
Marshall, D., Sprott, J.: Simple driven chaotic oscillators with complex variables. Chaos Interdiscip. J. Nonlinear Sci. 19(1), 013124 (2009)
Marshall, D., Sprott, J.C.: Simple conservative, autonomous, second-order chaotic complex variable systems. Int. J. Bifurc. Chaos 20(03), 697–702 (2010)
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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