Research Article
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Determination of Romantic Relationship Categories and Investigatıon of Their Dynamical Properties

Year 2022, Volume 4, Issue 1, 37 - 44, 30.03.2022
https://doi.org/10.51537/chaos.1000608

Abstract

In studies on dynamical modeling of romantic relationships, it is seen that individuals are divided into four different romantic styles. Most of these studies focused on the mathematical analysis of the dynamic expression of individuals' attitudes or tried to determine what kind of relationship evolution randomly assigned romantic style parameters will create. The categorization of relationship types and finding the general characteristics of the relationships in each category by identifying all combinations of four different romantic styles, to our knowledge, have not been attempted before. To fill this gap in the literature, this study divided individuals into four different romantic styles and identified ten different types of relationships formed by the combination of these four styles. The evolution of the love/hate situation of individuals in each type of relationship was modeled with a linear differential equation system and the short-term development of the relationship to evolve from an initial state was determined. According to the results, it was observed that in some types of relationships, couples achieved harmony in the love/hate mood over time, while in some types of relationships, a couple was reluctant. It has even been determined that the willingness in the relationship enters a periodic cycle. With the findings obtained, it can be determined what kind of relationship the couples are in, guidance can be provided and feedback correction can be provided to their attitudes in the relationship. Overall, this study aimed to be a starting point for the applicability of dynamic modeling with psychometric research.

References

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  • Bae, Y., 2015 Chaotic behavior in a dynamic love model with different external forces. International Journal of Fuzzy Logic and Intelligent Systems 15: 283–288.
  • Bagarello, F., 2011 Damping in quantum love affairs. Physica A: Statistical Mechanics and its Applications 390: 2803–2811.
  • Bagarello, F. and F. Oliveri, 2010 An operator-like description of love affairs. SIAM Journal on Applied Mathematics 70: 3235– 3251.
  • Barley, K. and A. Cherif, 2011 Stochastic nonlinear dynamics of interpersonal and romantic relationships. Applied Mathematics and Computation 217: 6273–6281.
  • Bielczyk, N., U. Fory´s, and T. Płatkowski, 2013 Dynamical models of dyadic interactions with delay. The Journal of mathematical sociology 37: 223–249.
  • Deng, W., X. Liao, T. Dong, and B. Zhou, 2017 Hopf bifurcation in a love-triangle model with time delays. Neurocomputing 260: 13–24.
  • Gottman, J., J. Murray, C. Swanson, R. Tyson, and K. Swanson, 2002 The mathematics of marriage: Dynamic nonlinear approach.
  • Goyal, M., A. Prakash, and S. Gupta, 2019 Numerical simulation for time-fractional nonlinear coupled dynamical model of romantic and interpersonal relationships. Pramana 92: 1–12.
  • Gragnani, A., S. Rinaldi, and G. Feichtinger, 1996 Complex dynamics in romantic relationships.
  • Hollis, S., 2010 Eigenvalues and linear phase portraits.
  • Jafari, S., J. C. Sprott, and S. Golpayegani, 2016 Layla and majnun: a complex love story. Nonlinear Dynamics 83: 615–622.
  • Liao, X. and J. Ran, 2007 Hopf bifurcation in love dynamical models with nonlinear couples and time delays. Chaos, Solitons & Fractals 31: 853–865.
  • Owolabi, K. M., 2019 Mathematical modelling and analysis of love dynamics: A fractional approach. Physica A: Statistical Mechanics and its Applications 525: 849–865.
  • Ozalp, N. and I. Koca, 2012 A fractional order nonlinear dynamical model of interpersonal relationships. Advances in Difference Equations 2012: 1–7.
  • Patro, S. K., 2016 On a model of love dynamics: A neutrosophic analysis. Florentin Smarandache, Surapati Pramanik p. 279.
  • Rapoport, A. and R. Anatol, 1960 Fights, games, and debates. University of Michigan Press.
  • Rinaldi, S., 1998 Love dynamics: The case of linear couples. Applied Mathematics and Computation 95: 181–192.
  • Rinaldi, S., F. Della Rossa, F. Dercole, A. Gragnani, and P. Landi, 2015 Modeling love dynamics, volume 89. World Scientific.
  • Satsangi, D. and A. K. Sinha, 2012 Dynamics of love and happiness: a mathematical analysis. International Journal of Modern Education and Computer Science 4: 31.
  • Son, W.-S. and Y.-J. Park, 2011 Time delay effect on the love dynamical model. arXiv preprint arXiv:1108.5786 .
  • Strogatz, S. H., 1988 Love affairs and differential equations. Mathematics Magazine 61: 35–35.
  • Wauer, J., D. Schwarzer, G. Cai, and Y. Lin, 2007 Dynamical models of love with time-varying fluctuations. Applied Mathematics and Computation 188: 1535–1548.

Year 2022, Volume 4, Issue 1, 37 - 44, 30.03.2022
https://doi.org/10.51537/chaos.1000608

Abstract

References

  • Ahmad, W. M. and R. El-Khazali, 2007 Fractional-order dynamical models of love. Chaos, Solitons & Fractals 33: 1367–1375.
  • Bae, Y., 2015 Chaotic behavior in a dynamic love model with different external forces. International Journal of Fuzzy Logic and Intelligent Systems 15: 283–288.
  • Bagarello, F., 2011 Damping in quantum love affairs. Physica A: Statistical Mechanics and its Applications 390: 2803–2811.
  • Bagarello, F. and F. Oliveri, 2010 An operator-like description of love affairs. SIAM Journal on Applied Mathematics 70: 3235– 3251.
  • Barley, K. and A. Cherif, 2011 Stochastic nonlinear dynamics of interpersonal and romantic relationships. Applied Mathematics and Computation 217: 6273–6281.
  • Bielczyk, N., U. Fory´s, and T. Płatkowski, 2013 Dynamical models of dyadic interactions with delay. The Journal of mathematical sociology 37: 223–249.
  • Deng, W., X. Liao, T. Dong, and B. Zhou, 2017 Hopf bifurcation in a love-triangle model with time delays. Neurocomputing 260: 13–24.
  • Gottman, J., J. Murray, C. Swanson, R. Tyson, and K. Swanson, 2002 The mathematics of marriage: Dynamic nonlinear approach.
  • Goyal, M., A. Prakash, and S. Gupta, 2019 Numerical simulation for time-fractional nonlinear coupled dynamical model of romantic and interpersonal relationships. Pramana 92: 1–12.
  • Gragnani, A., S. Rinaldi, and G. Feichtinger, 1996 Complex dynamics in romantic relationships.
  • Hollis, S., 2010 Eigenvalues and linear phase portraits.
  • Jafari, S., J. C. Sprott, and S. Golpayegani, 2016 Layla and majnun: a complex love story. Nonlinear Dynamics 83: 615–622.
  • Liao, X. and J. Ran, 2007 Hopf bifurcation in love dynamical models with nonlinear couples and time delays. Chaos, Solitons & Fractals 31: 853–865.
  • Owolabi, K. M., 2019 Mathematical modelling and analysis of love dynamics: A fractional approach. Physica A: Statistical Mechanics and its Applications 525: 849–865.
  • Ozalp, N. and I. Koca, 2012 A fractional order nonlinear dynamical model of interpersonal relationships. Advances in Difference Equations 2012: 1–7.
  • Patro, S. K., 2016 On a model of love dynamics: A neutrosophic analysis. Florentin Smarandache, Surapati Pramanik p. 279.
  • Rapoport, A. and R. Anatol, 1960 Fights, games, and debates. University of Michigan Press.
  • Rinaldi, S., 1998 Love dynamics: The case of linear couples. Applied Mathematics and Computation 95: 181–192.
  • Rinaldi, S., F. Della Rossa, F. Dercole, A. Gragnani, and P. Landi, 2015 Modeling love dynamics, volume 89. World Scientific.
  • Satsangi, D. and A. K. Sinha, 2012 Dynamics of love and happiness: a mathematical analysis. International Journal of Modern Education and Computer Science 4: 31.
  • Son, W.-S. and Y.-J. Park, 2011 Time delay effect on the love dynamical model. arXiv preprint arXiv:1108.5786 .
  • Strogatz, S. H., 1988 Love affairs and differential equations. Mathematics Magazine 61: 35–35.
  • Wauer, J., D. Schwarzer, G. Cai, and Y. Lin, 2007 Dynamical models of love with time-varying fluctuations. Applied Mathematics and Computation 188: 1535–1548.

Details

Primary Language English
Subjects Physics, Applied
Journal Section Research Articles
Authors

Kadir Can ERBAŞ (Primary Author)
başkent üniversitesi
0000-0002-6446-829X
Türkiye

Publication Date March 30, 2022
Published in Issue Year 2022, Volume 4, Issue 1

Cite

APA Erbaş, K. C. (2022). Determination of Romantic Relationship Categories and Investigatıon of Their Dynamical Properties . Chaos Theory and Applications , 4 (1) , 37-44 . DOI: 10.51537/chaos.1000608

Chaos Theory and Applications in Applied Sciences and Engineering: An interdisciplinary journal of nonlinear science 23830