Research Article
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Modeling Love with 4D Dynamical System

Year 2022, Volume 4, Issue 3, 135 - 143, 30.11.2022
https://doi.org/10.51537/chaos.1131966

Abstract

The dynamical modeling of romantic relationships is explained with a differential equation system designed to explain the development of love/hate feeling between two people over time. In this study, it was assumed that the individual's emotion was two-component, intimacy and passion, instead of a single-component feeling of love. As a result of this assumption, the relationship dynamics is represented by a four-dimensional system of equations. The possible results of this new 4D model were compared with the results of the classical 2D model and it was seen that they could give very different outputs from each other. In addition, situations that cannot be explained by classical models such as the end of passion in long-term relationships, relationships that turn from friendship to love, and couples reunited after separation are interpreted.

References

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  • Aykutoğlu, B., 2015 The Relationship between intimacy and passion: gender, relationship length, physical attractiveness as moderators. Master’s thesis, Middle East Technical University.
  • Aykutoğlu, B. and A. Uysal, 2017 The relationship between intimacy change and passion: A dyadic diary study. Frontiers in psychology 8: 2257.
  • Barley, K. and A. Cherif, 2011 Stochastic nonlinear dynamics of interpersonal and romantic relationships. Applied Mathematics and Computation 217: 6273–6281.
  • Baumeister, R. F. and E. Bratslavsky, 1999 Passion, intimacy, and time: Passionate love as a function of change in intimacy. Personality and social psychology review 3: 49–67.
  • Bielczyk, N., M. Bodnar, and U. Fory ́s, 2012 Delay can stabilize: Love affairs dynamics. Applied Mathematics and Computation 219: 3923–3937.
  • Chen, K., W. Liu, and J. Park, 2016 Modified models for love and their dynamical properties. Miskolc Mathematical Notes 17: 119–132.
  • Erba ̧s, K. C., 2022 Determination of romantic relationship categories and investigatıon of their dynamical properties. Chaos Theory and Applications 4: 37–44.
  • 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.
  • Hatfield, E., R. J. Sternberg, and M. L. Barnes, 1988 Passionate and companionate love. the psychology of love. Sternberg RJ & Barnes MSL .
  • Hazan, C. and P. Shaver, 2017 Romantic love conceptualized as an attachment process. In Interpersonal Development, pp. 283–296, Routledge.
  • Huang, L. and Y. Bae, 2018a Analysis of chaotic behavior in a novel extended love model considering positive and negative external environment. Entropy 20: 365.
  • Huang, L. and Y. Bae, 2018b Chaotic dynamics of the fractional love model with an external environment. Entropy 20: 53.
  • Jafari, S., J. C. Sprott, and S. Golpayegani, 2016 Layla and majnun: a complex love story. Nonlinear Dynamics 83: 615–622.
  • Kacar, S., Z. Wei, A. Akgul, and B. Aricioglu, 2018 A novel 4d chaotic system based on two degrees of freedom nonlinear mechanical system. Zeitschrift für Naturforschung A 73: 595–607.
  • Koca, I. and N. Ozalp, 2014 On a fractional order nonlinear dynamic model of a triadic relationship. Journal: Journal of Advances in Mathematics 5.
  • Kumar, P., V. S. Erturk, and M. Murillo-Arcila, 2021 A complex fractional mathematical modeling for the love story of layla and majnun. Chaos, Solitons & Fractals 150: 111091.
  • Lee, J. A. et al., 1988 Love-styles. The psychology of love pp. 38–67.
  • Liao, X. and J. Ran, 2007 Hopf bifurcation in love dynamical models with nonlinear couples and time delays. Chaos, Solitons & Fractals 31: 853–865.
  • Liu, W. and K. Chen, 2015 Chaotic behavior in a new fractional order love triangle system with competition. J. Appl. Anal. Comput 5: 103–113.
  • 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.
  • Rinaldi, S., 1998a Laura and petrarch: An intriguing case of cyclical love dynamics. SIAM Journal on Applied Mathematics 58: 1205–1221.
  • Rinaldi, S., 1998b Love dynamics: The case of linear couples. Applied Mathematics and Computation 95: 181–192.
  • Rinaldi, S. and F. Della Rossa, 2020 From individual traits to couple behavior. International Journal of Bifurcation and Chaos 30: 2050219.
  • Rinaldi, S., F. Della Rossa, and P. Landi, 2013a A mathematical model of “gone with the wind”. Physica A: Statistical Mechanics and its Applications 392: 3231–3239.
  • Rinaldi, S., P. Landi, and F. D. ROSSA, 2013b Small discoveries can have great consequences in love affairs: the case of beauty and the beast. International Journal of Bifurcation and Chaos 23: 1330038.
  • Rinaldi, S., F. D. Rossa, and F. Dercole, 2010 Love and appeal in standard couples. International Journal of Bifurcation and Chaos 20: 2443–2451.
  • Rubin, Z., 1970 Measurement of romantic love. Journal of personality and social psychology 16: 265.
  • Sprott, J., 2004 Dynamical models of love. Nonlinear dynamics, psychology, and life sciences 8: 303–314.
  • Sprott, J. C., 2010 Elegant chaos: algebraically simple chaotic flows. World Scientific.
  • Sternberg, R. J., 1986 A triangular theory of love. Psychological review 93: 119.
  • Strogatz, S. H., 1988 Love affairs and differential equations. Mathematics Magazine 61: 35–35.
  • Sunday, J., D. Zirra, and M. Mijinyawa, 2012 A computational approach to dynamical love model: The romeo and juliet scenario. International Journal of Pure and Applied Sciences and Technology 11: 10.
  • Wang, X., Y. Feng, and Y. Chen, 2022 A new four-dimensional chaotic system and its circuit implementation. Frontiers in Physics p. 376.
  • 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 3, 135 - 143, 30.11.2022
https://doi.org/10.51537/chaos.1131966

Abstract

References

  • Ahmad, W. M. and R. El-Khazali, 2007 Fractional-order dynamical models of love. Chaos, Solitons & Fractals 33: 1367–1375.
  • Aykutoğlu, B., 2015 The Relationship between intimacy and passion: gender, relationship length, physical attractiveness as moderators. Master’s thesis, Middle East Technical University.
  • Aykutoğlu, B. and A. Uysal, 2017 The relationship between intimacy change and passion: A dyadic diary study. Frontiers in psychology 8: 2257.
  • Barley, K. and A. Cherif, 2011 Stochastic nonlinear dynamics of interpersonal and romantic relationships. Applied Mathematics and Computation 217: 6273–6281.
  • Baumeister, R. F. and E. Bratslavsky, 1999 Passion, intimacy, and time: Passionate love as a function of change in intimacy. Personality and social psychology review 3: 49–67.
  • Bielczyk, N., M. Bodnar, and U. Fory ́s, 2012 Delay can stabilize: Love affairs dynamics. Applied Mathematics and Computation 219: 3923–3937.
  • Chen, K., W. Liu, and J. Park, 2016 Modified models for love and their dynamical properties. Miskolc Mathematical Notes 17: 119–132.
  • Erba ̧s, K. C., 2022 Determination of romantic relationship categories and investigatıon of their dynamical properties. Chaos Theory and Applications 4: 37–44.
  • 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.
  • Hatfield, E., R. J. Sternberg, and M. L. Barnes, 1988 Passionate and companionate love. the psychology of love. Sternberg RJ & Barnes MSL .
  • Hazan, C. and P. Shaver, 2017 Romantic love conceptualized as an attachment process. In Interpersonal Development, pp. 283–296, Routledge.
  • Huang, L. and Y. Bae, 2018a Analysis of chaotic behavior in a novel extended love model considering positive and negative external environment. Entropy 20: 365.
  • Huang, L. and Y. Bae, 2018b Chaotic dynamics of the fractional love model with an external environment. Entropy 20: 53.
  • Jafari, S., J. C. Sprott, and S. Golpayegani, 2016 Layla and majnun: a complex love story. Nonlinear Dynamics 83: 615–622.
  • Kacar, S., Z. Wei, A. Akgul, and B. Aricioglu, 2018 A novel 4d chaotic system based on two degrees of freedom nonlinear mechanical system. Zeitschrift für Naturforschung A 73: 595–607.
  • Koca, I. and N. Ozalp, 2014 On a fractional order nonlinear dynamic model of a triadic relationship. Journal: Journal of Advances in Mathematics 5.
  • Kumar, P., V. S. Erturk, and M. Murillo-Arcila, 2021 A complex fractional mathematical modeling for the love story of layla and majnun. Chaos, Solitons & Fractals 150: 111091.
  • Lee, J. A. et al., 1988 Love-styles. The psychology of love pp. 38–67.
  • Liao, X. and J. Ran, 2007 Hopf bifurcation in love dynamical models with nonlinear couples and time delays. Chaos, Solitons & Fractals 31: 853–865.
  • Liu, W. and K. Chen, 2015 Chaotic behavior in a new fractional order love triangle system with competition. J. Appl. Anal. Comput 5: 103–113.
  • 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.
  • Rinaldi, S., 1998a Laura and petrarch: An intriguing case of cyclical love dynamics. SIAM Journal on Applied Mathematics 58: 1205–1221.
  • Rinaldi, S., 1998b Love dynamics: The case of linear couples. Applied Mathematics and Computation 95: 181–192.
  • Rinaldi, S. and F. Della Rossa, 2020 From individual traits to couple behavior. International Journal of Bifurcation and Chaos 30: 2050219.
  • Rinaldi, S., F. Della Rossa, and P. Landi, 2013a A mathematical model of “gone with the wind”. Physica A: Statistical Mechanics and its Applications 392: 3231–3239.
  • Rinaldi, S., P. Landi, and F. D. ROSSA, 2013b Small discoveries can have great consequences in love affairs: the case of beauty and the beast. International Journal of Bifurcation and Chaos 23: 1330038.
  • Rinaldi, S., F. D. Rossa, and F. Dercole, 2010 Love and appeal in standard couples. International Journal of Bifurcation and Chaos 20: 2443–2451.
  • Rubin, Z., 1970 Measurement of romantic love. Journal of personality and social psychology 16: 265.
  • Sprott, J., 2004 Dynamical models of love. Nonlinear dynamics, psychology, and life sciences 8: 303–314.
  • Sprott, J. C., 2010 Elegant chaos: algebraically simple chaotic flows. World Scientific.
  • Sternberg, R. J., 1986 A triangular theory of love. Psychological review 93: 119.
  • Strogatz, S. H., 1988 Love affairs and differential equations. Mathematics Magazine 61: 35–35.
  • Sunday, J., D. Zirra, and M. Mijinyawa, 2012 A computational approach to dynamical love model: The romeo and juliet scenario. International Journal of Pure and Applied Sciences and Technology 11: 10.
  • Wang, X., Y. Feng, and Y. Chen, 2022 A new four-dimensional chaotic system and its circuit implementation. Frontiers in Physics p. 376.
  • 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 Computer Science, Interdisciplinary Application, Physics, Mathematical, Physics, Applied
Journal Section Research Articles
Authors

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

Publication Date November 30, 2022
Published in Issue Year 2022, Volume 4, Issue 3

Cite

APA Erbaş, K. C. (2022). Modeling Love with 4D Dynamical System . Chaos Theory and Applications , 4 (3) , 135-143 . DOI: 10.51537/chaos.1131966

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