\`x^2+y_1+z_12^34\`
Advanced Search
Article Contents
Article Contents

Some remarks on the Gottman-Murray model of marital dissolution and time delays

Abstract Full Text(HTML) Related Papers Cited by
  • In the paper we consider mathematical model proposed by Gottman, Murray and collaborators to describe marital dissolution. This model is described in the framework of discrete dynamical system reflecting emotional states of wife and husband during consecutive rounds of talks between spouses. The model is, however, non-symmetric. To make it symmetric, one need to assume that the husband reacts with delay. Following this idea we consider the influence of time delays in the reaction terms of wife or/and husband. The delay means that one or both of spouses split their attention between present and previous rounds of talks. We study possibility of the change of stability with increasing delay. Surprisingly, it occurs that the delay has no impact on the stability, that is the condition of stability proposed by Murray remains unchanged.

    Mathematics Subject Classification: Primary: 91D99; Secondary: 37C75, 37N99.

    Citation:

    \begin{equation} \\ \end{equation}
  • 加载中
  •   R. M. Baron, P. G. Amazeen and P. J. Beek, Local and global dynamics of social interactions, In R. R. Vallacher & A. Nowak (Eds. ), Dynamical systems in social psychology, (1994), 111–138. San Diego, CA: Academic Press.
      N. Bielczyk , M. Bodnar  and  U. Foryś , Delay can stabilize: Love affairs dynamics, Applied Mathematics and Computation, 219 (2012) , 3923-3937.  doi: 10.1016/j.amc.2012.10.028.
      N. Bielczyk , U. Foryś  and  T. Płatkowski , Dynamical models of dyadic interactions with delay, Journal of Mathematical Sociology, 37 (2013) , 223-249.  doi: 10.1080/0022250X.2011.597279.
      K. L. Cooke  and  P. van den Driessche , On zeros of some transcendental equations, Funkcialaj Ekvacioj, 29 (1986) , 77-90. 
      F. Dercole and S. Rinaldi, Love stories can be unpredictable: Juliet at Jim in the vortex of life Chaos 24 (2014), 023134, 9pp. doi: 10.1063/1.4882685.
      D. H. Felmlee  and  D. F. Greenberg , A dynamic systems model of dyadic interaction, Journal of Mathematical Sociology, 23 (1999) , 155-180. 
      U. Foryś , Biological delay systems and the Mikhailov criterion of stability, Journal of Biological Systems, 12 (2004) , 1-16. 
      U. Foryś, Time delays and the Gottman, Murray et al. model of marital interactions, In Proceedings of XXII National Conference, 2016.
      J. M. Gottman, J. D. Murray, C. C. Swanson, R. Tyson and K. R. Swanson, The Mathematics of Marriage: Dynamic Nonlinear Models, Cambridge, MA: MIT Press, 2002.
      S. G. Krantz, Rouché's Theorem, In Handbook of Complex Variables. Boston, MA: Birkhäuser, 1999.
      B. Latane and A. Nowak, Attitudes as catastrophes: From dimensions to categories with increasing involvement, In R. R. Vallacher & A. Nowak (Eds. ), Dynamical systems in social psychology, (1994), 219–249. San Diego, CA: Academic Press.
      R. Leek  and  B. Meeker , Exploring nonlinear path models via computer simulation, Social Science Computer Review, 14 (1996) , 253-268. 
      X. Liao  and  J. Ran , Hopf bifurcation in love dynamical models with nonlinear couples and time delays, Chaos, Solitons, Fract., 31 (2007) , 853-865.  doi: 10.1016/j.chaos.2005.10.037.
      L. S. Liebovitch , V. Naudot , R. Vallacher , A. Nowak , L. Biu-Wrzosinska  and  P. Coleman , Dynamics of two-actor cooperation-conflict models, Physica A, 387 (2008) , 6360-6378. 
      J. D. Murray, Mathematical Biology: Vol. 1. An Introduction, New York, NY: Springer-Verlag, 2002.
      A. Nowak and R. R. Vallacher, Dynamical Social Psychology, New York, NY: Guilford Press, 1998.
      S. Rinaldi  and  A. Gragnani , Love dynamics between secure individuals: A modeling approach, Nonlinear Dynamics, Psychology, and Life Sciences, 2 (1998) , 283-301. 
      S. Rinaldi , Love Dynamics: The case of linear couples, Applied Mathematics and Computation, 95 (1998) , 181-192.  doi: 10.1016/S0096-3003(97)10081-9.
      S. Rinaldi , F. Della Rosa  and  F. Dercole , Love and appeal in standard couples, International Journal of Bifurcation and Chaos, 20 (2010) , 2443-2451. 
      S. Rinaldi, P. Landi and F. Della Rosa, Small discoveries can have great consequences in love affairs: The case of Beauty and the Beast, International Journal of Bifurcation and Chaos, 23 (2013), 1330038, 8 pp. doi: 10.1142/S0218127413300383.
      C. Rusbult  and  P. van Lange , Interdependence, interaction and relationships, Annual Review of Psychology, 54 (2003) , 351-375. 
      J. Skonieczna  and  U. Foryś , Stability switches for some class of delayed population models, Applied Mathematics (Warsaw), 38 (2011) , 51-66.  doi: 10.4064/am38-1-4.
      S. Strogatz, Love affairs and differential equations, Mathematics Magazine, 65 (1988), p35.
      S. Strogatz, Nonlinear Dynamics and Chaos: With Applications to Physics, Biology, Chemistry, Reading, MA: Perseus Books, 1994.
      A. Turowicz, Geometria zer wielomianów (in Polish), Warsaw, PWN, 1967.
  • 加载中
SHARE

Article Metrics

HTML views(1445) PDF downloads(234) Cited by(0)

Access History

Other Articles By Authors

Catalog

    /

    DownLoad:  Full-Size Img  PowerPoint
    Return
    Return