625
Views
3
CrossRef citations to date
0
Altmetric
Original Articles

Social Balance and the Bernoulli Equation

References

  • Arnold, L. (1971). On Wigner’s semicircle law for the eigenvalues of random matrices. Z. Wahrscheinlichkeitstheorie Verw. Geb. 19: 191–198.
  • Bernoulli, J. (1695). Explicationes, Annotationes & Additiones ad ea, quae in Actis sup. de Curva Elastica, Isochrona Paracentrica, & Velaria, hinc inde memorata, & paratim controversa legundur; ubi de Linea mediarum directionum, alliisque novis. Acta Eruditorum. 537–553.
  • Cartwright, D., Harary, F. (1956). Structural balance: a generalization of Heider’s theory. Psychological Review. 63(5): 277–293.
  • Chicone, C. (2006). Ordinary Differential Equations, 2nd ed. New York: Springer.
  • Harary, F. (1953). On the notion of balance of a signed graph. Michigan Math. J. 2(2): 143–146.
  • Heider, F. (1946). Attitudes and cognitive organization. J. Psychol. 21: 107–112.
  • König, D. (1916). Über Graphen und Ihre Anwendung auf Determinantentheorie und Mengenlehre. Mathematische Annalen. 77: 453–465.
  • Marvel, S., Kleinberg, J., Kleinberg, R., Strogatz, S. (2011). Continuous–time model of structural balance, Proceedings of the National Academy of Sciences. 108(5): 1771–1776.
  • Mathews, J., Walker, J. R. (1970). Mathematical Methods of Physics, 2nd ed. New York: W. A. Benjamin.
  • Rapoport, A. (1963). Mathematical models of social interaction. In: Galanter, R. A., Lace, R. R., Bush, E., eds. Handbook of Mathematical Sociology, Vol2. New York: Wiley & Sons, pp. 493–580.
  • Reid, W. T. (1946). A matrix differential equation of Riccati type. Amer. J. Math. 68(2): 237–246.
  • Tao, T., Vu, V. (2015). Random matrices: Universality of local spectral statistics of non-Hermitian matrices. Ann. Prob. 43(2): 782–874.
  • Teschl, G. (2012). Ordinary Differential Equations and Dynamical Systems. Graduate Studies in Mathematics, Vol.140. Providence, RI: American Mathematical Society.
  • Traag, V. A., Van Dooren, P., De Leenheer, P. (2013). Dynamical models explaining social balance and evolution of cooperation. PLOS One. 8(4): e60063.

Reprints and Corporate Permissions

Please note: Selecting permissions does not provide access to the full text of the article, please see our help page How do I view content?

To request a reprint or corporate permissions for this article, please click on the relevant link below:

Academic Permissions

Please note: Selecting permissions does not provide access to the full text of the article, please see our help page How do I view content?

Obtain permissions instantly via Rightslink by clicking on the button below:

If you are unable to obtain permissions via Rightslink, please complete and submit this Permissions form. For more information, please visit our Permissions help page.