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Journal of Biological Dynamics Volume 13, 2019 - Issue sup1: Selected Papers from the Sixth International Conference on Mathematical Modeling and Analysis of Populations in Biological Systems (ICMA VI), University of Arizona, USA, 20-22 October 2017
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Articles

Equilibrium Distributions of Populations of Biological Species on Networks of Social Sites

Min WangMathematical Biosciences Institute, Ohio State University, Columbus, Ohio, USAView further author information
,
Wen ZhouDepartment of Statistics, Colorado State University, Fort Collins, Colorado, USAView further author information
&
Zhijun WuDepartment of Mathematics, Iowa State University, Ames, Iowa, USACorrespondence[email protected]
View further author information
Pages 74-98 | Received 10 Feb 2018, Accepted 25 Jul 2018, Published online: 16 Aug 2018

References

  • J. Alcock, Animal Behavior: An Evolutionary Approach, Sinauer Associates Inc., Sunderland, MA, 2009.
  • I.M. Bomze, Evolution towards the maximum clique, J. Glob. Optim. 10 (1997), pp. 143–164. doi: 10.1023/A:1008230200610
  • I. Bomze, Regularity vs. degeneracy in dynamics, games, and optimization: a unified approach to different aspects, SIAM Rev. 44 (2002), pp. 394–414. doi: 10.1137/S00361445003756
  • I.M. Bomze, M. Budinich, P.M. Pardalos, and M. Pelillo, The maximum clique problem, Handb. Comb. Optim. 4 (1999), pp. 1–74.
  • C. Cannings and G. T. Vickers, Patterns of ESS's II. Journal of Theoretical Biology 132 (1988), pp. 409–420.
  • X. Chen, A. Szolnoki, and M. Perc, Competition and cooperation among different punishing strategies in the spatial public goods game, Phys. Rev. E 92 (2015), pp. 012819.
  • R. Fletcher, Practical Methods of Optimization, Wiley, New York, 2000.
  • J.H. Fowler and N.A. Christakis, Dynamic spread of happiness in a large social network: longitudinal analysis over 20 years in the Framingham Heart Study, Br. Med. J. 337 (2008), pp. a2338–a2338. doi: 10.1136/bmj.a2338
  • M.R. Garey and D.S. Johnson, Computer and Intractability: A Guide to the Theory of NP-Completeness, W. H. Freeman and Company, New York, 1979.
  • C. Hidalgo, Networks Complexity and Its Applications, Springer, New York, 2011.
  • J. Hofbauer and K. Sigmund, Evolutionary Games and Population Dynamics, Cambridge University Press, Cambridge, UK, 1998.
  • Y. Huang, Y. Hao, M. Wang, W. Zhou, and Z. Wu, Optimality and stability of symmetric evolutionary games with applications in genetic selection, J. Math. Biosci. Eng. 12 (2015), pp. 503–523. doi: 10.3934/mbe.2015.12.503
  • M.O. Jackson, Networks and economic behavior, Annu. Rev. Econ. 1 (2009), pp. 489–511. doi: 10.1146/annurev.economics.050708.143238
  • M.J. Keeling and K.T.D. Eames, Networks and epidemic models, J. R. Soc. Interface 2 (2005), pp. 295–307. doi: 10.1098/rsif.2005.0051
  • D.Y. Kenett, M. Perc, and S. Boccaletti, Networks of networks – an introduction, Chaos, Solitons & Fractals 80 (2015), pp. 1–6. doi: 10.1016/j.chaos.2015.03.016
  • G.E. Leventhal, A.L. Hill, M.A. Nowak, and S. Bonhoeffer, Evolution and emergence of infectious diseases in theoretical and real world networks, Nat. Commun. 6 (2014), pp. 6101–6112. doi: 10.1038/ncomms7101
  • T.G. Lewis, Network Science: Theory and Applications, Wiley, New York, 2009.
  • T.S. Motzkin and E.G. Straus, Maxima for graphs and a new proof of a theorem of Turan, Can J. Math. 17 (1965), pp. 533–540. doi: 10.4153/CJM-1965-053-6
  • J. Nocedal and S.J. Wright, Numerical Optimization, Springer, New York, 2006.
  • H. Ohtsuki, C. Hauert, E. Lieberman, and M.A. Nowak, A simple rule for the evolution of cooperation on graphs and social networks, Nature 441 (2006), pp. 502–505. doi: 10.1038/nature04605
  • P.M. Pardalos, Y. Ye, and C. Han, Algorithms for the solution of quadratic knapsack problems, Linear Algebra Its Appl. 152 (1991), pp. 69–91. doi: 10.1016/0024-3795(91)90267-Z
  • M. Perc, J.J. Jordan, D.G. Rand, Z. Wang, S. Boccaletti, and A. Szolnoki, Statistical physics of human cooperation, Phys. Rep. 687 (2017), pp. 1–51. doi: 10.1016/j.physrep.2017.05.004
  • M. Perc and A. Szolnoki, Coevolutionary games – a mini review, BioSystems 99 (2010), pp. 109–125. doi: 10.1016/j.biosystems.2009.10.003
  • W.H. Sandholm, Population Games and Evolutionary Dynamics, The MIT Press, Cambridge, MA, 2010.
  • J. Scott, Social Network Analysis: A Handbook, SAGE Publication Ltd., London, UK, 2000.
  • G. Szabo and G. Fath, Evolutionary games on graphs, Phys. Rep. 446 (2007), pp. 97–216. doi: 10.1016/j.physrep.2007.04.004
  • G.T. Vickers and C. Cannings, On the number of stable equilibria in a one-locus, multi-allelic system, J. Theor. Biol. 131 (1988), pp. 273–277. doi: 10.1016/S0022-5193(88)80225-X
  • G.T. Vickers and C. Cannings, Patterns of ESS's I. Journal of Theoretical Biology 132 (1988), pp. 387–408.
  • Q. Wang, N. He, and X. Chen, Replicator dynamics for public goods game with resource allocation in large populations, Appl. Math. Comput. 328 (2018), pp. 162–170.
  • Z. Wang, A. Szolnoki, and M. Perc, Interdependent network reciprocity in evolutionary games, Sci. Rep. 3 (2013), pp. 1183. doi: 10.1038/srep01183
  • Z. Wang, L. Wang, A. Szolnoki, and M. Perc, Evolutionary games on multilayer networks: a colloquium, Eur. Phys. J. B 88 (2015), pp. 124. doi: 10.1140/epjb/e2015-60270-7
  • S. Wasserman and K. Faust, Social Network Analysis: Methods and Applications, Cambridge University Press, Cambridge, UK, 1994.
  • J.W. Weibull, Evolutionary Game Theory, The MIT Press, Cambridge, MA, 1995.

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