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Innovation diffusion on time-varying activity driven networks

  • Alessandro Rizzo
  • Maurizio Porfiri
Regular Article

Abstract

Since its introduction in the 1960s, the theory of innovation diffusion has contributed to the advancement of several research fields, such as marketing management and consumer behavior. The 1969 seminal paper by Bass [F.M. Bass, Manag. Sci. 15, 215 (1969)] introduced a model of product growth for consumer durables, which has been extensively used to predict innovation diffusion across a range of applications. Here, we propose a novel approach to study innovation diffusion, where interactions among individuals are mediated by the dynamics of a time-varying network. Our approach is based on the Bass’ model, and overcomes key limitations of previous studies, which assumed timescale separation between the individual dynamics and the evolution of the connectivity patterns. Thus, we do not hypothesize homogeneous mixing among individuals or the existence of a fixed interaction network. We formulate our approach in the framework of activity driven networks to enable the analysis of the concurrent evolution of the interaction and individual dynamics. Numerical simulations offer a systematic analysis of the model behavior and highlight the role of individual activity on market penetration when targeted advertisement campaigns are designed, or a competition between two different products takes place.

Keywords

Statistical and Nonlinear Physics 

References

  1. 1.
    E.M. Rogers, Diffusion of innovations (Simon and Schuster, 2010)Google Scholar
  2. 2.
    V. Mahajan, E. Muller, F.M. Bass, J. Marketing 54, 1 (1990)CrossRefGoogle Scholar
  3. 3.
    F.M. Bass, Manag. Sci. 15, 215 (1969)CrossRefGoogle Scholar
  4. 4.
    F.M. Bass, J. Business 53, S51 (1980)CrossRefGoogle Scholar
  5. 5.
    F.M. Bass, Manag. Sci. 50, 1833 (2004) CrossRefGoogle Scholar
  6. 6.
    W.J. Hopp, Manag. Sci. 50, 1763 (2004) CrossRefGoogle Scholar
  7. 7.
    M.G. Dekimpe, P.M. Parker, M. Sarvary, Technological Forecasting and Social Change 57, 105 (1998)CrossRefGoogle Scholar
  8. 8.
    S. Sundqvist, L. Frank, K. Puumalainen, J. Business Res. 58, 107 (2005)CrossRefGoogle Scholar
  9. 9.
    C. Michalakelis, D. Varoutas, T. Sphicopoulos, Telecommun. Policy 32, 234 (2008)CrossRefGoogle Scholar
  10. 10.
    J. Lim, C. Nam, S. Kim, H. Rhee, E. Lee, H. Lee, Telecomm. Policy 36, 858 (2012)CrossRefGoogle Scholar
  11. 11.
    J.L. Toole, M. Cha, M.C. González, PloS One 7, e29528 (2012) CrossRefADSGoogle Scholar
  12. 12.
    E. Kiesling, M. Günther, C. Stummer, L.M. Wakolbinger, Centr. Eur. J. Oper. Res. 20, 183 (2012)CrossRefGoogle Scholar
  13. 13.
    A. Vespignani, Nat. Phys. 8, 32 (2011)CrossRefGoogle Scholar
  14. 14.
    N. Perra, B. Gonçalves, R. Pastor-Satorras, A. Vespignani, Sci. Rep. 2, 469 (2012)CrossRefADSGoogle Scholar
  15. 15.
    A. Mellor, M. Mobilia, S. Redner, A.M. Rucklidge, J.A. Ward, Phys. Rev. E 92, 012806 (2015) CrossRefADSGoogle Scholar
  16. 16.
    S. Niu, Math. Probl. Eng. 8, 249 (2002)CrossRefMathSciNetGoogle Scholar
  17. 17.
    Y. Moreno, M. Nekovee, A.F. Pacheco, Phys. Rev. E 69, 066130 (2004) CrossRefADSGoogle Scholar
  18. 18.
    P. Andriani, F. Conti, L. Fortuna, M. Frasca, G. Passiante, A. Rizzo, Nonlin. Dyn. 44, 263 (2006)CrossRefMathSciNetGoogle Scholar
  19. 19.
    J. Zhou, Z. Liu, B. Li, Phys. Lett. A 368, 458 (2007) CrossRefADSGoogle Scholar
  20. 20.
    D.H. Zanette, Phys. Rev. E 65, 041908 (2002) CrossRefADSGoogle Scholar
  21. 21.
    G. Fibich, A. Gavious, E. Solan, Proc. Natl. Acad. Sci. 109, 19545 (2012) CrossRefADSGoogle Scholar
  22. 22.
    T. Zaman, E.B. Fox, E.T. Bradlow, Ann. Appl. Statist. 8, 1583 (2014)CrossRefMathSciNetGoogle Scholar
  23. 23.
    R. Illner, J. Ma, An SIS-type marketing model on random networks, http://www.math.uvic.ca/faculty/rillner/papers/sismarketing10.pdf
  24. 24.
    M. Li, R. Illner, R. Edwards, J. Ma, Commun. Math. Sci. 13, 497 (2015)CrossRefMathSciNetGoogle Scholar
  25. 25.
    P. Holme, Phys. Rev. E 71, 046119 (2005) CrossRefADSGoogle Scholar
  26. 26.
    C. Cattuto, W. Van den Broeck, V. Colizza, J.F. Pinton, A. Vespignani, PLoS One 5, e11596 (2010) CrossRefADSGoogle Scholar
  27. 27.
    J. Tang, S. Scellato, M. Musolesi, C. Mascolo, V. Latora, Phys. Rev. E 81, 055101 (2010) CrossRefADSGoogle Scholar
  28. 28.
    S. Gómez, J. Gómez-Gardeñes, Y. Moreno, A. Arenas, Phys. Rev. E 84, 036105 (2011) CrossRefADSGoogle Scholar
  29. 29.
    S. Liu, N. Perra, M. Karsai, A. Vespignani, Phys. Rev. Lett. 112, 118702 (2014) CrossRefADSGoogle Scholar
  30. 30.
    A. Rizzo, M. Frasca, M. Porfiri, Phys. Rev. E 90, 042801 (2014) CrossRefADSGoogle Scholar
  31. 31.
    K. Sun, A. Baronchelli, N. Perra, Eur. Phys. J. B 88, 326 (2015)CrossRefADSMathSciNetGoogle Scholar
  32. 32.
    E. Kiesling, M. Günther, C. Stummer, L.M. Wakolbinger, Centr. Eur. J. Oper. Res. 20, 183 (2012)CrossRefGoogle Scholar
  33. 33.
    F. Sultan, J.U. Farley, D.R. Lehmann, J. Marketing Res. 27, 70 (1990)CrossRefGoogle Scholar
  34. 34.
    J. Goldenberg, B. Libai, E. Muller, Acad. Mark. Sci. Rev. 9, 1 (2001)Google Scholar
  35. 35.
    G. Fibich, R. Gibori, Oper. Res. 58, 1450 (2010) CrossRefMathSciNetGoogle Scholar
  36. 36.
    G. Fibich, A. Gavious, E. Solan, Proc. Natl. Acad. Sci. 109, 19545 (2012) CrossRefADSGoogle Scholar
  37. 37.
    J. Goldenberg, B. Libai, E. Muller, J. Marketing 66, 1 (2002)CrossRefGoogle Scholar
  38. 38.
    T. Garber, J. Goldenberg, B. Libai, E. Muller, Mark. Sci. 23, 419 (2004)CrossRefGoogle Scholar
  39. 39.
    F. Alkemade, C. Castaldi, Comput. Econ. 25, 3 (2005)CrossRefGoogle Scholar
  40. 40.
    S.A. Delre, W. Jager, T.H.A. Bijmolt, M.A. Janssen, J. Business Research 60, 826 (2007)CrossRefGoogle Scholar
  41. 41.
    M.E.J. Newman, Contemp. Phys. 46, 323 (2005)CrossRefADSGoogle Scholar

Copyright information

© EDP Sciences, SIF, Springer-Verlag Berlin Heidelberg 2016

Authors and Affiliations

  1. 1.Department of Mechanical and Aerospace EngineeringNew York University Tandon School of EngineeringBrooklynUSA
  2. 2.Dipartimento di Ingegneria Automatica e Informatica,TorinoItaly

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