Mathematical models of innovation diffusion with stage structure

Applied Mathematical Modelling

Volumn 30, Issue 1, 2006, Pages 129-146

  Wang, Wendi ^a   Fergola, P ^b   Lombardo, S ^c   Mulone, G ^c  

^a SOUTHWEST UNIVERSITY   (China)

^b UNIVERSITY OF NAPLES FEDERICO II   (Italy)

^c UNIVERSITY OF CATANIA   (Italy)

Author keywords

Bistable equilibria; Innovation diffusion; Stability switches; Stage structure; Time delay

Indexed keywords

BIFURCATION (MATHEMATICS); DECISION THEORY; NUMERICAL METHODS; ORDINARY DIFFERENTIAL EQUATIONS; POLYNOMIAL APPROXIMATION; THEOREM PROVING;

BASS MODEL; BISTABLE EQUILIBRIA; INNOVATION DIFFUSION; STABILITY SWITCHES; STAGE STRUCTURE;

MATHEMATICAL MODELS;

MATHEMATICAL MODELING;

EID: 28444456967     PISSN: 0307904X     EISSN: None     Source Type: Journal    
DOI: 10.1016/j.apm.2005.03.011     Document Type: Article

References (24)

1. R.M. Anderson R.M. May Infectious diseases of humans: Dynamics and control 1991 Oxford University Press Oxford
2. F.M. Bass A new product growth model for consumer durables Manage. Sci. 15 1969 215-227
3. J. Belair S.A. Campbell Stability and bifurcation of equilibria in a multiple-delayed differential equation SIAM J. Appl. Math. 54 1994 1402-1424
4. R. Bellman K.L. Cooke Differential-difference equations 1963 Academic Press New York
5. E. Beretta Y. Kuang Geometric stability switch criteria in delay differential systems with delay-dependent parameters SIAM J. Math. Anal. 33 2001 1144-1165
6. F. Brauer C. Castillo-Chavez Mathematical models in population biology and epidemiology Texts in Applied Mathematics 40 2001 Springer-Verlag New York
7. O. Diekmann J.A.P. Heesterbeek Mathematical epidemiology of infectious diseases. Model building, analysis and interpretation Wiley Series in Mathematical and Computational Biology 2000 John Wiley & Sons, Ltd. Chichester
8. A.N. Giovanis C.H. Skiadas A stochastic logistic innovation diffusion model studying the electricity consumption in greece and the united states Technol. Forecasting Social Change 61 1999 235-246
9. J. Guckenheimer P.J. Holmes Nonlinear Oscillations, Dynamical Systems, and Bifurcations of Vector Fields 1996 Springer-Verlag New York
10. J.K. Hale Flows on center manifolds for scalar functional differential equations Proc. Roy. Soc. Edinburgh 101A 1985 193-201
11. J.K. Hale S.M.V. Lunel Introduction to Functional Differential Equations 1993 Springer-Verlag New York
12. P. Fergola C. Tenneriello Z. Ma F. Petrillo Delayed innovation diffusion processes with positive and negative word-of-mouth Int. J. Diff. Equa. Appl. 1 2000 131-147
13. P. Fergola, C. Tenneriello, Z. Ma, F. Petrillo, An innovation diffusion model with time delay: Positive and negative word of mouth "WASCOM 99", in: 10th Conference on Waves and Stability in Continuous Media (Vulcano), World Sci. Publishing, River Edge, NJ, 2001, pp. 167-177.
14. Y. Kuang Delay differential equations with applications in population dynamics 1993 Academic Press, Inc. Boston
15. A. Mahler E.M. Rogers The diffusion of interactive communication innovations and the critical mass: The adoption of telecommunications services by German banks Telecommun. Policy 23 1999 719-740
16. G.L. Lilien A. Rangaswarmy C. Van den Bulte Diffusion models: Managerial applications and software in: V. Mahajan E. Muller Y. Wind (Eds) New product diffusion models 2000 Kluwer Academic Publishers Nowell, MA 259-336
17. V. Mahajan E. Muller R.A. Kerin Introduction strategy for a new products with positive and negative word-of-mouth Manage. Sci. 30 1984 1389-1404
18. V. Mahajan, E. Muller, F.M. Bass, New Product Diffusion Models, in: J. Eliashberg, G.L. Lilien, (Eds.), Marketing, North-Holland, Amsterdam, pp. 349-408.
19. V. Mahajan R. Peterson Models for Innovation Diffusion 1985 Sage Publication Beverly Hills
20. L. Perko Differential Equations and Dynamical Systems 1996 Springer-Verlag New York
21. W.P. Putsis V. Srinivasan Estimation techniques for macro diffusion models in: V. Mahajan E. Muller Y. Wind (eds) New product diffusion models 2002 Kluwer Academic Publishers Nowell, MA 263-291
22. E.M. Rogers Diffusion of innovations fourth ed. 1995 The Free Press New York
23. T.W. Valente Network models of the diwusion of innovations 1995 Hampton Press Creskill, NJ
24. W. Wang P. Fergola C. Tenneriello Innovation diffusion model in patch environment Appl. Math. Comput. 134 2003 51-67