An innovation diffusion model for three competitive products

Computers and Mathematics with Applications

Volumn 46, Issue 10-11, 2003, Pages 1473-1481

  Yu, Yumei ^a   Wang, Wendi ^b   Zhang, Yong ^b  

^a SOOCHOW UNIVERSITY   (China)

^b SOUTHWEST UNIVERSITY   (China)

Author keywords

Competition; Diffusion; Global stability; Innovation

Indexed keywords

ASYMPTOTIC STABILITY; COMPETITION; EIGENVALUES AND EIGENFUNCTIONS; INTEGRAL EQUATIONS; MARKETING; MATRIX ALGEBRA; THEOREM PROVING; VECTORS;

GLOBAL STABILITY; INNOVATION DIFFUSION MODEL; THREE COMPETITIVE PRODUCTS;

MATHEMATICAL MODELS;

EID: 0346777252     PISSN: 08981221     EISSN: None     Source Type: Journal    
DOI: 10.1016/S0898-1221(03)90184-2     Document Type: Article

References (18)

1. E.M. Rogers, Diffusion of Innovations, Third Edition, The Free Press, London, (1983).
2. E.M. Rogers, Diffusion of Innovations, Fourth Edition, The Free Press, New York, (1995).
3. J.A. Dodson and E. Muller, Models of new product diffusion through advertising and word of mouth, Management Science 24, 568-578, (1978).
4. V. Mahajan, E. Muller and R.A. Kerin, Introduction strategy for a new product with positive and negative word-of-mouth, Management Science 30, 1389-1404, (1984).
5. V. Mahajan, E. Muller and F. Bass, New product diffusion models in marketing: A review and directions for research, Journal of Marketing 54, 1-26, (1990).
6. V. Mahajan and Y. Wind, Innovation Diffusion Models of New Product Acceptance, Bellinger, Cambridge, MA, (1986).
7. V. Mahajan and R. Peterson, Models for Innovation Diffusion, Sage Publication, Beverly Hills, CA, (1985).
8. P. Fergola, C. Tenneriello, Z. Ma and F. Petrillo, Delayed innovation diffusion processes with positive and negative word-of-mouth, Int. J. Diff. Equa. Appl. 1, 131-147, (2000).
9. P. Fergola, C. Tenneriello, Z. Ma and F. Petrillo, An innovation diffusion model with time delay: Positive and negative word-of-mouth, In WASCOM 99, 10th Conference on Waves and Stability in Continuous Media (Vulcano), pp. 167-177, World Sci. Publishing, River Edge, NJ, (2001).
10. P. Fergola and F. Petrillo, Some new results on the stability of a dedayed innovation diffusion model (to appear).
11. C. Tenneriello, P. Fergola, Z. Ma and W. Wang, Stability of competitive innovation diffusion model, Journal of Napoli University (to appear).
12. M.W. Hirsch, System of differential equations that are competitive or cooperative. I: Limit sets, SIAM. J. Math. Anal. 13, 167-179, (1982).
13. M.W. Hirsch, System of differential equations that are competitive or cooperative. II: Convergence almost everywhere, SIAM. J. Math. Anal. 16, 432-439, (1985).
14. M.W. Hirsch, System of differential equations that are competitive or cooperative. III: Competing species, Nonlinearity 1, 51-71, (1988).
15. M.W. Hirsch, System of differential equations that are competitive or cooperative. IV: Structural stability in three-dimensional systems, SIAM. J. Math. Anal. 21, 1225-1234, (1990).
16. M.W. Hirsch, System of differential equations that are competitive or cooperative. V: Convergence in 3-dimensional systems, J. Differential Equations 80, 94-106, (1989).
17. H. Smith, Monotone Dynamical Systems, An Introduction to Theory of Competitive and Cooperative Systems, Math. Surveys Monogr., Volume 41, AMS, Providence, RI, (1995).
18. C.-W. Chi, S.-B. Hsu and L.-I. Wu, On the asymmetric May-Leonard model of three competing species, SIAM. J. Appl. Math. 58, 211-226, (1998).