Analysis of Permanence and Extinction of Enterprise Cluster Based On Ecology Theory
This paper is concerned with the permanence and extinction problem of enterprises cluster constituted by m satellite enterprises and a dominant enterprise. We present the model involving impulsive effect based on ecology theory, which effectively describe the competition and cooperation of enterprises cluster in real economic environment. Applying comparison theorem of impulsive differential equation, we establish sufficient conditions which ultimately affect the fate of enterprises: permanence, extinction, and co-existence. Finally, we present numerical examples to explain the economical significance of mathematical results.
[1] L.G. Gu, K. Fang, Ecology Research about Enterprise, Science &
Technology Progress and Policy, (in Chinese) 24 (10) (2007) 119-123.
[2] H. Zhou, Enterprises cluster co-existence model and stability analysis,
Systems Engineering, (in Chinese) 21 (4) (2003) 32-37.
[3] B.T. Wang, H.Y. Shu, Research on competition in mobile communications
market: ecological model, Journal of Beijing Union University(Natural
Science Edition), (in Chinese) 20 (2) (2006) 27-30.
[4] Q. Guo, Competitive strategies in an enterprise: an ecological model,
Contemporary Economic Management, (in Chinese) 27 (2) (2005) 49-52.
[5] Z. Wang, R.Y. Pan, Analysis to the equilibrium of industrial clusters based
on ecological model, Statistical Thinktank, (in Chinese) 8 (2008) 32-35.
[6] W.H. Li, F.R. Han, Studies on coordinated evolution laws between industry
populations and imperial analysis, Chinese Journal of Management
Science, (in Chinese) 12 (5) (2004) 137-143.
[7] R. Zhang, X.S. Qian, Z. Gao, A competitive model of enterprises based
on ecology theory, System Engineering, (in Chinese) 26 (2008) 116-119.
[8] H.Y. Yi, W. Liu, Identifying the core competitive power of company based
on the model of product population competition, Journal of Management
Sciences, (in Chinese) 20 (3) 2007 16-22.
[9] M.E. Porter, Cluster and the new economics of competition, Harvard
Business Review, (1998)(November-December) 77-90.
[10] J.C. Wang, The Space of Innovation-enterprise Cluster and Region
Development, Beijing University Press, Beijing, 2001.
[11] J. Hou, H.H. Liu, Permanence and asymptotic behavior of the nonautonomous
Lotka-Volterra competitive system with impulses, Journal of
Biomathematics, (in Chinese) 24 (2) (2009) 213-221.
[12] Z.J. Yao, Permanence and extinction of impulsive Lotka-Volterra system,
Journal of Hangzhou Normal University, (in Chinese) 7 (4) (2009) 246-
251.
[13] S. Ahmad, I.M. Stamova, Asymptotic stability of an N-dimensional
impulsive competitive system, Nonlinear Anal. Real World Appl, 8 (2007)
654-663.
[14] P. Georgescu, I.M. Stamova, An impulsively controlled predator-pest
model with disease in the pest, Nonlinear Anal. Real World Appl, 11
(2010) 270-287.
[15] X.H. Tian, Q.K. Nie, On model construction of enterprises- interactive
relationship from the perspective of business ecosystem, Southern Economics
Journal, (in Chinese) 4 (2006) 50-57.
[16] H.J. Guo, L.S. Chen, The effect of impulsive harvest on a predator-prey
system with distributed time delay, Nonlinear Science and Numerical
Simulation, 14 (5) (2009) 2301-2309.
[17] V. Lakshmikantham, D.D. Bainov, P.S. Simeonov, Theory of impulsive
differential equations, Singapore: World Scientific Press, 1989.
[18] Y.H. Fan, L.L. Wang, Global asymptotical stability of a Logistic model
with feedback control, Nonlinear Anal. Real World Appl, 11 (2010) 2686-
2697.
[1] L.G. Gu, K. Fang, Ecology Research about Enterprise, Science &
Technology Progress and Policy, (in Chinese) 24 (10) (2007) 119-123.
[2] H. Zhou, Enterprises cluster co-existence model and stability analysis,
Systems Engineering, (in Chinese) 21 (4) (2003) 32-37.
[3] B.T. Wang, H.Y. Shu, Research on competition in mobile communications
market: ecological model, Journal of Beijing Union University(Natural
Science Edition), (in Chinese) 20 (2) (2006) 27-30.
[4] Q. Guo, Competitive strategies in an enterprise: an ecological model,
Contemporary Economic Management, (in Chinese) 27 (2) (2005) 49-52.
[5] Z. Wang, R.Y. Pan, Analysis to the equilibrium of industrial clusters based
on ecological model, Statistical Thinktank, (in Chinese) 8 (2008) 32-35.
[6] W.H. Li, F.R. Han, Studies on coordinated evolution laws between industry
populations and imperial analysis, Chinese Journal of Management
Science, (in Chinese) 12 (5) (2004) 137-143.
[7] R. Zhang, X.S. Qian, Z. Gao, A competitive model of enterprises based
on ecology theory, System Engineering, (in Chinese) 26 (2008) 116-119.
[8] H.Y. Yi, W. Liu, Identifying the core competitive power of company based
on the model of product population competition, Journal of Management
Sciences, (in Chinese) 20 (3) 2007 16-22.
[9] M.E. Porter, Cluster and the new economics of competition, Harvard
Business Review, (1998)(November-December) 77-90.
[10] J.C. Wang, The Space of Innovation-enterprise Cluster and Region
Development, Beijing University Press, Beijing, 2001.
[11] J. Hou, H.H. Liu, Permanence and asymptotic behavior of the nonautonomous
Lotka-Volterra competitive system with impulses, Journal of
Biomathematics, (in Chinese) 24 (2) (2009) 213-221.
[12] Z.J. Yao, Permanence and extinction of impulsive Lotka-Volterra system,
Journal of Hangzhou Normal University, (in Chinese) 7 (4) (2009) 246-
251.
[13] S. Ahmad, I.M. Stamova, Asymptotic stability of an N-dimensional
impulsive competitive system, Nonlinear Anal. Real World Appl, 8 (2007)
654-663.
[14] P. Georgescu, I.M. Stamova, An impulsively controlled predator-pest
model with disease in the pest, Nonlinear Anal. Real World Appl, 11
(2010) 270-287.
[15] X.H. Tian, Q.K. Nie, On model construction of enterprises- interactive
relationship from the perspective of business ecosystem, Southern Economics
Journal, (in Chinese) 4 (2006) 50-57.
[16] H.J. Guo, L.S. Chen, The effect of impulsive harvest on a predator-prey
system with distributed time delay, Nonlinear Science and Numerical
Simulation, 14 (5) (2009) 2301-2309.
[17] V. Lakshmikantham, D.D. Bainov, P.S. Simeonov, Theory of impulsive
differential equations, Singapore: World Scientific Press, 1989.
[18] Y.H. Fan, L.L. Wang, Global asymptotical stability of a Logistic model
with feedback control, Nonlinear Anal. Real World Appl, 11 (2010) 2686-
2697.
@article{"International Journal of Engineering, Mathematical and Physical Sciences:54194", author = "Ping Liu and Yongkun Li", title = "Analysis of Permanence and Extinction of Enterprise Cluster Based On Ecology Theory", abstract = "This paper is concerned with the permanence and extinction problem of enterprises cluster constituted by m satellite enterprises and a dominant enterprise. We present the model involving impulsive effect based on ecology theory, which effectively describe the competition and cooperation of enterprises cluster in real economic environment. Applying comparison theorem of impulsive differential equation, we establish sufficient conditions which ultimately affect the fate of enterprises: permanence, extinction, and co-existence. Finally, we present numerical examples to explain the economical significance of mathematical results.
", keywords = "Enterprise cluster, permanence, extinction, impulsive, comparison theorem.", volume = "5", number = "8", pages = "1229-6", }
