Discrete Dynamics in Nature and Society
Volume 2008 (2008), Article ID 467972, 12 pages
Research Article

Complex Dynamics of an Adnascent-Type Game Model

Baogui Xin, Junhai Ma, and Qin Gao

Nonlinear Dynamics and Chaos Group, School of Management, Tianjin University, Tianjin 300072, China

Received 23 August 2008; Revised 13 November 2008; Accepted 24 December 2008

Academic Editor: E. Casetti

Copyright © 2008 Baogui Xin et al. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.


The paper presents a nonlinear discrete game model for two oligopolistic firms whose products are adnascent. (In biology, the term adnascent has only one sense, “growing to or on something else,” e.g., “moss is an adnascent plant.” See Webster's Revised Unabridged Dictionary published in 1913 by C. & G. Merriam Co., edited by Noah Porter.) The bifurcation of its Nash equilibrium is analyzed with Schwarzian derivative and normal form theory. Its complex dynamics is demonstrated by means of the largest Lyapunov exponents, fractal dimensions, bifurcation diagrams, and phase portraits. At last, bifurcation and chaos anticontrol of this system are studied.