Study on self-adaptive proportional control method for a class of output models

Zhao-Han Sheng; Tingwen Huang; Jian-Guo Du; Qiang Mei; Hui Huang

doi:10.3934/dcdsb.2009.11.459

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2009, Volume 11, Issue 2: 459-477. Doi: 10.3934/dcdsb.2009.11.459

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Study on self-adaptive proportional control method for a class of output models

1.
School of Management Science and Engineering, Nanjing University, Nanjing 210093
2.
Texas A&M University at Qatar, Doha, P.O.Box 5825
3.
School of Business Administration, Jiangsu University, Zhenjiang 212013
4.
Fundamental Study Department, Chongqing Logistics and Engineering College

Received: November 30, 2007

Revised: July 31, 2008

Published: August 2009

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Abstract

In this paper, self-adaptive proportional control method in economic chaotic system is discussed. It is not necessarily required for the fixed point having stable manifold in the method we used. One can stabilize chaos via time-dependent adjustments of control parameters; also can suppress chaos by adjusting external control signals. Two kinds of chaos about the output systems in duopoly are stabilized in a neighborhood of an unstable fixed point by using the chaos controlling method. The results show that performances of the system are improved by controlling chaos. Furthermore, their applications in practice are presented. The results also show that players can control chaos by adjusting their planned output or variable cost per unit according to the sign of marginal profit.

Keywords:

Duopoly games,
chaos control,
self-adaptive proportional control method,
performance measure.

Mathematics Subject Classification: Primary: 91B62; Secondary: 93D99.

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