The Dynamics and Bifurcation Control of a Singular Biological Economic Model

作     者：Ning Li Hai-Yi Sun Qing-Ling Zhang 

作者机构：Institute of Systems Science Northeastern University Shenyang 110819 PRC College of Science Shenyang Jianzhu University Shenyang 110168 PRC 

出 版 物：《International Journal of Automation and computing》 (国际自动化与计算杂志（英文版）)

年 卷 期：2012年第9卷第1期

页      面：1-7页

核心收录：

学科分类：0711[理学-系统科学] 07[理学] 08[工学] 081104[工学-模式识别与智能系统] 070104[理学-应用数学] 0802[工学-机械工程] 0701[理学-数学] 0811[工学-控制科学与工程] 0812[工学-计算机科学与技术（可授工学、理学学位）] 071102[理学-系统分析与集成] 081103[工学-系统工程] 

基　　金：supported by National Natural Science Foundation of China (No.60974004) Science Foundation of Ministry of Housing and Urban-Rural Development (No.2011-K5-31) 

主　　题：Differential-algebraic equation transcritical bifurcation Hopf bifurcation limit cycle singularity induced bifurcation,bifurcation control. 

摘      要：The objective of this paper is to study systematically the dynamics and control strategy of a singular biological economic model that is described by a differential-algebraic equation. It is shown that when the economic profit passes through zero, this model exhibits the transcritical bifurcation, the Hopf bifurcation, and the limit cycle. In particular, the system undergoes the singularity induced bifurcation at the positive equilibrium, which can result in impulse. Then, state feedback controllers closer to the actual control strategies are designed to eliminate the unexpected singularity induced bifurcation and stabilize the positive equilibrium under the positive profit. Finally, numerical simulations verify the results and illustrate the effectiveness of the controllers. Also, the model with positive economic profit is shown numerically to have different dynamics.