Logistic模型阈值控制悖论及复杂性分析

PARADOX AND COMPLEXITY ANALYSIS FOR LOGISTIC MODEL UNDER LIMITER CONTROL

研究了Logistic模型稳态均值在阈值控制下产生反直觉变化现象与复杂响应的机理.结果表明,阈值控制能引起映射区间改变和映射分布变化,二者之间的竞争导致了受控Logistic模型稳态均值的反直觉变化现象与复杂响应.在阈值下限接近0或阈值上限接近1时,映射分布变化是影响稳态均值复杂响应的主导因素.阈值下限大于其临界值或阈值上限小于其临界值时,稳态均值变化主要由映射区间改变决定,此时,受控Logistic模型稳态均值会出现反直觉变化现象.理论分析结果通过数值仿真得到进一步证实.

In this paper, the mechanism of the counterintuitive phenomena and complex response of Logistic model＇s steady mean under limiter control is studied. The results show that limiter control can induce the mapping interval＇s change and the mapping distribution＇s variation. The competition between the two gives rise to the counterintuitive phenomena and complex response of the controlled Logistic model＇s steady mean. When the lower limiter is close to 0 or the upper limiter is close to 1, the variation of mapping distribution is the principle factor for influence on the complex response of steady mean. When the lower limiter is greater than its critical value or the upper limiter is less than its critical value, the variation of the steady mean is dominated by the change of mapping interval, and the counterintuitive phenomena of the steady mean in the controlled Logistic model will arise. Finally, some numerical simulations are provided to verify the theoretical results.