具有时滞和下临界企业竞争模型的稳定性和Hopf分支分析

发布时间：2019-04-13 15:59

【摘要】：为了研究下临界和时滞对企业产量的影响,主要考虑具有下临界的企业竞争模型,针对企业生产所产生的生产周期和信息时滞对企业生产产量的影响,将时滞引入具有下临界企业竞争模型中,提出了具有时滞和下临界的企业竞争模型。以时滞为参数,在适当的条件下,得到了系统在内部平衡点处的局部稳定性和产生Hopf分支的条件,发现当参数经过临界值时,企业的生产产量产生周期性震荡。进一步利用中心流形定理和规范型方法,得到分支的方向和周期解的稳定性。最后通过数值模拟验证所得到的结论。结果表明,时滞和下临界能够影响企业产量的稳定性,得到企业产量稳定的临界条件,在一定范围内,企业产量能够保持局部稳定。
[Abstract]:In order to study the influence of lower criticality and time delay on enterprise output, this paper mainly considers the enterprise competition model with lower critical value, aiming at the influence of production cycle and information delay on production output of enterprise. In this paper, the time delay is introduced into the enterprise competition model with lower critical value, and the competition model with time delay and lower critical value is proposed. Taking the time delay as the parameter, the local stability of the system at the internal equilibrium point and the conditions for generating Hopf bifurcation are obtained under appropriate conditions. It is found that when the parameters pass through the critical value, the production output of the enterprise will produce periodic oscillation. Furthermore, the direction of bifurcation and the stability of periodic solutions are obtained by using the central manifold theorem and the normal form method. Finally, the conclusion is verified by numerical simulation. The results show that the delay and the subcritical value can affect the stability of the output of the enterprise, and the critical condition of the stability of the output of the enterprise can be obtained. In a certain range, the output of the enterprise can keep the local stability.
【作者单位】：武汉理工大学理学院;
【基金】：湖北省自然科学基金资助项目(2013CFB347)
【分类号】：O175

【相似文献】