【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。更多还原

【Abstract】 In order to study the influence of the lower critical and delays on enterprises production,this paper considers the enterprise competition model with lower critical.In view of the enterprise production cycle and information delay influence on the enterprises production,the time delays is introduced into the competitive model of the lower critical enterprise.The enterprise competition model with time delays and lower critical is put forward.Based on time delay parameters,under appropriate conditions,the local stability of the system at the internal equilibrium point and the conditions of generating the Hopf bifurcation are obtained.It shows that when the parameter goes through the critical value,the production yields periodic shocks.By further using the center manifold theorem and normal form method,the stability of the direction of bifurcation and periodic solution are obtained.Finally,the obtained results are verified by the numerical simulation.The results show that the lower critical and delays affect the stability of the output.Moreover,the critical value are obtained and the production can keep the local stability within the critical value.更多还原