【作者】 张杰；

【导师】 姚洪兴；

【作者基本信息】 江苏大学 ， 应用数学， 2016， 硕士

【摘要】 为了维持自然界的持续发展,发现许多实际的系统都可抽象为数学模型来分析了解这些系统的特性,对于合理利用和控制资源等方面具有深远的意义。然而决定一个系统能否正常运行的前提便是稳定,而时滞的出现会破坏系统稳定性,发生更加复杂的动力学行为。本文针对目前研究广泛的两种模型——含时滞的捕食者-食饵模型和产业集群内创新风险传播模型的优化,更加贴近实际现象。首先,考虑了带有双时滞、参数调节和状态反馈控制的捕食者-食饵模型。选用两个时滞作为分岔参数,运用Routh-Hurwitz判别法,得到受控捕食系统中各平衡点处的局部稳定性特征;运用Hopf分岔理论,得到Hopf分岔在平衡点位置存在的条件。并经过Matlab对模型中参数调节检验了控制的有效性。其次,构建了带有时滞的产业集群内创新风险传播模型,将企业看成生态系统中的物种,产业集群与附近的环境构成产业集群系统,结合生物种群中传染病在种群中传播的特点,运用Routh-Hurwitz判别法对模型平衡点处的稳定性分析,通过构造合适的李雅普诺夫函数对模型的全局稳定性展开分析,最后,通过对基本再生数中参数的模拟,得出产业集群创新过程中影响风险传播的因素,了解传播的原因并相应的采取行之有效的措施。更多还原

【Abstract】 In order to maintain the sustainable development state of nature, it is found that many practics system can be abstracted as mathematics model, and we also learn the character of systems through analyze these mathematical models. In the resources reasonable use and control has far-reaching significance. However, the most important condition to make sure a system work normally is stable. The time delay can destroy the stability of the system at the equilibrium point, make the system produce some behavior more complex dynamic than before, In this paper, two widely studied model--the predator-prey model and innovation risk propagation model based on the time delay were improved, which made the model closer to reality.Firstly, a predator-prey control model with two delays, parameter adjustment and feedback control for the predator is investigated. Choosing the two delays as the bifurcation parameter, according to the Routh-Hurwize discriminant method, we obtained the local stability at the balance, utilizing Hopf bifurcation theorem, the existence of Hopf bifurcation is established. Finally, the effectiveness of the controller is verified by numerical simulation.Secondly, construct a delayed propagation model of within the industrial cluster innovation, the enterprise as the ecological system of the species, constitute the organization of industrial clusters ecosystem and environment. According to the characteristic of biological in the spread of infectious disease in the population, based on the Routh-Hurwize discriminant method, the stability of the model at the equilibrium point is analyzed. By constructing suitable lyapunov function to analyze the global stability of the model. Finally, using numerical simulation to analysis the factors of risk propagation, and propose the risk control strategies.更多还原