人造板施胶的数学建模与时滞微分方程的高余维分支研究

The solution mapping of delayed differential equation is considered on infinite dimension space, and high codimensional bifurcations may occur frequently. Near a critical point of bifurcation, system may undergo some complex dynamic behaviors. Therefore, it is necessary to discover and describe the varied and complex dynamic behaviors near the critical points of high codimensional bifurcations in actual system. Supplying glue system of artificial board production is one of the main symbols for measuring the technological level of artificial board production, and its control performance will directly affect the quality and cost of products. This proposal aims to study several types of local systems in supplying glue process of artificial board production. Time delay, nonlinear and coupled effects are introduced on the basis of the existing ordinary differential equations in order to model the more realistic functional differential equations. By using the bifurcation theory and normal form method in functional differential equation, we will analyze the dynamics properties of the systems, and interpret or predict complicated phenomena, and analyze the causes of complex phenomena and control the systems to be the states we prefer. Finally, numerical simulations are presented to demonstrate the novel dynamic phenomena. The research will not only provide a theoretical reference for enriching the results of functional differential equations bifurcation theory, but also explain and control the complex dynamic behaviors of supplying glue system in artificial board production, and guide practice well.

泛函微分方程的解映射是在无穷维空间上考虑的，高余维分支现象常常出现，而在各类分支临界值附近又伴有复杂的动力学行为，研究泛函微分方程高余维分支现象对于发现描述实际系统多样复杂的动力学行为具有重要的理论和实际意义。人造板生产过程中的施胶系统是衡量人造板生产技术水平的主要标志之一，其控制性能直接影响产品质量和生产成本。本项目将研究人造板施胶过程的几类局部系统，在现有常微分方程的基础上引入时滞、非线性、耦合等影响因素，建立更符合实际的泛函微分方程模型。应用泛函微分方程分支理论和规范型方法，分析系统的动力学性质，解释和预测系统的复杂动力学现象，阐明系统产生复杂现象的根源，从而实现控制系统达到预期状态的目的，并通过数值仿真将这些新奇的动力学现象加以展示。该项目的成功实施不仅可以在理论上为完善泛函微分方程的分支理论提供参考，还可以更好的分析、解释和控制人造板施胶系统的复杂动力学行为，从而更好的指导实践。

泛函微分方程的解映射是在无穷维空间上考虑的，高余维分支现象常常出现，而在各类分支临界值附近又伴有复杂的动力学行为，研究泛函微分方程高余维分支现象对于发现描述实际系统多样复杂的动力学行为具有重要的理论和实际意义。本研究讨论了刨花板生产过程中的几类局部系统，在现有常微分方程的基础上引入时滞、非线性、耦合等影响因素，建立更符合实际的时滞非线性微分方程模型。应用泛函微分方程分支理论和规范型方法，分析系统的动力学性质，解释和预测系统的复杂动力学现象，阐明系统产生复杂现象的根源，从而实现控制系统达到预期状态的目的，并通过数值仿真将这些新奇的动力学现象加以展示。该研究的成功实施不仅可以在理论上为完善泛函微分方程的分支理论提供参考，还可以更好的分析、解释和控制刨花板生产过程的复杂动力学行为，从而更好的指导实践。