Delay, discrete and spatial models with applications to mathematical biology

具有分布时滞的方程涉及多种模型，包括积分-微分方程组和具有多个集中时滞项的常微分方程组。这类方程的定性性质，如稳定性、振动性和吸引集，将在拟议的研究框架内进行研究。这些结果将应用于数学生物学的方程。主要焦点之一将是研究具有可变参数的方程，并建立连续和离散模型之间的联系。这项研究将匹配微分方程组和差分方程组，并将所获得的结果应用于离散和连续情况下的种群动力学模型。这种混合方法将适合于混合模型的研究，如脉冲系统和动态方程。

Equations with a distributed delay involve a variety of models, including integro-differential equations and ordinary differential equations with several concentrated delay terms. Qualitative properties of such equations, such as stability, oscillation and attractive sets will be investigated in the framework of the proposed research. The results will be applied to equations of mathematical biology. One of the main focal points will be the study of equations with variable parameters and establishing connections between continuous and discrete models. The research will match differential and difference equations and apply the results obtained to models of population dynamics, both in the discrete and the continuous cases. This mixed approach will accommodate the study of hybrid models, such as impulsive systems and dynamic equations.