Delay, discrete and spatial models with applications to mathematical biology

具有分布延迟的方程涉及多种模型，包括具有多个集中延迟项的积分-微分方程和常微分方程。这类方程的定性性质，如稳定性、振荡性和吸引集将在本研究的框架内进行研究。研究结果将应用于数学生物学方程。主要的焦点之一将是研究变参数方程和建立连续和离散模型之间的联系。该研究将匹配微分方程和差分方程，并将所得结果应用于离散和连续情况下的种群动力学模型。这种混合方法将适应混合模型的研究，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.