Khusayinov T. Design and investigation of mathematical models of dynamical systems with after-effect

This dissertation considers linear systems with after-effect, systems of this type are classified. Koshi problem solution for two-dimension homogeneous systems with weak delay is obtained. Koshi problem solution for homogeneous and heterogeneous with pure delay are obtained, problem of relative control is solved. Koshi problem solutions for systems with delay and commutation matrices are obtained. Effective market mathematical pricing model with delay is developed. It has a form of nonlinear differential-difference system with constant delay and rational quadratic right-hand side. Stability of equilibrium is investigated, stability area is estimated, and solution convergence is estimated. Finit-dimensional Lyapunov function with Razumikhin condition method and Lyapunov-Krasovskiy functional method is used. Lesley model is investigated. Singular points for nonlinear systems are found, parameters bifurcation values are calculated, autonomous solution stability condition are obtained. The model is formulated in terms of product life-cycle and company finance dynamics. Banking payment model is constructed.