STABILITY OF A DYNAMICAL SYSTEM WITH APPROXIMATE PARAMETERS FOUND BY THE TIKHONOV REGULARIZATION METHOD
This work is devoted to the study of stability with a small change (perturbation) of the parameters of a dynamical system. The purpose of this work is to clarify the stability of the stability of a dynamical system with approximate parameters found by the Tikhonov regularization method. First, a mathematical model of a dynamical system is investigated, which is described as a system of ordinary differential equations. The stability of this dynamical system is considered for a small perturbation of its parameters. Then, the inverse problem of restor-ins the parameters of the studied mathematical model was posed and solved. Tikhonov's regularization method was used to solve the inverse problem. Instead of the exact parameters of the dynamical system, their approximations are found. Finally, it is shown that the studied dynamical system retains its stability for approximate parameters found by the Tikhonov regularization method. Hence, instead of the exact parameters of the studied dynamic system, we can use their approximate value to study and predict the volatility of its state over time.