Author: Jonqobilov, J.T.

Annotation: This article examines the theory of nonlinear differential equations, their properties, and their significance in modeling dynamic systems. The main concepts of stability theory, bifurcation phenomena, and elements of chaos theory are analyzed. In addition, the advantages of usingnonlinear equations in modeling real-world processes are highlighted. The results of the study show that nonlinear differential equations represent a powerful mathematical tool that allows for a more accurate description of real processes. Their in-depth study is important not only for theoretical mathematics but also for solving practical problems.

Keywords: nonlinear differential equation, dynamical system, stability, bifurcation, chaos, Lyapunov function.

Pages in journal: 206 - 211