Lyapunov exponents of systems with noise and fluctuating parameters

This paper deals with the problem of determination of Lyapunov exponents in dynamical systems with noise or fluctuating parameters. The method for identifying the character of motion in such systems is proposed. This approach is based on the phenomenon of complete synchronization in double-oscillator systems via diagonal, master-slave coupling between them. The idea of effective Lyapunov exponents is introduced for quantifying the local stability in the presence of noise. Examples of the method application and its comparison with bifurcation diagrams representing the system dynamics are demonstrated. Finally, the properties of the method are discussed.