Two
methods of stability analysis of systems described by dynamical equations are
being considered. They are based on an analysis of eigenvalues spectrum for the
evolutionary matrix or the spectral equation and they allow determining the
conditions of stability and instability, as well as the possibility of chaotic
behavior of systems in case of a stability loss. The methods are illustrated
for nonlinear Lorenz and Rossler model problems.
References
[1]
Landa, I.P. (1997) Nonlinear Waves and Oscillations. Nauka, Moscow, 496 p.
[2]
Feigenbaum, M. (1983) Versality in Nonlinear Systems Behavior. UFN, 14, 342-374.
[3]
Kuznetsov, S.P. (2006) Dynamical Chaos, FM. M. Ppysmatgis, Moscow, 355 p.
[4]
Perevoznikov, E.N. and Skvortsov, G.E. (2010) Dynamics of Perturbations and Analysis of Nonequilibrium Systems Stability. SPbTEI, St-Petersburg, 139 p.
