Abstract
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.
Highlights
The work is dedicated to the methods of practical stability analysis for systems described by nonlinear autonomous equations
The analysis of such systems is of a particular interest due to the dynamical chaos phenomena, which can be observed in cases of stability loss [1]-[3]
A stability analysis of nonlinear Lorenz and Rössler systems [1] [3] is used as an example, illustrating the possibilities of the suggested methods
Summary
The work is dedicated to the methods of practical stability analysis for systems described by nonlinear autonomous equations. The analysis of such systems is of a particular interest due to the dynamical chaos phenomena, which can be observed in cases of stability loss [1]-[3]. A stability analysis of nonlinear Lorenz and Rössler systems [1] [3] is used as an example, illustrating the possibilities of the suggested methods
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