Neutrality Criteria for Stability Analysis of Dynamical Systems through Lorentz and Rossler Model Problems
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.
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.
KEYWORDS
Nonlinear Dynamical Systems, Stability Analysis Methods, Dynamical Chaos, Lorenz and Rössler Model Problems
Nonlinear Dynamical Systems, Stability Analysis Methods, Dynamical Chaos, Lorenz and Rössler Model Problems
Cite this paper
Perevoznikov, E. and Mikhailova, O. (2015) Neutrality Criteria for Stability Analysis of Dynamical Systems through Lorentz and Rossler Model Problems. Journal of Applied Mathematics and Physics, 3, 569-576. doi: 10.4236/jamp.2015.35070.
Perevoznikov, E. and Mikhailova, O. (2015) Neutrality Criteria for Stability Analysis of Dynamical Systems through Lorentz and Rossler Model Problems. Journal of Applied Mathematics and Physics, 3, 569-576. doi: 10.4236/jamp.2015.35070.
References
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[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. [5] Perevoznikov, E.N. (2006) News of Higher Educational Institutions. Physics, 10, 34-39. [6] Perevoznikov, E.N. (2013) Stability Criterion for Nonlinear Systems. Springer Science, Business Media, New York. [7] Perevoznikov, E.N. (2013) Short-Wave Charge Instability of Weakly Ionized Plazma Flows. IF Journal, 86, 11-16.