On the perron sign change effect for Lyapunov characteristic exponents of solutions of differential systems

被引：4
作者：
Korovin, S. K. [1 ]
Izobov, N. A.
机构：
[1] Moscow MV Lomonosov State Univ, Moscow, Russia
来源：
DIFFERENTIAL EQUATIONS | 2010年 / 46卷 / 10期
基金：
俄罗斯基础研究基金会;
关键词：
Lyapunov Exponent; Nontrivial Solution; Characteristic Exponent; Lyapunov Characteristic Exponent; Negative Lyapunov Exponent;
D O I：
10.1134/S0012266110100034
中图分类号：
O1 [数学];
学科分类号：
0701 ; 070101 ;
摘要：
The Perron effect is the effect in which the characteristic Lyapunov exponents of solutions of a differential system change sign from negative to positive when passing to a perturbed system. We show that this effect is realized on all nontrivial solutions of two two-dimensional systems: an original linear system with negative characteristic exponents and a perturbed system with small perturbations of arbitrary order m > 1 in a neighborhood of the origin, all of whose nontrivial solutions have positive characteristic exponents. We compute the exact positive value of the characteristic exponents of solutions of the two-dimensional nonlinear Perron system with small second-order perturbations, which realizes only a partial Perron effect.
引用
收藏
页码：1395 / 1408
页数：14
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[21]   On the Computability of Lyapunov Exponents of Linear Differential Systems Along Geometric Time Progressions [J].
A. V. Lipnitskii .
Differential Equations, 2005, 41 :1687-1693
[22]   Description of the mutual arrangement of singular exponents of a linear differential systems and exponents of its solutions [J].
Barabanov, E. A. ;
Fominykh, E. I. .
DIFFERENTIAL EQUATIONS, 2006, 42 (12) :1657-1673
[23]   Description of the mutual arrangement of singular exponents of a linear differential systems and exponents of its solutions [J].
E. A. Barabanov ;
E. I. Fominykh .
Differential Equations, 2006, 42 :1657-1673
[24]   Structure of the semicontinuity sets of the Lyapunov exponents of linear differential systems continuously depending on a parameter [J].
M. V. Karpuk .
Differential Equations, 2015, 51 :1397-1401
[25]   Structure of the Semicontinuity Sets of the Lyapunov Exponents of Linear Differential Systems Continuously Depending on a Parameter [J].
Karpuk, M. V. .
DIFFERENTIAL EQUATIONS, 2015, 51 (10) :1397-1401
[26]   Stability Assessment of Stochastic Differential-Algebraic Systems via Lyapunov Exponents with an Application to Power Systems [J].
Gonzalez-Zumba, Andres ;
Fernandez-de-Cordoba, Pedro ;
Cortes, Juan-Carlos ;
Mehrmann, Volker .
MATHEMATICS, 2020, 8 (09)
[27]   The characteristic Lyapunov exponents and the sensitivity of quasi-periodically excited systems with white noise to the initial conditions [J].
Vladimirov S.N. .
Russian Physics Journal, 2005, 48 (4) :375-382
[28]   Exact boundaries of upper mobility of the Lyapunov exponents of linear differential systems under exponentially decaying perturbations of the coefficient matrices [J].
Voidelevich, A. S. .
DIFFERENTIAL EQUATIONS, 2014, 50 (10) :1300-1313
[29]   Exact boundaries of upper mobility of the Lyapunov exponents of linear differential systems under exponentially decaying perturbations of the coefficient matrices [J].
A. S. Voidelevich .
Differential Equations, 2014, 50 :1300-1313
[30]   Necessary and sufficient conditions for the stability of Lyapunov exponents of linear differential systems with exponentially decaying perturbations [J].
E. A. Barabanov ;
N. S. Denisenko .
Differential Equations, 2007, 43 :168-179
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