Lyapunov type stability and Lyapunov exponent for exemplary multiplicative dynamical systems

被引：27

作者：

Aniszewska, Dorota ^{[1
]}

Rybaczuk, Marek ^{[1
]}

机构：

[1] Wroclaw Univ Technol, Inst Mat Sci & Appl Mech, PL-50370 Wroclaw, Poland

来源：

NONLINEAR DYNAMICS | 2008年 / 54卷 / 04期

关键词：

Multiplicative calculus; Lyapunov stability; Lyapunov exponent;

D O I：

10.1007/s11071-008-9333-7

中图分类号：

TH [机械、仪表工业];

学科分类号：

0802 ;

摘要：

This paper presents analysis of Lyapunov type stability for multiplicative dynamical systems. It has been formally defined and numerical simulations were performed to explore nonlinear dynamics. Chaotic behavior manifested for exemplary multiplicative dynamical systems has been confirmed by calculated Lyapunov exponent values.

引用

页码：345 / 354

页数：10

共 9 条

[1] Analysis of the multiplicative Lorenz system [J].

Aniszewska, D ;

Rybaczuk, M .

CHAOS SOLITONS & FRACTALS, 2005, 25 (01) :79-90

[2] Multiplicative runge-kutta methods [J].

Aniszewska, Dorota .

NONLINEAR DYNAMICS, 2007, 50 (1-2) :265-272

[3]

[Anonymous], 1938, OPERATIONS INFINITES

[4]

Kasprzak W., 2004, MEASUREMENTS DIMENSI

[5]

Lyapunov A., 1966, Stability of Motion

[6] The fractal growth of fatigue defects in materials [J].

Rybaczuk, M ;

Stoppel, P .

INTERNATIONAL JOURNAL OF FRACTURE, 2000, 103 (01) :71-94

[7] The concept of physical and fractal dimension II. The differential calculus in dimensional spaces [J].

Rybaczuk, M ;

Kedzia, A ;

Zielinski, W .

CHAOS SOLITONS & FRACTALS, 2001, 12 (13) :2537-2552

[8]

Sparrow C., 1982, LORENZ EQUATIONS BIF

[9] DETERMINING LYAPUNOV EXPONENTS FROM A TIME-SERIES [J].

WOLF, A ;

SWIFT, JB ;

SWINNEY, HL ;

VASTANO, JA .

PHYSICA D, 1985, 16 (03) :285-317

← 1 →