DECAY/GROWTH RATE ESTIMATION USING INSTANTANEOUS LYAPUNOV EXPONENT

被引：2

作者：

Totoki, Yusuke ^{[1
]}

Matsuo, Takami ^{[1
]}

机构：

[1] Oita Univ, Dept Mechatron, Oita 8701192, Japan

来源：

INTERNATIONAL JOURNAL OF BIFURCATION AND CHAOS | 2012年 / 22卷 / 03期

关键词：

Lyapunov exponent; decay rate; growth rate; linearized flow; nonlinear flow; SYSTEMS; MODEL; SYNCHRONIZATION; STABILITY;

D O I：

10.1142/S0218127412500472

中图分类号：

O1 [数学];

学科分类号：

0701 ; 070101 ;

摘要：

The Lyapunov exponent gives a measure of the mean decay/growth rates of the flows of nonlinear systems. However, the Lyapunov exponent needs an infinite time interval of flows and the Jacobian matrix of system dynamics. In this paper, we propose an instantaneous decay/growth rate that is a kind of generalized Lyapunov exponent and call the instantaneous Lyapunov exponent (ILE) with respect to a decay function. The instantaneous Lyapunov exponent is one of the measures that estimate the decay and growth rates of flows of nonlinear systems by assigning a comparison function and can apply a stable system whose decay rate is slower than an exponential function. Moreover, we propose a synchronization measure of two signals using the ILE.

引用

页数：13

共 50 条

[41] Predictive Vehicle Stability Assessment Using Lyapunov Exponent Under Extreme Conditions [J].

Lian, Renzong ;

Li, Zhiheng ;

Li, Wenchang ;

Ge, Jingwei ;

Li, Li .

IEEE TRANSACTIONS ON INTELLIGENT TRANSPORTATION SYSTEMS, 2024, 25 (12) :21559-21571

[42] Using Largest Lyapunov Exponent to Confirm the Intrinsic Stability of Boiling Water Reactors [J].

Gavilan-Moreno, Carlos J. ;

Espinosa-Paredes, Gilberto .

NUCLEAR ENGINEERING AND TECHNOLOGY, 2016, 48 (02) :434-447

[43] Observability of fidelity decay at the Lyapunov rate in few-qubit quantum simulations [J].

Porter, Max D. ;

Joseph, Ilon .

QUANTUM, 2022, 6

[44] Study on Fault Analysis of Rotor Machinery Using Lyapunov Exponent-Fractal Dimension [J].

Wang, Bingcheng ;

Ren, Zhaohui ;

Hou, Rongtao .

2009 INTERNATIONAL WORKSHOP ON CHAOS-FRACTALS THEORIES AND APPLICATIONS (IWCFTA 2009), 2009, :404-+

[45] Identification of most vulnerable line for divergent trend of power flow using Lyapunov Exponent [J].

Nangrani, S. P. ;

Bhat, S. S. .

PROCEEDINGS OF 2015 IEEE INTERNATIONAL CONFERENCE ON POWER, INSTRUMENTATION, CONTROL AND COMPUTING (PICC), 2015,

[46] A Very Simple Method to Calculate the (Positive) Largest Lyapunov Exponent Using Interval Extensions [J].

Mendes, Eduardo M. A. M. ;

Nepomuceno, Erivelton G. .

INTERNATIONAL JOURNAL OF BIFURCATION AND CHAOS, 2016, 26 (13)

[47] Predictability of epileptic seizures: Comparative study using Lyapunov exponent and entropy based measures [J].

Sabesan, S ;

Narayanan, K ;

Prasad, A ;

Spanias, A ;

Sackellares, JC ;

Iasemidis, LD .

BIOMEDICAL SCIENCES INSTRUMENTATION, VOL 39, 2003, 39 :129-135

[48] Stochastic Stabilization of Quasi-Partially Integrable Hamiltonian Systems by Using Lyapunov Exponent [J].

W. Q. Zhu ;

Z. L. Huang .

Nonlinear Dynamics, 2003, 33 :209-224

[49] On Tail Decay Rate Estimation of Loss Function Distributions [J].

Haxholli, Etrit ;

Lorenzi, Marco .

JOURNAL OF MACHINE LEARNING RESEARCH, 2024, 25 :1-47

[50] Lyapunov functionals and practical stability for stochastic differential delay equations with general decay rate [J].

Caraballo, Tomas ;

Ezzine, Faten ;

Hammami, Mohamed Ali .

ELECTRONIC JOURNAL OF QUALITATIVE THEORY OF DIFFERENTIAL EQUATIONS, 2022, (60) :1-22

← 1 2 3 4 5 →