scholarly journals Flow-driven spectral chaos (FSC) method for simulating long-time dynamics of arbitrary-order non-linear stochastic dynamical systems

2020 ◽  
pp. 110044
Author(s):  
Hugo Esquivel ◽  
Arun Prakash ◽  
Guang Lin
Keyword(s):  
Dynamical Systems ◽  
Arbitrary Order ◽  
Stochastic Dynamical Systems ◽  
Time Dynamics ◽  
Non Linear ◽  
Long Time ◽  
Long Time Dynamics

CHAOTIC AND QUASIPERIODIC MOTIONS OF THREE PLANAR CHARGED PARTICLES

2001 ◽  
Vol 11 (07) ◽  
pp. 1937-1951
Author(s):  
SHU-MING CHANG ◽  
WEN-WEI LIN ◽  
TAI-CHIA LIN
Keyword(s):  
Dynamical System ◽  
Dynamical Systems ◽  
Charged Particles ◽  
Time Dynamics ◽  
Long Time ◽  
Long Time Dynamics

We study two dynamical systems for the motion of three planar charged particles with charges nj ∈ {±1}, j = 1, 2, 3. Both dynamical systems are parametric with a parameter α ∈ [0, 1] and have the same nonlinear terms. As α = 0, 1, the dynamical systems have no chaos. However, one dynamical system may create chaos as α varies from zero to one. This may provide an example to show that the homotopy deformation of dynamical systems cannot preserve the long-time dynamics even though the dynamical systems have the same nonlinear terms.

Slow manifolds for dynamical systems with non-Gaussian stable Lévy noise

2019 ◽  
Vol 17 (03) ◽  
pp. 477-511 ◽  
Author(s):  
Shenglan Yuan ◽  
Jianyu Hu ◽  
Xianming Liu ◽  
Jinqiao Duan
Keyword(s):  
Biological Sciences ◽  
Dynamical Systems ◽  
Scale Parameter ◽  
Lévy Noise ◽  
Stochastic Dynamical Systems ◽  
Time Dynamics ◽  
Slow Manifolds ◽  
Long Time ◽  
Non Gaussian ◽  
Levy Noise

This work is concerned with the dynamics of a class of slow–fast stochastic dynamical systems driven by non-Gaussian stable Lévy noise with a scale parameter. Slow manifolds with exponentially tracking property are constructed, and then we eliminate the fast variables to reduce the dimensions of these stochastic dynamical systems. It is shown that as the scale parameter tends to zero, the slow manifolds converge to critical manifolds in distribution, which helps to investigate long time dynamics. The approximations of slow manifolds with error estimate in distribution are also established. Furthermore, we corroborate these results by three examples from biological sciences.

scholarly journals Long time dynamics for the one dimensional non linear Schrödinger equation

2013 ◽  
Vol 63 (6) ◽  
pp. 2137-2198 ◽  
Author(s):  
Nicolas Burq ◽  
Laurent Thomann ◽  
Nikolay Tzvetkov
Keyword(s):  
Schrödinger Equation ◽  
Schrodinger Equation ◽  
One Dimensional ◽  
Time Dynamics ◽  
Non Linear ◽  
Long Time ◽  
The One ◽  
Long Time Dynamics

Long-time dynamics of a class of nonlocal extensible beams with time delay

2021 ◽  
pp. 108128652110194
Author(s):  
Fengjuan Meng ◽  
Cuncai Liu ◽  
Chang Zhang
Keyword(s):  
Time Delay ◽  
Stability Property ◽  
Beam Equation ◽  
Exponential Attractors ◽  
Time Dynamics ◽  
Bounded Smooth Domain ◽  
Finite Dimensional ◽  
Long Time ◽  
Bounded Smooth ◽  
Long Time Dynamics

This work is devoted to the following nonlocal extensible beam equation with time delay: [Formula: see text] on a bounded smooth domain [Formula: see text]. The main purpose of this paper is to consider the long-time dynamics of the system. Under suitable assumptions, the quasi-stability property of the system is established, based on which the existence and regularity of a finite-dimensional compact global attractor are obtained. Moreover, the existence of exponential attractors is proved.

scholarly journals Singular Limit and Long-Time Dynamics of Bresse Systems

2017 ◽  
Vol 49 (4) ◽  
pp. 2468-2495 ◽  
Author(s):  
To Fu Ma ◽  
Rodrigo Nunes Monteiro
Keyword(s):  
Singular Limit ◽  
Time Dynamics ◽  
Long Time ◽  
Long Time Dynamics

Long-time dynamics via direct summation of infinite continued fractions

1992 ◽  
Vol 68 (11) ◽  
pp. 1637-1640 ◽  
Author(s):  
Zhi-Xiong Cai ◽  
Surajit Sen ◽  
S. D. Mahanti
Keyword(s):  
Continued Fractions ◽  
Time Dynamics ◽  
Long Time ◽  
Long Time Dynamics ◽  
Direct Summation
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