On the influence of noise on the largest Lyapunov exponent of attractors of stochastic dynamic systems

1998 ◽  
Vol 9 (6) ◽  
pp. 959-963 ◽  
Author(s):  
John Argyris ◽  
Ioannis Andreadis
Keyword(s):  
Lyapunov Exponent ◽  
Dynamic Systems ◽  
Largest Lyapunov Exponent ◽  
Stochastic Dynamic ◽  
The Largest Lyapunov Exponent ◽  
Stochastic Dynamic Systems ◽  
Influence Of Noise

Numerical Simulation of Dynamic Stability of Fractional Stochastic Systems

2018 ◽  
Vol 18 (10) ◽  
pp. 1850128 ◽  
Author(s):  
Jian Deng
Keyword(s):  
Numerical Simulation ◽  
Lyapunov Exponent ◽  
Dynamic Stability ◽  
Stochastic Systems ◽  
Simulation Method ◽  
Largest Lyapunov Exponent ◽  
Stochastic Dynamic ◽  
Data Normalization ◽  
Moment Lyapunov Exponent ◽  
The Largest Lyapunov Exponent

The modern theory of stochastic dynamic stability is founded on two main exponents: the largest Lyapunov exponent and moment Lyapunov exponent. Since any fractional viscoelastic system is indeed a system with memory, data normalization during iterations will disregard past values of the response and therefore the use of data normalization seems not appropriate in numerical simulation of such systems. A new numerical simulation method is proposed for determining the [Formula: see text]th moment Lyapunov exponent, which governs the [Formula: see text]th moment stability of the fractional stochastic systems. The largest Lyapunov exponent can also be obtained from moment Lyapunov exponents. Examples of the two-dimensional fractional systems under wideband noise and bounded noise excitations are presented to illustrate the simulation method.

scholarly journals Approximate Controllability of Sobolev Type Nonlocal Fractional Stochastic Dynamic Systems in Hilbert Spaces

2013 ◽  
Vol 2013 ◽  
pp. 1-10 ◽  
Author(s):  
Mourad Kerboua ◽  
Amar Debbouche ◽  
Dumitru Baleanu
Keyword(s):  
Control Systems ◽  
Hilbert Spaces ◽  
Dynamic Systems ◽  
Approximate Controllability ◽  
Dynamic Control ◽  
Sufficient Conditions ◽  
Sobolev Type ◽  
Stochastic Dynamic ◽  
Deterministic Control ◽  
Stochastic Dynamic Systems

We study a class of fractional stochastic dynamic control systems of Sobolev type in Hilbert spaces. We use fixed point technique, fractional calculus, stochastic analysis, and methods adopted directly from deterministic control problems for the main results. A new set of sufficient conditions for approximate controllability is formulated and proved. An example is also given to provide the obtained theory.

Sign in / Sign up

Export Citation Format

Share Document