A kind of noise-induced transition to noisy chaos in stochastically perturbed dynamical system

2012 ◽  
Vol 28 (5) ◽  
pp. 1416-1423 ◽  
Author(s):  
Chun-Biao Gan ◽  
Shi-Xi Yang ◽  
Hua Lei
Keyword(s):  
Dynamical System ◽  
Noisy Chaos ◽  
Stochastically Perturbed

Limit theorems for stochastically perturbed dynamical systems

1995 ◽  
Vol 32 (2) ◽  
pp. 459-469 ◽  
Author(s):  
Krzysztof Łoskot ◽  
Ryszard Rudnicki
Keyword(s):  
Dynamical System ◽  
Dynamical Systems ◽  
Discrete Time ◽  
Classical Limit ◽  
Limit Theorems ◽  
Polish Space ◽  
Recurrence Formula ◽  
Stationary Measure ◽  
Random Elements ◽  
Stochastically Perturbed

We consider a discrete-time stochastically perturbed dynamical system on the Polish space given by the recurrence formula Xn = S(Xn–1, Yn), where Yn are i.i.d. random elements. We prove the existence of unique stationary measure and versions of classical limit theorems for the process (Xn).

Limit theorems for stochastically perturbed dynamical systems

1995 ◽  
Vol 32 (02) ◽  
pp. 459-469 ◽  
Author(s):  
Krzysztof Łoskot ◽  
Ryszard Rudnicki
Keyword(s):  
Dynamical System ◽  
Dynamical Systems ◽  
Discrete Time ◽  
Classical Limit ◽  
Limit Theorems ◽  
Polish Space ◽  
Recurrence Formula ◽  
Stationary Measure ◽  
Random Elements ◽  
Stochastically Perturbed

We consider a discrete-time stochastically perturbed dynamical system on the Polish space given by the recurrence formulaXn=S(Xn–1,Yn),whereYnare i.i.d. random elements. We prove the existence of unique stationary measure and versions of classical limit theorems for the process (Xn).

On the Harmonic Oscillations for the Motion of a Dynamical System

2017 ◽  
Vol 13 (2) ◽  
pp. 4657-4670
Author(s):  
W. S. Amer
Keyword(s):  
Dynamical System ◽  
Numerical Solutions ◽  
Equation Of Motion ◽  
Parameter Method ◽  
Kutta Method ◽  
Small Parameter Method ◽  
Harmonic Oscillations ◽  
Pivot Point ◽  
Runge Kutta Method ◽  
High Consistency

This work touches two important cases for the motion of a pendulum called Sub and Ultra-harmonic cases. The small parameter method is used to obtain the approximate analytic periodic solutions of the equation of motion when the pivot point of the pendulum moves in an elliptic path. Moreover, the fourth order Runge-Kutta method is used to investigate the numerical solutions of the considered model. The comparison between both the analytical solution and the numerical ones shows high consistency between them.

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