Stationary probability density of a class of non-linear dynamical systems to stochastic excitation

1997 ◽  
Vol 63 (5) ◽  
pp. 158-160 ◽  
Author(s):  
R. Wang ◽  
K. Yasuda
Keyword(s):  
Dynamical Systems ◽  
Probability Density ◽  
Stationary Probability ◽  
Stochastic Excitation ◽  
Linear Dynamical Systems ◽  
Stationary Probability Density ◽  
Non Linear

The stationary moments of Poisson-driven non-linear dynamical systems

1982 ◽  
Vol 19 (3) ◽  
pp. 702-706
Author(s):  
Charles E. Smith ◽  
Loren Cobb
Keyword(s):  
Dynamical Systems ◽  
Probability Density ◽  
Stochastic Systems ◽  
Transition Probability ◽  
Kolmogorov Equation ◽  
Transition Probability Density ◽  
Linear Dynamical Systems ◽  
Stationary Density ◽  
Non Linear ◽  
Noise Input

Moment recursion relations have previously been derived for the stationary probability density functions of continuous-time stochastic systems with Wiener (white noise) input. These results are extended in this paper to the case of Poisson (shot noise) input. The non-linear dynamical systems are expressed, in general, as stochastic differential equations, with an independent increment input. The transition probability density function evolves according to the appropriate Kolmogorov equation. Moments of the stationary density are obtained from the Fourier transform of the stationary density. The moment relations can be used to estimate the parameters of linear and non-linear stochastic systems from empirical moments, given either Wiener or Poisson input.

The stationary moments of Poisson-driven non-linear dynamical systems

1982 ◽  
Vol 19 (03) ◽  
pp. 702-706
Author(s):  
Charles E. Smith ◽  
Loren Cobb
Keyword(s):  
Dynamical Systems ◽  
Probability Density ◽  
Stochastic Systems ◽  
Transition Probability ◽  
Kolmogorov Equation ◽  
Transition Probability Density ◽  
Linear Dynamical Systems ◽  
Stationary Density ◽  
Non Linear ◽  
Noise Input

Moment recursion relations have previously been derived for the stationary probability density functions of continuous-time stochastic systems with Wiener (white noise) input. These results are extended in this paper to the case of Poisson (shot noise) input. The non-linear dynamical systems are expressed, in general, as stochastic differential equations, with an independent increment input. The transition probability density function evolves according to the appropriate Kolmogorov equation. Moments of the stationary density are obtained from the Fourier transform of the stationary density. The moment relations can be used to estimate the parameters of linear and non-linear stochastic systems from empirical moments, given either Wiener or Poisson input.

A novel approach for the stability problem in non-linear dynamical systems

2003 ◽  
Vol 155 (1) ◽  
pp. 21-30 ◽  
Author(s):  
Tarcı́sio M. Rocha Filho ◽  
Iram M. Gléria ◽  
Annibal Figueiredo
Keyword(s):  
Dynamical Systems ◽  
Stability Problem ◽  
Linear Dynamical Systems ◽  
Novel Approach ◽  
Non Linear ◽  
The Stability
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