Non Linear Systems Under Complex α-Stable Le´vy White Noise

2003 ◽  
Author(s):  
M. Di Paola ◽  
M. Vasta
Keyword(s):  
Nonlinear Systems ◽  
Characteristic Function ◽  
White Noise ◽  
Linear Systems ◽  
Poisson White Noise ◽  
Input And Output ◽  
Non Linear Systems ◽  
Linear And Nonlinear ◽  
White Noises ◽  
Linear And Nonlinear Systems

The problem of predicting the response of linear and nonlinear systems under Le´vy white noises is examined. A method of analysis is proposed based on the observation that these processes have impulsive character, so that the methods already used for Poisson white noise or normal white noise may be also recast for Le´vy white noises. Since both the input and output processes have no moments of order two and higher, the response is here evaluated in terms of characteristic function.

Mathematical modeling of conversion of non-Gaussian random processes, signals and noise in linear and nonlinear systems

2018 ◽  
pp. 66-78
Author(s):  
V. M. Artyushenko ◽  
V. I. Volovach
Keyword(s):  
Mathematical Modeling ◽  
Nonlinear Systems ◽  
Random Processes ◽  
Mathematical Transformation ◽  
Positive And Negative Feedback ◽  
Non Linear Systems ◽  
Linear And Nonlinear ◽  
Non Gaussian ◽  
Linear And Nonlinear Systems ◽  
Inertial Systems

The questions connected with mathematical modeling of transformation of non-Gaussian random processes, signals and noise in linear and nonlinear systems are considered and analyzed. The mathematical transformation of random processes in linear inertial systems consisting of both series and parallel connected links, as well as positive and negative feedback is analyzed. The mathematical transformation of random processes with polygamous density of probability distribution during their passage through such systems is considered. Nonlinear inertial and non-linear systems are analyzed.

APPROXIMATION OF THE FRACTAL TRANSITION USING ATTRACTORS EXCITED BY PERIODIC INPUTS

2003 ◽  
Vol 13 (04) ◽  
pp. 943-950 ◽  
Author(s):  
HISAKI OKA ◽  
KAZUTOSHI GOHARA
Keyword(s):  
Dynamical Systems ◽  
Nonlinear Systems ◽  
Linear Systems ◽  
Upper Bound ◽  
Hausdorff Distance ◽  
Numerical Experiments ◽  
Linear And Nonlinear ◽  
Periodic Inputs ◽  
Linear And Nonlinear Systems ◽  
Accuracy Of Approximation

Dissipative continuous dynamical systems with multiple external inputs are studied. When inputs are stochastically switched, the dynamics is characterized by trajectories with attractive fractal-like structures. We call this dynamics the fractal transition. This paper shows that a set of attractors obtained by periodic inputs can approximate trajectories of the fractal transition that have equal switching probabilities. The Hausdorff distance D is used to estimate the accuracy of approximation. We also present two numerical experiments, using harmonic and Duffing oscillators, corresponding to linear and nonlinear systems, respectively. We numerically show that D ≃ 0 given a large enough number of periodic inputs. For linear systems, under some conditions, we analytically derive the upper bound of D and show that D converges to 0.

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