scholarly journals Impact of Correlated Noises on Additive Dynamical Systems

2014 ◽  
Vol 2014 ◽  
pp. 1-6 ◽  
Author(s):  
Chujin Li ◽  
Jinqiao Duan
Keyword(s):  
Dynamical Systems ◽  
White Noise ◽  
Probability Density ◽  
Probability Density Functions ◽  
Hurst Parameter ◽  
Random Solution ◽  
Small Noise ◽  
Fractional Brownian Motions ◽  
Noise Limit ◽  
Correlated Noises

Impact of correlated noises on dynamical systems is investigated by considering Fokker-Planck type equations under the fractional white noise measure, which correspond to stochastic differential equations driven by fractional Brownian motions with the Hurst parameterH>1/2. Firstly, by constructing the fractional white noise framework, one small noise limit theorem is proved, which provides an estimate for the deviation of random solution orbits from the corresponding deterministic orbits. Secondly, numerical experiments are conducted to examine the probability density evolutions of two special dynamical systems, as the Hurst parameterHvaries. Certain behaviors of the probability density functions are observed.

scholarly journals Improving AoA Localization Accuracy in Wireless Acoustic Sensor Networks with Angular Probability Density Functions

Sensors ◽  
2019 ◽  
Vol 19 (4) ◽  
pp. 900 ◽  
Author(s):  
Bart Thoen ◽  
Stijn Wielandt ◽  
Lieven De Strycker
Keyword(s):  
Sensor Networks ◽  
White Noise ◽  
Probability Density ◽  
Probability Density Functions ◽  
Density Functions ◽  
Acoustic Sensor ◽  
Angle Of Arrival ◽  
Matching Algorithm ◽  
Acoustic Sensor Networks ◽  
Mems Microphone

Advances in energy efficient electronic components create new opportunities for wireless acoustic sensor networks. Such sensors can be deployed to localize unwanted and unexpected sound events in surveillance applications, home assisted living, etc. This research focused on a wireless acoustic sensor network with low-profile low-power linear MEMS microphone arrays, enabling the retrieval of angular information of sound events. The angular information was wirelessly transmitted to a central server, which estimated the location of the sound event. Common angle-of-arrival localization approaches use triangulation, however this article presents a way of using angular probability density functions combined with a matching algorithm to localize sound events. First, two computationally efficient delay-based angle-of-arrival calculation methods were investigated. The matching algorithm is described and compared to a common triangulation approach. The two localization algorithms were experimentally evaluated in a 4.25 m by 9.20 m room, localizing white noise and vocal sounds. The results demonstrate the superior accuracy of the proposed matching algorithm over a common triangulation approach. When localizing a white noise source, an accuracy improvement of up to 114% was achieved.

scholarly journals The Stochastic Stability of Internal HIV Models with Gaussian White Noise and Gaussian Colored Noise

2019 ◽  
Vol 2019 ◽  
pp. 1-8 ◽  
Author(s):  
Xiying Wang ◽  
Yuanxiao Li ◽  
Xiaomei Wang
Keyword(s):  
White Noise ◽  
Probability Density ◽  
Stochastic Stability ◽  
Colored Noise ◽  
Gaussian White Noise ◽  
Probability Density Functions ◽  
Stochastic Dynamic ◽  
Density Functions ◽  
Gaussian Colored Noise ◽  
The Stability

In this paper, the stochastic stability of internal HIV models driven by Gaussian white noise and Gaussian colored noise is analyzed. First, the stability of deterministic models is investigated. By analyzing the characteristic values of endemic equilibrium, we could obtain that internal HIV models reach a steady state under the influence of RTI and PI drugs. Then we discuss the stochastic stability of internal HIV models driven by Gaussian white noise and Gaussian colored noise, based on probability density functions. The functional methods are carried out to derive the approximate Fokker-Planck equation of stochastic internal HIV systems and further obtain the marginal probability density functions. Finally, numerical results show that the noise intensities have a great influence on uninfected cell, infected cell, and virus particles, for predicting the stability of stochastic dynamic systems subjected to Gaussian white noise and Gaussian colored noise.

scholarly journals RANDOM ATTRACTORS OF STOCHASTIC LATTICE DYNAMICAL SYSTEMS DRIVEN BY FRACTIONAL BROWNIAN MOTIONS

2013 ◽  
Vol 23 (03) ◽  
pp. 1350041 ◽  
Author(s):  
ANHUI GU
Keyword(s):  
Dynamical System ◽  
Dynamical Systems ◽  
Existence And Uniqueness ◽  
Random Attractor ◽  
Hurst Parameter ◽  
Random Dynamical System ◽  
Brownian Motions ◽  
Fractional Brownian Motions ◽  
Random Attractors ◽  
Lattice Dynamical Systems

This paper is devoted to consider stochastic lattice dynamical systems (SLDS) driven by fractional Brownian motions with Hurst parameter bigger than 1/2. Under usual dissipativity conditions these SLDS are shown to generate a random dynamical system for which the existence and uniqueness of a random attractor are established. Furthermore, the random attractor is, in fact, a singleton sets random attractor.

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