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Noise on ODEs

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  • Kostas Chlouverakis
    Hi, I want to investigate the effects of gaussian noise on a solution for my system. My system is similar to Lorenz s. My idea was to just run the code for it
    Message 1 of 3 , Aug 4, 2002
      Hi,
      I want to investigate the effects of gaussian noise on a solution for my system. My system is similar to Lorenz's.
      My idea was to just run the code for it and add in the dx/dt deritive random generators from the C++ libraries.
      Also,I have heard about noise with auto-correlation sources.
      Does anybody has any idea to give me some help?
      Kostas
    • César Monroy
      Hi Kostas: Noise is tinted with colors. White noise, for instance, is a pure random signal whose fractal dimension fills completely the space available and has
      Message 2 of 3 , Aug 4, 2002
        Hi Kostas:
         
        Noise is tinted with colors. White noise, for instance, is a pure random signal whose fractal dimension fills completely the space available and has equal energy per frequency. Pink noise, in contrast, is a filtered random signal whose fractal dimension also fills completely the space, but is characterized by having equal energy per octave. As noise is more easily related to hearing, it's only natural to talk about it in these terms. For instance, you may know that human hearing responds to sound in a logarithmic manner so pink and white noise sound differently: the first is perceived as if all frequencies have the same level, the second sound as if the high frequencies were loudest.
         
        There is also another kind of noise, known as brown and related to brownian motion. This noise isn't random, because the signal correlates someway with past and future individual signals. Correlation is the direct differential of two consecutive signals and anticorrelation is the inverse differential. Also note that brown noise really has a fractal nature (between one dimension and the next). Altough this three kind of noises are used to feed random generators, you must be aware of their differences.
         
        Brown noise is best used to explain deterministic behaviour of complex systems, like stock market and the like. Pink noise is used mostly in biological systems. White noise is preferred in mathematical applications.
         
        Let me know if this info served you and if you want a brown random generator (code or algorithm)
         
        Greetings,
         
        César
         
         
        ----- Original Message -----
        Sent: Sunday, August 04, 2002 8:05 AM
        Subject: [caostheory] Noise on ODEs

        Hi,
        I want to investigate the effects of gaussian noise on a solution for my system. My system is similar to Lorenz's.
        My idea was to just run the code for it and add in the dx/dt deritive random generators from the C++ libraries.
        Also,I have heard about noise with auto-correlation sources.
        Does anybody has any idea to give me some help?
        Kostas


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      • Kostas Chlouverakis
        Cesar, Thank you very much for your reply and the useful info. I knew white and pink noise but I never had heard the brown one. I am into chaotic dynamics 3
        Message 3 of 3 , Aug 4, 2002
          Cesar,
          Thank you very much for your reply and the useful info. I knew white and pink noise but I never had heard the brown one.
          I am into chaotic dynamics 3 years now and this is my first attempt of adding noise to a system of mine (similar to Lorenz as I already mentioned before).
          I want to do something similar to what I found in this page : http://cires.colorado.edu/~ricardo/noise/
          Of course I would like you to send me your code for the brown noise and if it is possible to send it in : kchlou@...
          I would appreciate it a lot.
          I may be wrong , but in simulations especially in engineering the use white or pink noise. How can the noise be connected with auto-correlation functions and why?
          Best regards
          Kostas
           
          ----- Original Message -----
          Sent: Sunday, August 04, 2002 9:10 PM
          Subject: Re: [caostheory] Noise on ODEs

          Hi Kostas:
           
          Noise is tinted with colors. White noise, for instance, is a pure random signal whose fractal dimension fills completely the space available and has equal energy per frequency. Pink noise, in contrast, is a filtered random signal whose fractal dimension also fills completely the space, but is characterized by having equal energy per octave. As noise is more easily related to hearing, it's only natural to talk about it in these terms. For instance, you may know that human hearing responds to sound in a logarithmic manner so pink and white noise sound differently: the first is perceived as if all frequencies have the same level, the second sound as if the high frequencies were loudest.
           
          There is also another kind of noise, known as brown and related to brownian motion. This noise isn't random, because the signal correlates someway with past and future individual signals. Correlation is the direct differential of two consecutive signals and anticorrelation is the inverse differential. Also note that brown noise really has a fractal nature (between one dimension and the next). Altough this three kind of noises are used to feed random generators, you must be aware of their differences.
           
          Brown noise is best used to explain deterministic behaviour of complex systems, like stock market and the like. Pink noise is used mostly in biological systems. White noise is preferred in mathematical applications.
           
          Let me know if this info served you and if you want a brown random generator (code or algorithm)
           
          Greetings,
           
          César
           
           
          ----- Original Message -----
          Sent: Sunday, August 04, 2002 8:05 AM
          Subject: [caostheory] Noise on ODEs

          Hi,
          I want to investigate the effects of gaussian noise on a solution for my system. My system is similar to Lorenz's.
          My idea was to just run the code for it and add in the dx/dt deritive random generators from the C++ libraries.
          Also,I have heard about noise with auto-correlation sources.
          Does anybody has any idea to give me some help?
          Kostas


          Your use of Yahoo! Groups is subject to the Yahoo! Terms of Service.


          Your use of Yahoo! Groups is subject to the Yahoo! Terms of Service.
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