Paper-Project 2: PL fluctuations of chemical concentrations

Max system:

• Basic dynamics: d/dt y = + x y - x y^2 - c y
• Fluctuations: x --> x + dx(t), multiplicative exp-correlated noise (tau_cor)
  
• Inverted PL for P(x) in the limit of small tau_cor
• Idea: P(x) corresponds to the stationary, long-time case. Then x(t) is effectively white. Small tau_cor means just small effective variance of the white x(t).
• Check if Fokker-Plack-Eq. is solvable analytically or numerically.
  

A similar system and result is discussed for gen expression in Nacher06:

• Basic dynamics: d/dt y = + p - x y.
• Fluctuations: p --> p + dp(t), additive white noise. Seems to be not so important.
  
• x --> x + dx(t), multiplicative white noise
• Stationary limit of Fokker-Plack-Eq. is solvable for large conc. x and gives a PL.
• PL is of normal decaying type