보존과 임계성 - 랑제방 접근

\(\partial_t\rho(\vec x,t)=a\rho-b\rho^2+D\nabla^2\rho +\sigma\sqrt{\rho}\eta(\vec x,t)\)

\(\partial_t\rho(\vec x,t)&=&a\rho-b\rho^2+w\rho E+D\nabla^2\rho +\sigma\sqrt{\rho}\eta(\vec x,t)\\ \partial_t E(\vec x,t)&=&D_E\nabla^2\rho(\vec x,t)\)

\(E(\vec x,t)=E(\vec x,0)+D_E\int_0^t dt'\nabla^2\rho(\vec x,t')\)

\(\partial_t\rho(\vec x,t)&=&a\rho-b\rho^2+w\rho E+D\nabla^2\rho +\sigma\sqrt{\rho}\eta(\vec x,t)\\ \partial_t E(\vec x,t)&=&D_E\nabla^2\rho(\vec x,t)\)

\(\partial_t E(\vec x,t)=D_E\nabla^2\rho(\vec x,t)-\epsilon\rho(\vec x,t)\)