A population on the move

This example is a model of two populations P1 and P2 that move according to certain rules between two regions R1 and R2. An individual from P1 will tend to move between R1 and R2 in such a way as to avoid living together with individuals from P2. On the other hand, individuals from P2 tries to live where P1-individuals live. These rules are clearly visible in the animation above where P2-individuals "follow" those from P1. The red asterisk is the expected value and spirals in towards the middle (it is thus of a very limiting insight). The probability density slowly smears out and reaches a kind of crater formation in the long-time limit.

(Plot info: the coordinate system covers the domain [-60,60]-by-[-60,60] and thus each axis tick is 20 individuals. The contour levels have been chosen by Matlab)


  • S. Engblom: Spectral Approximation of Solutions to the Chemical Master Equation, in J. Comput. Appl. Math. 229(1):208--221, 2009: (doi)
  • S. Engblom: Galerkin Spectral Method applied to the Chemical Master Equation, in Commun. Comput. Phys. 5(5):871--896, 2009: (abstract), (pdf).

  • Stefan Engblom
    Last modified: Mon May 5 13:38:18 MEST 2008