fd2d_predator_prey


fd2d_predator_prey, a FORTRAN90 code which solves a predator-prey system in a two dimensional region. The code requires both some interactive input from the user, and two simple routines that define the initial values.

The nondimensional problem has the form

        du/dt =         del u + ( 1 - u ) * u        - v * h(u/alpha)

        dv/dt = delta * del v     - gamma * v + beta * v * h(u/alpha)
      
in a square [A,B]x[A,B], with initial conditions:
        u(x,y,0) = u0(x,y)
        v(x,y,0) = v0(x,y)
      
and Neumann boundary conditions along the boundary of the square:
        du/dn = 0
        dv/dn = 0
      
The Type II functional response employed here is
        h(eta) = eta / ( 1 + eta )
      
The parameters ALPHA, BETA, GAMMA and DELTA are strictly positive.

The user must input a value H specifying the desired space step to be used in discretizing the space dimension.

A finite difference scheme is employed to integrate the problem from time 0 to a maximum time T. The user must input the value T, as well as an appropriate time step DELT.

A typical input for this problem is:

        ALPHA =   0.4
        BETA  =   2.0
        GAMMA =   0.6
        DELTA =  10.0
        A     =   0.0
        B     = 500.0
        H     =   1.0
        T     = 150.0
        DELT  =   0.041666666666666
        SOLVE =   0
      
with the following initial values of U and V supplied in auxiliary subroutines:
        ustar = gamma * alpha / ( beta - gamma )

        u0(i,j) = ustar - 2.0E-07 * ( x(i,j) - 0.1 * y(i,j) - 225.0 )
          * ( x(i,j) - 0.1 * y(i,j) - 675.0 )

        vstar = ( 1.0 - ustar ) * ( alpha + ustar )

        v0(i,j) = vstar - 3.0E-05 * ( x(i,j) - 450.0 )
          - 1.2E-04 * ( y(i,j) - 150.0 )
      

Licensing:

The computer code and data files made available on this web page are distributed under the GNU LGPL license.

Languages:

fd2d_predator_prey is available in a FORTRAN90 version and a MATLAB version.

Related Data and codes:

FD1D_PREDATOR_PREY, a FORTRAN90 code which uses finite differences to solve a 1D predator prey problem.

fd2d_predator_prey_test

Reference:

  1. Marcus Garvie,
    Finite-Difference Schemes for Reaction-Diffusion Equations Modeling Predator-Prey Interactions in MATLAB,
    Bulletin of Mathematical Biology,
    Volume 69, Number 3, 2007, pages 931-956.

Source Code:


Last revised on 30 June 2020.