fd1d_predator_prey, a Fortran77 code which solves a predator-prey system in a one dimensional region, by Marcus Garvie.
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)
with initial conditions:
u(x,0) = u0(x)
v(x,0) = v0(x)
and boundary conditions at the left and right endpoints [A,B]:
du/dx = 0
dv/dx = 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.
Typical data for this problem is:
ALPHA = 0.3
BETA = 2.0
GAMMA = 0.8
DELTA = 1.0
A = 0.0
B = 200.0
H = 0.5
T = 40.0
DELT = 0.0104
GAUSS = 0 (0 = direct solution, 1 = Jacobi )
with the initial values of U and V set, for instance, to:
u0(1:n) = exp ( - ( x(1:n) - 100.0 )**2 ) / 5.0
v0(1:n) = 2.0 / 5.0
The computer code and data files described and made available on this web page are distributed under the MIT license
fd1d_predator_prey is available in a Fortran90 version and a MATLAB version and an Octave version.
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