LV Model Parameter Files

These are parameter files for various Lotka-Volterra systems:

paramsa.dat    N = 16    xmin > 1e-6    LE > 1e-3

paramsb.dat    N = 24    xmin > 1e-6    LE > 1e-3

paramsc.dat    N = 24    xmin > 1e-6    LE > 1e-3

paramsd.dat    N = 48    xmin > 1e-6    LE > 1e-3

paramse.dat    N = 48    xmin > 1e-6    LE > 1e-3

paramsf.dat    N = 48    xmin > 1e-6    LE > 1e-3    4 nearest neighbors in a ring

paramsg.dat    N = 64    xmin > 1e-6    LE > 1e-3

paramsh.dat    N = 25    xmin > 1e-6    LE > 1e-3    8 nearest neighbors on 5x5 grid

paramsi.dat    N = 100   xmin > 1e-6    LE > 1e-3

paramsj.dat    N = 64    xmin > 1e-6    LE > 1e-3    8 nearest neighbors on 8x8 grid

paramsk.dat    N = 100   xmin > 1e-6    LE > 1e-3    8 nearest neighbors on 10x10 grid

paramsl.dat    N = 100   xmin > 1e-6    LE > 1e-3    sparse matrix (many zero terms)

paramsm.dat    N = 100   xmin > 1e-6    LE > 1e-3    4 nearest neighbors in a ring

paramsn.dat    N = 144   xmin > 1e-6    LE > 1e-3    8 nearest neighbors on 12x12 grid

paramso.dat    N = 256   xmin > 1e-6    LE > 1e-3    8 nearest neighbors on 16x16 grid

paramsp.dat    N = 256   xmin > 1e-6    LE > 1e-3    4 nearest neighbors in a ring

paramsq.dat    N = 400   xmin > 1e-6    LE > 1e-3    8 nearest neighbors on 20x20 grid

paramsr.dat    N = 400   xmin > 1e-6    LE > 1e-3    4 nearest neighbors in a ring

paramss.dat    N = 144   xmin > 1e-6    LE > 1e-3

paramst.dat    N = 256   xmin > 1e-6    LE > 1e-3    sparse matrix (many zero terms)

paramsu.dat    N = 5     xmin > 1e-6    LE > 1e-3

paramsv.dat    N = 48    xmin > 1e-6    LE > 1e-3    4 nearest neighbors in a uniform ring

paramsw.dat    N = 100   xmin > 1e-6    LE > 1e-3    4 nearest neighbors in a uniform ring

paramsx.dat    N = 100   xmin > 1e-6    LE > 1e-3    3 nearest neighbors in a uniform ring

paramsy.dat    N = 100   xmin > 1e-6    LE > 4e-3    4 nearest neighbors in a uniform ring

paramsz.dat    N = 100   xmin > 1e-6    LE > 1e-3    2 (of 4) nearest neighbors in a uniform ring

params1.dat    N = 100   xmin > 1e-6    LE > 1e-3    10 (of 24) nearest neighbors on 10x10 uniform grid

Format for the above files:

Seed for random number generator

N (number of species)

xo(i) (initial conditions, N values)

r(i) (growth rates, N values)

a(i,j) (matrix of interations, N*N values)

x(i) (final conditions, N values)

LE (Lyapunov exponent)

Program details:

These parameter files were generated with variants of the program evolve.exe whose source code is at evolve.bas. You can examine any of the cases by launching the program with a command line trailer, such as "evolve paramsa.dat".

The algorithm that produced the above files is as follow:

Off-diagonal elements of a(i,j) are chosen initially from an exponential distribution -log(rnd), and initial conditions for x(i) are chosen iid uniform in the range (0,1).
The Lotka-Volterra equations are advanced in time with a time step of 0.05 while calculating the largest Lyapunov exponent.
At each time step, any x(i) that falls below 1e-6 is set to 1e-6, and the values of a(i,j) are reduced to a(i,j)[1-0.0001x(j)] for all j<>i.
If the largest Lyapunov exponent after 100 time units (2000 time steps) is less than 0.001, then all a(i,j) are increased to 1.001a(i,j) for all i,j except j=i, and time is set to zero.
If the time exceeds 50,000 (1e6 time steps) without the LE dropping below 0.001, the solution is declared successful, and the program stores the parameters in the params.dat file and continues calculating while saving the biomass and biodiversity to the files biomass.dat and diverse.dat. A new params.dat file is written every 50,000 time units.