The .ode file format

A model is a plain text file, usually ending in .ode. XPP Lab reads exactly the format of XPPAUT 8.0, so files written for XPPAUT work unchanged. Each statement goes on its own line, and the file ends with done. Upper and lower case are the same in names.

A complete example

# Lotka-Volterra predator-prey model
x' = a*x - b*x*y
y' = -c*y + d*x*y
par a=1, b=0.5, c=0.75, d=0.25
init x=2, y=1
aux total = x + y
@ total=50, dt=0.02, xp=x, yp=y, xlo=0, xhi=8, ylo=0, yhi=6
done

Equations

Form	Meaning
x' = f or dx/dt = f	A differential equation.
x(t+1) = f	A map (difference equation); use method discrete.
x(t) = f	A Volterra integral equation (f may contain int{...}).
0 = f	An algebraic constraint (with solv variables: a DAE).
s = expression	A fixed (intermediate) quantity, computed at each step.
aux name = expression	An auxiliary output: plotted and saved, but not integrated.

Declarations

Statement	Meaning
par a=1, b=2	Parameters.
init x=0.1, y=0	Initial values (x(0)=0.1 also works).
number pi2=6.2832	A constant that cannot be changed while running.
f(u,v) = u^2 - v	A user function, with up to 9 arguments.
!d = 2*a	A derived parameter, recomputed when parameters change.
table g g.tab	A function tabulated in a file.
wiener w	A Wiener process for noise; use euler or backeul.
markov z 2	A Markov chain variable with 2 states (transition table follows).
global 1 x-1 {x=0}	An event: when x-1 crosses zero upwards, reset x=0.
bdry x-1	A boundary condition for boundary-value problems.
set name {a=2, total=50}	A named parameter set.
#include file.inc	Insert another file.

Arrays save typing: x[1..10]' = -x[j] + x[j-1] defines ten equations, with j running from 1 to 10.

Expressions

Arithmetic: + - * / ^ and parentheses. Comparisons and logic (< > <= >= == != & |) give 1 or 0, so (x>0)*x is max(x, 0).

Functions: sin cos tan asin acos atan atan2 sinh cosh tanh exp ln log log10 sqrt abs heav sign mod max min flr ran normal besselj bessely erf erfc hom_bcs, and if(cond)then(a)else(b).

Special terms: t is time. delay(x, tau) or x(t-tau) is a delayed value. pi is 3.14159...

Options (@ lines)

Options set how the model runs. They can be combined on one line: @ total=100, dt=0.05, meth=stiff.

Option	Meaning
total, dt, t0, trans	Integration time, step, start time, transient to discard.
meth	Method: rungekutta, euler, modeuler, adams, gear, stiff, cvode, 5dp, 83dp, 2rb, backeul, qualrk, volterra, ymp, discrete.
tol, atol	Relative and absolute tolerances of adaptive methods.
dtmin, dtmax	Limits on the adaptive step.
bound	Stop if a variable exceeds this size.
nout	Store every n-th step.
maxstor	Maximum number of stored points.
delay	Maximum delay, for delay equations.
xp, yp, xlo, xhi, ylo, yhi	The phase-plane variables and window.
nmesh	Grid for nullclines.
poimap, poivar, poipln, poisgn	Poincare sections.
ds, dsmin, dsmax, parmin, parmax, nmax, npr, ntst	AUTO settings.

Comments

Lines starting with # are comments. The first comment lines of a file are shown as its description in the Models window, so describe your model there. Lines starting with " are XPPAUT's interactive tutorial text.