Examples gallery¶
The 141 example models that ship with XPPAUT, run by XPP Lab. Open any of them from the app's Models window, or in Python with xs.load("name.ode").
6x6¶
6x6 array
Variables: X11, X12, X13, X14, X15, X16, X21, X22, X23, X24 .... Parameters: a, b, c. Model file
acoaster¶
Hey, define your roller coaster track here! Use parametric equations in M.
Variables: X, Z, M, L, LALT. Parameters: alpha, beta, gamma, delta, drag, mass, g, sv. Model file
ai¶
No description in the file.
Variables: BR, IAPP, PHI, PER, V, W. Parameters: none. Model file
amari¶
amari bump
Variables: U0, U1, U2, U3, U4, U5, U6, U7, U8, U9 .... Parameters: c, b, dx, h. Model file
amari2¶
amari bump
Variables: U0, U1, U2, U3, U4, U5, U6, U7, U8, U9 .... Parameters: c, b, dx, h. Model file
amarig¶
amari bump with gaussian
Variables: U0, U1, U2, U3, U4, U5, U6, U7, U8, U9 .... Parameters: c, b, dx, h. Model file
angela¶
No description in the file.
Variables: U. Parameters: none. Model file
atcoaster¶
Hey, define your roller coaster track here! Use parametric equations in M.
Variables: X, Z, M, L, LALT. Parameters: alpha, beta, gamma, delta, drag, mass, g, sv. Model file
bnn¶
No description in the file.
Variables: U, W, Z. Parameters: beta, th, c, k. Model file
bob¶
No description in the file.
Variables: X, Y. Parameters: none. Model file
borcol¶
Borelli and Coleman wine glass
Variables: X1, X2, X3, X4. Parameters: none. Model file
cable¶
Linear Cable Model cable.ode
Variables: V, VX. Parameters: a, b, v0, lam2. Model file
chemotax¶
bacterial chemotaxis model
Variables: B0, B1, B2, B3, B4, B5, B6, B7, B8, B9 .... Parameters: chi, d, k, mu, r, z. Model file
coaster2D¶
Hey, define your roller coaster track here! Use parametric equations in M.
Variables: X, Z, M, L, LALT. Parameters: drag, mass, g. Model file
cobweb2¶
way to fool XPP into cobwebbing first I define a function that every other step evaluates the map -- in the alternate steps, it just keeps the same value so that it alternates between horizontal and vertical
Variables: Y, X. Parameters: a. Model file
crazy¶
No description in the file.
Variables: X, Y. Parameters: none. Model file
cuplamdif¶
cuplamdif.ode the functions F(u,v), G(u1,v1)
Variables: U, V, U1, V1. Parameters: lam, q, d, u0, u10. Model file
dae¶
plot y
Variables: X. Parameters: none. Model file
dae_ex1¶
dae_ex1.ode
Variables: X. Parameters: none. Model file
dae_ex2¶
dae_ex2.ode
Variables: X. Parameters: none. Model file
dae_ex3¶
dae_ex3.ode
Variables: W. Parameters: none. Model file
dde¶
No description in the file.
Variables: X. Parameters: tau, a, b, c. Model file
del_log¶
illustrates a period 7 continuation for the delayed logistic map
Variables: Y, X. Parameters: r, eps. Model file
delay¶
delayed feedback delay.ode
Variables: X. Parameters: tau, b, a, p. Model file
delta¶
delta coupled oscillators delta.ode
Variables: X, Y. Parameters: b, phi, w. Model file
dlog¶
No description in the file.
Variables: X. Parameters: tau, a. Model file
doubpend¶
parameters
Variables: T1, T2, T2P, T1P. Parameters: L1, L2, m1, m2, g, mu. Model file
duck¶
duck.ode the infamous drinking duck modeled as a pendulum with some extra forces M is the total mass of the two parts of the duck
Variables: MU, X, XDOT. Parameters: l1, l2, mmin, f, k, xlo, eps, xdip, mutot, beta. Model file
duckx¶
duck.ode the infamous drinking duck modeled as a pendulum with some extra forces M is the total mass of the two parts of the duck
Variables: MU, X, XDOT. Parameters: l1, l2, mmin, f, k, xlo, eps, xdip, mutot, beta .... Model file
dumbbvp¶
No description in the file.
Variables: X, Y. Parameters: a. Model file
ecofilip¶
No description in the file.
Variables: X1, X2. Parameters: p, e, a, c, d1, d2, q, b. Model file
efm¶
No description in the file.
Variables: S. Parameters: ibar, isig, tau. Model file
efmplot¶
No description in the file.
Variables: S. Parameters: ibar, isig, tau. Model file
efmx¶
gcc -fPIC -dynamiclib -arch i386 efmx.c -o efx.so
Variables: S. Parameters: ibar, isig, nsig, tau, nit, nn, ntr. Model file
efmxfb¶
No description in the file.
Variables: S, IBAR. Parameters: isig, nsig, tau, nit, nn, ntr, taui, k, c. Model file
efmxplot¶
plots the rhs of s' gcc -fPIC -dynamiclib -arch i386 efmx.c -o efx.so File Edit Load-dll - choose efx.so choose efmx for the function
Variables: S, SDOT. Parameters: ibar, isig, nsig, tau, nit, nn, ntr. Model file
efmxplott¶
plots the rhs of s' gcc -fPIC -dynamiclib efmx.c -o efx.so File Edit Load-dll - choose efx.so choose efmx for the function
Variables: S, SD, TIM. Parameters: ibar, isig, nsig, tau, nit, nn, ntr. Model file
efmxrun¶
No description in the file.
Variables: S, SDOT. Parameters: ibar, isig, nsig, tau, nit, nn, ntr. Model file
elaspen¶
the pendulum on a spring the dimensionless parameter is a= k l/m g where k is the spring constant r is the length and th is the angle
Variables: R, RP, TH, THP. Parameters: a, fk, ft, scale. Model file
ev1¶
na'=-mugnaminf(v)*(v-ena)-(na-namin)/tauna sks=na^q/(na^q+nah^q)
Variables: V, N. Parameters: q, nah, namin, mu, tauna, gks, va, vb, vc, vd .... Model file
evelyn¶
No description in the file.
Variables: V, NA, N. Parameters: q, nah, namin, mu, tauna, gks, va, vb, vc, vd .... Model file
fancylorenz¶
the lorenz equations with some fancy graphics options
Variables: X, Y, Z. Parameters: r, s, b, xplane, yplane, zplane. Model file
fhn¶
Forced Fitzhugh-Nagumo fhn.ode
Variables: V, W. Parameters: a, eps, gamma, I_0, al, omega. Model file
fhn3d¶
Forced Fitzhugh-Nagumo fhn.ode
Variables: V, I, W. Parameters: a, eps, gamma. Model file
fhn_noise¶
Forced Fitzhugh-Nagumo fhn.ode
Variables: V, W. Parameters: a, eps, gamma, I_0, sig. Model file
fieldnoy¶
The Field-Noyes Equations. A very hard problem for most numerical integrators. A stiff method is absolutely necessary
Variables: X, Y, Z. Parameters: q, s, f, w. Model file
forcpend¶
No description in the file.
Variables: X, Y. Parameters: f, w, a. Model file
fr¶
fabry-perot cavity
Variables: TAU, X, V, FR, FI. Parameters: q, xs, a, th, r, c, eps. Model file
gausvolt¶
No description in the file.
Variables: X. Parameters: a, t0. Model file
geisel¶
an example due to Geisel with 1/f spectral properties
Variables: X, Y, U, V. Parameters: a, b. Model file
getfrefm¶
No description in the file.
Variables: NIT, SD, TIM, S. Parameters: ibar, isig, nsig, tau, nn, ntr, gee. Model file
gill_bruss¶
gillesp_bruss.ode gillespie algorithm for brusselator x1 -> y1 (c1) x2+y1 -> y2+Z (c2)
Variables: TR, Y1, Y2. Parameters: c1x1, c2x2, c3, c4. Model file
greg¶
paramters to be varied to see the effect of fitcurve
Variables: A. Parameters: k. Model file
henhei¶
henon-heiles illustrates the use of the symplectic integrator try integration to 20000 with nout=100 and plot the energy try again with Runge-Kutta
Variables: X, PX, Y, PY. Parameters: none. Model file
hhred¶
The reduced Hodgkin Huxley equations showing fixed parameters and a bunch of auxiliary columns left for post processing
Variables: V, N. Parameters: om, VNA, VK, VL, GNABAR, GKBAR, GLBAR, GL, I0, IP .... Model file
iaf¶
No description in the file.
Variables: V. Parameters: i. Model file
idoubpend¶
parameters
Variables: T1, T2, T2P, T1P. Parameters: L1, L2, m1, m2, g, mu. Model file
ielaspen¶
the pendulum on a spring the dimensionless parameter is a= k l/m g where k is the spring constant r is the length and th is the angle
Variables: R, RP, TH, THP. Parameters: a, f, scale. Model file
invpend¶
the inverted pendulum driven periodically start at 0 and give it a push
Variables: TH, V. Parameters: a, omega, k. Model file
itoy¶
The 24 points
Variables: T1, T1P, T2, T2P. Parameters: a, d, dd, f0, nu. Model file
jcoaster¶
Coaster demo showing how to use derivative and value matching to join two coaster tracks together. Note, we're use cubic splines parametric in M to do this. Here's the MATLAB code to find the spline coefficients
Variables: X, Z, M, L, LALT. Parameters: xs0, xs1, xs2, xs3, zs0, zs1, zs2, zs3, drag, mass .... Model file
jcoaster1¶
Coaster demo showing how to use derivative and value matching to join two coaster tracks together. Note, we're use cubic splines parametric in M to do this. Here's the MATLAB code to find the spline coefficients
Variables: X, Z, M, L, LALT. Parameters: xs0, xs1, xs2, xs3, zs0, zs1, zs2, zs3, drag, mass .... Model file
julia¶
julia set for z -> z^2+c
Variables: X, Y. Parameters: cx, cy. Model file
junk¶
junk.ode
Variables: V0, V1, V2, V3, V4, V5, V6, V7, V8, V9 .... Parameters: k, thr, beta, c, tau. Model file
junk2¶
junk2.ode
Variables: V0, V1, V2, V3, V4, V5, V6, V7, V8, V9 .... Parameters: k, thr, beta, c, tau. Model file
kepler¶
Kepler model kepler.ode
Variables: X1, X2, Z. Parameters: eps, a. Model file
koho¶
EXAMPLE 1. koho.ode implements kohonen algorithm with help from an external function
Variables: W0, W1, W2, W3, W4, W5, W6, W7, W8, W9 .... Parameters: ntot, k, sig, eps. Model file
koho2¶
this implements the kohonen algorithm using the findext code in xpp
Variables: WA0, WA1, WA2, WA3, WA4, WA5, WA6, WA7, WA8, WA9 .... Parameters: sig, k, eps, br, t0. Model file
koho3¶
this implements the kohonen algorithm using the findext code in xpp
Variables: WA0, WA1, WA2, WA3, WA4, WA5, WA6, WA7, WA8, WA9 .... Parameters: sig, k, eps, br, bc, t0. Model file
kohonen¶
this implements the kohonen algorithm using the findext code in xpp
Variables: W0, W1, W2, W3, W4, W5, W6, W7, W8, W9 .... Parameters: sig, k, eps, t0. Model file
kohox¶
kohox.ode
Variables: W0, W1, W2, W3, W4, W5, W6, W7, W8, W9 .... Parameters: ntot, k, sig, eps. Model file
lamomeg¶
the normal form of a Hopf bifurcation lamomeg.ode Boundary conditions are periodic and there is a frequency parameter -- om
Variables: X, Y. Parameters: q, om. Model file
lamprey¶
example of a chain of coupled oscillators
Variables: X1, X2, X3, X4, X5, X6, X7, X8, X9, X10 .... Parameters: grad, phi, af, ar, bend. Model file
lamvolt¶
lamvolt.ode the four variables:
Variables: U, V, U1, V1. Parameters: lam, q, d, u0, u10. Model file
lecar (Dan Dougherty's conflicted copy 2017-01-01)¶
The Morris-Lecar model as in our chapter in Koch & Segev A simple membrane oscillator.
Variables: V, W. Parameters: iapp, phi, v1, v2, v3, v4, gca, vk, vl, gk .... Model file
lecar (Dan Dougherty's conflicted copy 2017-06-03)¶
The Morris-Lecar model as in our chapter in Koch & Segev A simple membrane oscillator.
Variables: V, W. Parameters: iapp, phi, v1, v2, v3, v4, gca, vk, vl, gk .... Model file
lecar¶
The Morris-Lecar model as in our chapter in Koch & Segev A simple membrane oscillator.
Variables: V, W. Parameters: iapp, phi, v1, v2, v3, v4, gca, vk, vl, gk .... Model file
lecdiff200¶
The Morris-Lecar model as in our chapter in Koch & Segev A simple membrane oscillator.
Variables: V1, V2, V3, V4, V5, V6, V7, V8, V9, V10 .... Parameters: dif, iapp, phi, va, vb, vc, vd, gca, vk, vl .... Model file
lecsimp2¶
No description in the file.
Variables: V1, V2, W1, W2, S1, S2. Parameters: iapp, phi, va, vb, vc, vd, gca, vk, vl, gk .... Model file
lecwave¶
The Morris-Lecar model as in our chapter in Koch & Segev A simple membrane oscillator.
Variables: V, VP, W. Parameters: eta, iapp, phi, v1, v2, v3, v4, gca, vk, vl .... Model file
lin¶
Generic linear equation
Variables: X, Y. Parameters: a, b, c, d. Model file
linc¶
No description in the file.
Variables: X, Y. Parameters: none. Model file
lo¶
No description in the file.
Variables: X, Y. Parameters: lam, q. Model file
logbif¶
this is an example showing the logistic bifurcation diagram
Variables: X, A. Parameters: ind, amin, amax. Model file
lor2¶
the famous Lorenz equation set up for 3d view
Variables: X, Y, Z, XP, YP, ZP. Parameters: c, r, s, b. Model file
lorenz¶
the famous Lorenz equation set up for 3d view
Variables: X, Y, Z. Parameters: r, s, b. Model file
lorenz2¶
the famous Lorenz equation set up for animated waterwheel and some delayed coordinates as well
Variables: X, Y, Z, THETA. Parameters: r, s, b, c, del. Model file
lorknead¶
kneading sequences for the Lorenz equation
Variables: X, Y, Z, COUNT, P. Parameters: r, s, b, q, cmax. Model file
lorliap¶
the famous Lorenz equation set up for 3d view
Variables: X, Y, Z, XL, YL, ZL, TT, NORM, ACC. Parameters: r, s, b, dtout. Model file
lorpecor¶
the famous Lorenz equation set up for 3d view
Variables: X, Y, Z, XL, YL, ZL, TT, NORM, ACC. Parameters: r, s, b, a, c1, c2, c3, dtout. Model file
minode¶
include
Variables: X0, X1, X2, X3, X4, X5, X6, X7, X8, X9 .... Parameters: nlo, nhi. Model file
ml1¶
The Morris-Lecar equations ml1.ode NOTE: I use only the first letter for declarations! Declare the parameters
Variables: V, W. Parameters: gl, gca, gk, vk, vl, vca, v1, v2, v3, v4 .... Model file
mlvolt¶
cube volt.ode two equlations with passive media and then two active regions dV/dt = -a v + active stuff + d V_xx G(xhat,t) = exp(-a*t-xhat/t)/sqrt(pi t) xhat is a distance
Variables: V1, V2, W1, W2. Parameters: a, d, c, b, k, xhat, v10, v20, kk. Model file
myret¶
problem from hairer et al
Variables: Y0, Y1, Y2. Parameters: none. Model file
nf3¶
simple normal form for triple zero eigenvalue equivalent to the Rossler attractor this file illustrates how to compute a bifurcation diagram as c varies in -silent mode
Variables: X, Y, Z, C. Parameters: a, b. Model file
nnet¶
The Wilson-Cowan neural net equations The phaseplane is fun to create
Variables: X, Y. Parameters: w11, w12, w21, w22, tau, s1, s2. Model file
nnet2¶
neural network
Variables: U0, U1, U2, U3, U4, U5, U6, U7, U8, U9 .... Parameters: c, a, beta, thr. Model file
nochaos¶
this map is fractal but not chaotic
Variables: X1, X2. Parameters: none. Model file
nthet¶
stot=sum(0,99)of(shift(s0,i'))/100
Variables: S0, S1, S2, S3, S4, S5, S6, S7, S8, S9 .... Parameters: a, g, tau, sig. Model file
osc¶
No description in the file.
Variables: V, X. Parameters: beta, gam, Input, eps, sigma. Model file
pend-cart1-kick¶
pendulum on a cart uses DAE solver to solve for x'', th1'' pend-cart1.ode masses of cart and pendulum (kg)
Variables: X, XP, TH1, TH1P. Parameters: mc, mp, l, g, muc, mup, kick, r. Model file
pend-cart1¶
pendulum on a cart uses DAE solver to solve for x'', th1'' pend-cart1.ode masses of cart and pendulum (kg)
Variables: X, XP, TH1, TH1P. Parameters: mc, mp, l, g, muc, mup. Model file
pend¶
damped pendulum pend.ode
Variables: X, XP. Parameters: m, mu, g, l, scale. Model file
pendx¶
damped pendulum pend.ode
Variables: X, XP. Parameters: m, mu, g, l, scale. Model file
phs¶
No description in the file.
Variables: X, Y. Parameters: a. Model file
pp¶
cts predator prey model Test problem from the AUTO manual pp.ode Use AUTO with defaults -- just click Run
Variables: U0, U1. Parameters: p0, p1, p2, p3. Model file
r3b¶
planar restricted 3 body problem the parameter set "period" is an approximate periodic solution
Variables: X, Y, U, V. Parameters: m. Model file
ross-orbit¶
No description in the file.
Variables: X, Y, Z. Parameters: b, a. Model file
rosscmpliap¶
This code computes the Pecora-Carroll exponents for a complex eigenvalue You could use a different chaotic system if you wanted rossler attractor
Variables: X, Y, Z, VX, VY, VZ, UX, UY, UZ, SS. Parameters: a, b, c, eps, dt, mu, nu, kx, ky, kz. Model file
rossler-pecora¶
rossler attractor
Variables: X, Y, Z, XL, YL, ZL, TT, NORM, ACC. Parameters: a, b, c, alpha, c1, c2, c3, dtout. Model file
rossler¶
No description in the file.
Variables: X, Y, Z. Parameters: b, a. Model file
simplecube¶
No description in the file.
Variables: V, W. Parameters: a, d, c, b, K. Model file
sine-circel¶
example showing the del_shft orperator
Variables: X0, X1, X2, X3, X4, X5, X6, X7, X8, X9 .... Parameters: sig, tau, k. Model file
test¶
No description in the file.
Variables: Y. Parameters: none. Model file
testdll¶
No description in the file.
Variables: X. Parameters: flag. Model file
torus¶
A differential equation on the Torus. Use the "phAse spc" option to integrate it.
Variables: X, Y. Parameters: w1, w2, beta. Model file
toy_ok¶
The 24 points
Variables: T1, T1P, T2, T2P. Parameters: a, d, dd, f0, nu. Model file
transient¶
a problem with cool transients
Variables: X, Y, Z. Parameters: none. Model file
triple¶
No description in the file.
Variables: X, Y, Z. Parameters: c, a, b. Model file
tst¶
No description in the file.
Variables: X. Parameters: none. Model file
tstdel¶
No description in the file.
Variables: U0, U1, U2, U3, U4, U5, U6, U7, U8, U9. Parameters: c0, c1, c2. Model file
tstdelsp¶
No description in the file.
Variables: U0, U1, U2, U3, U4, U5, U6, U7, U8, U9 .... Parameters: c0, c1, c2. Model file
tstdll¶
EXAMPLE 2 compile the C program example.c creating example.so for LINUX (need some sort of flag to say 32 bit maybe -arch i386)
Variables: X, Y. Parameters: a, b, c, d. Model file
tstset¶
No description in the file.
Variables: X0, X1, X2, Y. Parameters: none. Model file
tstvol2¶
Volterra example from Peter Linz's book solution is f1=1,f2=t but it is unstable
Variables: F1, F2. Parameters: none. Model file
tstvol3¶
No description in the file.
Variables: X, U. Parameters: tau. Model file
vanderpol¶
No description in the file.
Variables: X, XP. Parameters: none. Model file
vdp¶
The van der Pol Oscillator with a frequuency parameter and periodic boundary conditions
Variables: X, XP. Parameters: om. Model file
vlsi¶
a model for a vlsi - poster at NIPS shows bistability of a limit cycle and fixed point
Variables: V, W. Parameters: iext, vlow, vhigh, vl, vh, ibh, ibl, itau, vdd, ut .... Model file
voltex1¶
Volterra solver example voltex1.ode
Variables: U. Parameters: none. Model file
voltex2¶
voltex2.ode - uses convolution to speed up soln
Variables: U. Parameters: none. Model file
voltex3¶
voltex2.ode - uses convolution to speed up soln
Variables: U. Parameters: none. Model file
voltex4¶
voltex4.ode - no convol
Variables: U. Parameters: none. Model file
vtst¶
this solves a continuous functional iteration problem in the Volterra solver, change MaxPoints to 10 to get fast performance fool XPP
Variables: U. Parameters: none. Model file
waterwheel¶
the waterwheel ala Lorenz but discrete
Variables: C0, C1, C2, C3, C4, C5, C6, C7, C8, C9 .... Parameters: flow, mu, n, l, mc, nu. Model file
wave (Dan Dougherty's conflicted copy 2017-01-01)¶
pulse wave
Variables: VV0, VV1, VV2, VV3, VV4, VV5, VV6, VV7, VV8, VV9 .... Parameters: a, d, eps, gamma, i. Model file
wave (Dan Dougherty's conflicted copy 2017-06-03)¶
pulse wave
Variables: VV0, VV1, VV2, VV3, VV4, VV5, VV6, VV7, VV8, VV9 .... Parameters: a, d, eps, gamma, i. Model file
wave¶
pulse wave
Variables: VV0, VV1, VV2, VV3, VV4, VV5, VV6, VV7, VV8, VV9 .... Parameters: a, d, eps, gamma, i. Model file
wcring¶
chain of 20 neurons
Variables: U0, U1, U2, U3, U4, U5, U6, U7, U8, U9 .... Parameters: a, beta. Model file
wcstim¶
No description in the file.
Variables: U, V. Parameters: aee, aie, te, aei, aii, ti, tau, s0, tdone, s1. Model file
wta¶
a model used by the author to study complex dynamics in winner take all neural networks change tau to 1.1 and then .25
Variables: X1, X2, X3, U. Parameters: tau, aee, aei, aie, c, te, ti. Model file