DynamicalSystems.jl

A collection of Julia functions that produce the systems of ODEs for various dynamical systems. The results of these functions are designed to be used as inputs for the RungeKutta.jl package.

NOTE: Requires Julia 0.4.

Setup

No dependencies are required, just install with

Pkg.clone("git://github.com/timothyrenner/DynamicalSystems.jl.git");

You might also want the Runge-Kutta solver package.

Pkg.clone("git://github.com/timothyrenner/RungeKutta.jl.git");

Functions

Each of the functions returns an Array of functions of the form

f[i](t,x) ==> x[i]

where i is the index, t is the time, and x is the point (one dimensional Array). Each of these functions returns the ith component of the next point in the solution to the ODE, which is precisely the format a Runge-Kutta method uses to solve it.

There are currently two functions implemented in this package.

harmonicOscillator

The harmonic oscillator equation is

The function signature is

harmonicOscillator(omega0; beta=0.0, gamma=0.0, omega=1.0)

where beta is the damping term, omega0 is the base frequency, gamma is the driving amplitude, and omega is the driving frequency. This harmonic oscillator is defined with a sinusoidal driving force.

Read more about the harmonic oscillator here.

duffingOscillator

The duffing oscillator equation is

The function signature is

duffingOscillator(delta, gamma; alpha=1.0, beta=-1.0, omega=1.0)

where delta is the damping term, gamma is the driving amplitude, alpha is the stiffness, beta is the restoring force non-linearity, and omega is the driving force frequency.

Read more about the Duffing oscillator here.

lorenzAttractor

The Lorenz attractor system of equations is

The function signature is

lorenzAttractor(sigma, rho, beta)

where sigma, rho, and beta are the corresponding terms in the system of equations.

Read more about the Lorenz attractor here.