In [1]:

    

using DifferentialEquations
# Define a problem
p = (1.0,2.0,1.5,1.25) # a,b,c,d
f = function (du,u,p,t) # Define f as an in-place update into du
    a,b,c,d = p
    du[1] = a*u[1] - b*u[1]*u[2]
    du[2] = -c*u[2]+ d*u[1]*u[2]
end
u0 = [1.0;1.0]; tspan = (0.0,10.0)
prob = ODEProblem(f,u0,tspan,p);


    

In [2]:

    

# Solve the problem
sol = solve(prob);


    

In [3]:

    

# Plot the solution using the plot recipe
using Plots; gr() # Using the Plotly Backend
plot(sol,title="All Plots.jl Attributes are Available")


    

    





    







    
Out[3]:

In [4]:

    

plot(sol,title="Phase Diagram",vars=(1,2))


    

    
Out[4]:

In [5]:

    

@show sol.t[3] # Time at the 3rd timestep
@show sol[3] # Value at the third timestep
@show sol(5) # Value at t=5 using the interpolation


    

    




sol.t[3] = 0.2927716363874482
sol[3] = [0.768635, 0.887673]
sol(5) = [1.45932, 0.99208]






    
Out[5]:





2-element Array{Float64,1}:
 1.4593178760243926
 0.992079865175654 

In [6]:

    

g = function (du,u,p,t)
    du[1] = .5*u[1] 
    du[2] = .1*u[2]
end
prob = SDEProblem(f,g,u0,tspan,p)
sol = solve(prob,dt=1/2^4)
plot(sol)


    

    
Out[6]: