How to analyze the solution?

General Usage
1

Hello everyone, I recently switched to julia from python and ran into a problem.
I solve a parameterized system:

Γ(x, λ, Θ) = 1 / (1 + exp(-λ*(x - Θ)))

function parametrized_2hr!(du, u, p, t)
    a = p[1]; b = p[2]; c = p[3]; d = p[4]; xr = p[5]; r = p[6]; s = p[7]; I = p[8]; vs = p[9]; λ = p[10]; Θ = p[11]; 
    k1 = p[12]; k2 = p[13]; k = p[14] 
    du[1] = u[2]+b*u[1]^2-a*u[1]^3-u[3]+I-k1*(u[1]-vs)*Γ(u[4], λ, Θ)+k*(u[4]-u[1])
    du[2] = c-d*u[1]^2-u[2]
    du[3] = r*(s*(u[1]-xr)-u[3])
    du[4] = u[5]+b*u[4]^2-a*u[4]^3-u[6]+I-k2*(u[4]-vs)Γ(u[1], λ, Θ)+k*(u[1]-u[4])
    du[5] = c-d*u[4]^2-u[5]
    du[6] = r*(s*(u[4]-xr)-u[6])
end

u0 = [-1.5, 0.0, 0.0, -1.5, 0.0, 0.0]
tspan = (0.0, 100.0)
p = [1.0, 3.0, 1.0, 5.0, -1.6, 0.01, 5.0, 4.0, 2.0, 10.0, -0.25, -0.17, -0.17, 0.0]
prob = ODEProblem(parametrized_2hr!,u0,tspan,p)
sol = solve(prob, reltol=1e-6)

I read this documentation but still don’t understand how can I get an array for each variable: t, u1, u2, u3, u4, u5, u6?

For example, I write:

sizeof(sol.t)

and I get 4776. But when I try to access the element:

sol.t[4775]

I get the error:

BoundsError: attempt to access 597-element Vector{Float64} at index [4775]

Can you please explain what I am doing wrong and how to process the output correctly? For example, if I need to take the variable u1 and discard the first few values, and then find the local maxima.

2

sizeof is the wrong function. You want length. (you can query the help with ?sizeof)

[uu[1] for uu in sol.u] should give you the u1 vector (there are probably better ways). Then findmax.

Have a look at Ordinary Differential Equations · DifferentialEquations.jl

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