SwarmOscillators.jl

#Swarm Oscillators
#三浦岳、発生の数理、京都大学学術出版会、2015、あとがき
#Julia v1.0

using LinearAlgebra
using Plots
gr(size=(340,300),titlefont=font("sans-serif",9))

const n=50
const L=25
const c1=1.5
const c2=0.5
const c3=2.0
const α=0.5
const dt=0.05

#psi=zeros(n)
#pos=zeros(n,2)

function dψ(ψ,r)
    a=zeros(n)
    for i=1:n
        sum=0
        for j=1:n
            if j==i; continue;end
            sum+=exp(-norm(r[j,:]-r[i,:]))*sin(ψ[j]-ψ[i]+α*norm(r[j,:]-r[i,:])-c1)
        end
        a[i]=sum
    end
    return a
end

function dr(ψ,r)
    a=zeros(n,2)
    for i=1:n
        sum=[0,0]
        for j=1:n
            if j==i; continue; end
            sum+=(normalize(r[j,:]-r[i,:]).*exp(-norm(r[j,:]-r[i,:]))*sin(ψ[j]-ψ[i]+α*norm(r[j,:]-r[i,:])-c2))
        end
        a[i,:]=sum
    end
    return c3*a
end

function init(ψ,r)
    ψ=rand(0:0.01:2π, n)
    r=rand(0:0.01:L,n,2)
    return ψ,r
end
    

function oneStep!(ψ,r)
    ψ.=mod.(ψ+dψ(ψ,r)*dt,2π)
    r.=mod.(r+dr(ψ,r)*dt,L)
    #return ψ,r
end

function draw(gen,ψ,r)
    t=round(gen*dt;digits=2)
    scatter(r[:,1],r[:,2],
        xlab="x",xlims=(0,L),
        ylab="y",ylims=(0,L),
        zcolor=ψ,
        leg=false,
        cbar=true,
        cbarlims=(0,2π),
        title="t = $t, (gen = $gen),\n c=[$c1,$c2,$c3],alpha=$α")
end

psi=rand(0:0.01:2π, n)
pos=rand(0:0.01:L,n,2)

@time anim = @animate for m in 0:5000
    oneStep!(psi,pos)
    draw(m,psi,pos)
end every 100

@time gif(anim,"tmp/swarm_osillators.gif",fps=4)