RateSystem

src/RateSys.jl

@@ -0,0 +1,53 @@
+#  |                    |                        |                  |
+# t_i    autonomous    t_ni   non-autonomous   t_nf   autonomous   t_f
+#  |                    |                        |                  |
+
+using DynamicalSystems
+using Plots
+
+# we write
+
+function RateSyst(tni,tnf,f,λ,p_λ,initvals)
+    func(u,p,t) = combined_system(u,t,tni,tnf,f,λ,p_λ);
+    return ContinuousDynamicalSystem(func, initvals, Float64[], t0=tni)
+end
+
+function combined_system(u,t,tni,tnf,f,λ,p_λ)
+    lambda = t < tni ? λ(u,p_λ,tni) : tni <= t <= tnf ? λ(u,p_λ,t) : λ(u,p_λ,tnf)
+    return f(u,lambda,t)
+end;
+
+
+###############
+# user writes
+
+function f(u::SVector{1, Float64},p::SVector{1, Float64},t::Float64)
+    x = u[1]
+    λ = p[1]
+    dx = (x+λ)^2 - 1
+    return SVector{1}(dx)
+end;
+
+function λ(p::Vector{Float64},t::Float64)
+    r,λ_max = p
+    lambda = (λ_max/2)*(tanh(λ_max*r*t/2) +1)
+    return SVector{1}(lambda)
+end;
+
+tni=-10.; tnf=10.; p_λ = [1.0,3.0]; initvals = [-4.];
+sys = RateSyst(tni,tnf,f,λ,p_λ,initvals)
+
+traj=trajectory(sys,40.,t0=-20.)
+
+trajic=[traj[1][i][1] for i in 1:length(traj[1])]
+plot(collect(traj[2]),trajic)
+
+
+# further ideas
+# function futureSyst(RateSyst)
+# Canard Trajectories
+
+# \dot(x) = f(x(t),λ(t))
+
+
+