@@ -700,7 +700,7 @@ function magnetic_pendulum(u = [sincos(0.12553*2π)..., 0, 0];
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γ = 1.0 , d = 0.3 , α = 0.2 , ω = 0.5 , N = 3 , γs = fill (γ, N))
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m = MagneticPendulum ([SVector (cos (2 π* i/ N), sin (2 π* i/ N)) for i in 1 : N])
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p = MagneticPendulumParams (γs, d, α, ω)
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- return ContinuousDynamicalSystem (m, u, p)
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+ return CoupledODEs (m, u, p)
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end
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"""
@@ -716,7 +716,7 @@ Famous excitable system which emulates the firing of a neuron, with rule
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More details in the [Scholarpedia](http://www.scholarpedia.org/article/FitzHugh-Nagumo_model) entry.
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"""
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function fitzhugh_nagumo (u = 0.5 ones (2 ); a= 3.0 , b= 0.2 , ε= 0.01 , I= 0.0 )
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- ds = ContinuousDynamicalSystem (fitzhugh_nagumo_rule, u, [a, b, ε, I])
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+ ds = CoupledODEs (fitzhugh_nagumo_rule, u, [a, b, ε, I])
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end
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function fitzhugh_nagumo_rule (x, p, t)
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u, w = x
@@ -741,7 +741,7 @@ It is noteworthy because its strange attractor is multifractal with fractal dime
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Chaos Theory and Applications 2(2),1-3, 2020
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"""
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more_chaos_example (u = [0.0246 , 0.79752 , 0.3535866 ]) =
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- ContinuousDynamicalSystem (more_chaos_rule, u, nothing )
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+ CoupledODEs (more_chaos_rule, u, nothing )
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function more_chaos_rule (u, p, t)
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x, y, z = u
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dx = y
@@ -772,8 +772,8 @@ See discussion in Section 4.4.3 of "Elegant Chaos" by J. C. Sprott.
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Thomas, R. (1999). *International Journal of Bifurcation and Chaos*,
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*9*(10), 1889-1905.
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"""
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- thomas_cyclical (u0 = [1.0 , 0 , 0 ]; b = 0.2 ) = ContinuousDynamicalSystem (thomas_rule, u0, [b])
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- labyrinth (u0 = [1.0 , 0 , 0 ]) = ContinuousDynamicalSystem (thomas_rule, u0, [0.0 ])
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+ thomas_cyclical (u0 = [1.0 , 0 , 0 ]; b = 0.2 ) = CoupledODEs (thomas_rule, u0, [b])
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+ labyrinth (u0 = [1.0 , 0 , 0 ]) = CoupledODEs (thomas_rule, u0, [0.0 ])
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function thomas_rule (u, p, t)
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x,y,z = u
@@ -805,7 +805,7 @@ between the boxes (polar and equatorial ocean basins) and ``\\eta_i`` are parame
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Stommel, Thermohaline convection with two stable regimes of flow. Tellus, 13(2)
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"""
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function stommel_thermohaline (u = [0.3 , 0.2 ]; η1 = 3.0 , η2 = 1 , η3 = 0.3 )
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- ds = ContinuousDynamicalSystem (stommel_thermohaline_rule, u, [η1, η2, η3],
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+ ds = CoupledODEs (stommel_thermohaline_rule, u, [η1, η2, η3],
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stommel_thermohaline_jacob)
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end
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function stommel_thermohaline_rule (x, p, t)
@@ -854,7 +854,7 @@ bsn, att = basins_of_attraction((xg, yg, zg), ds; mx_chk_att=4)
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Lorenz-84 low-order atmospheric circulation model, Chaos 18, 033121 (2008)
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"""
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function lorenz84 (u = [0.1 , 0.1 , 0.1 ]; F= 6.846 , G= 1.287 , a= 0.25 , b= 4.0 )
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- return ContinuousDynamicalSystem (lorenz84_rule, u, [F, G, a, b])
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+ return CoupledODEs (lorenz84_rule, u, [F, G, a, b])
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end
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@inline @inbounds function lorenz84_rule (u, p, t)
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F, G, a, b = p
@@ -901,7 +901,7 @@ bsn, att = basins_of_attraction((xg, yg), pmap)
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Int. Jour. Bifurcation and Chaos 24, 1450009 (2014)
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"""
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function lorenzdl (u = [0.1 , 0.1 , 0.1 ]; R= 4.7 )
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- return ContinuousDynamicalSystem (lorenzdl_rule, u, R,
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+ return CoupledODEs (lorenzdl_rule, u, R,
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lorenzdl_rule_jacob)
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end
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@inline @inbounds function lorenzdl_rule (u, p, t)
@@ -941,7 +941,7 @@ The equations are:
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function coupled_roessler (u0= [1 , - 2 , 0 , 0.11 , 0.2 , 0.1 ];
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ω1 = 0.18 , ω2 = 0.22 , a = 0.2 , b = 0.2 , c = 5.7 , k1 = 0.115 , k2 = 0.0 )
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p = [ω1, ω2, a, b, c, k1, k2]
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- return ContinuousDynamicalSystem (coupled_roessler_f, u0, p)
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+ return CoupledODEs (coupled_roessler_f, u0, p)
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end
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function coupled_roessler_f (u,p,t)
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ω1, ω2, a, b, c, k1, k2 = p
@@ -973,7 +973,7 @@ function kuramoto(D = 25, u0 = range(0, 2π; length = D);
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K = 0.3 , ω = range (- 1 , 1 ; length = D))
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p = KuramotoParams (K, ω)
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@warn " The kuramoto implementation does NOT have a Jacobian function!"
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- return ContinuousDynamicalSystem (kuramoto_f, u0, p, (J,z0, p, n) -> nothing )
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+ return CoupledODEs (kuramoto_f, u0, p)
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end
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using Statistics: mean
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function kuramoto_f (du, u, p, t)
@@ -1671,7 +1671,7 @@ function multispecies_competition(option = 1)
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p = CompetitionDynamicsParameters (option)
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N = size (p. Ks, 2 )
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u0 = [[0.1 for i= 1 : N]; [S for S in p. Ss]]
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- ds = ContinuousDynamicalSystem (multispecies_competition_rule!, u0, p, (J, x, p, t) -> nothing )
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+ ds = CoupledODEs (multispecies_competition_rule!, u0, p)
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return ds
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end
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