WindmiReduced

Systems · Continuous · Physical systems

Reduced WINDMI model of the solar-wind–magnetosphere–ionosphere coupling.

Dimension: 3 · Reference: Horton, Weigel & Sprott (2001), Phys. Plasmas 8, 2946-2952

Equations

\[ \begin{aligned} \dot{i} &= a_{1} \left(- v + vsw\right) \\ \dot{v} &= b_{1} i - \frac{b_{2} p}{2} - b_{3} v \\ \dot{p} &= - \frac{vsw^{0.5} \left(1 - \tanh{\left(\frac{\left|{d_{1} \left(i - 1\right) - 25.0}\right|}{2} - \frac{\left|{d_{1} \left(i - 1\right) + 25.0}\right|}{2} \right)}\right) \left|{p}\right|^{1.25}}{2} + vsw^{2} \end{aligned} \]

Parameters

parameter	default
a1	0.247
b1	10.8
b2	0.0752
b3	1.06
d1	2200
vsw	5

Variables: i, v, p

Usage

import tsdynamics as ts

sys = ts.WindmiReduced()
traj = sys.integrate(final_time=100.0, dt=0.01)

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