Blasius

Systems · Continuous · Physical systems

Three-level food chain with Holling type-II functional responses.

Dimension: 3 · Reference: Blasius, Huppert & Stone (1999), Nature 399, 354-359

Equations

\[ \begin{aligned} \dot{y_{0}} &= a y_{0} - \frac{\alpha_{1} y_{0} y_{1}}{k_{1} y_{0} + 1} \\ \dot{y_{1}} &= \frac{\alpha_{1} y_{0} y_{1}}{k_{1} y_{0} + 1} - \frac{\alpha_{2} y_{1} y_{2}}{k_{2} y_{1} + 1} - b y_{1} \\ \dot{y_{2}} &= \frac{\alpha_{2} y_{1} y_{2}}{k_{2} y_{1} + 1} - c \left(y_{2} - zs\right) \end{aligned} \]

Parameters

parameter	default
a	1
alpha1	0.2
alpha2	1
b	1
c	10
k1	0.05
k2	0
zs	0.006

Usage

import tsdynamics as ts

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

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