CoevolvingPredatorPrey

Systems · Continuous · Population dynamics

Dimension: 3

Equations

\[ \begin{aligned} \dot{y_{0}} &= y_{0} \left(\frac{a_{1} y_{2} \left(- k_{1} y_{0} \left(\delta y_{2} - y_{2}\right) + 1\right)}{b_{1} y_{2} + 1} - \frac{a_{3} y_{1}}{b_{2} y_{0} + 1} - d_{1} \left(- k_{2} \left(\delta^{2} y_{2}^{2} - y_{2}^{2}\right) + k_{4} \left(\delta^{4} y_{2}^{4} - y_{2}^{4}\right) + 1\right)\right) \\ \dot{y_{1}} &= y_{1} \left(\frac{a_{2} y_{0}}{b_{2} y_{0} + 1} - d_{2}\right) \\ \dot{y_{2}} &= vv \left(- \frac{a_{1} \delta k_{1} y_{0} y_{2}}{b_{1} y_{2} + 1} - d_{1} \left(4 \delta^{4} k_{4} y_{2}^{3} - 2 \delta^{2} k_{2} y_{2}\right)\right) \end{aligned} \]

Parameters

parameter	default
a1	2.5
a2	0.05
a3	0.4
b1	6.0
b2	1.333
d1	0.16
d2	0.004
delta	1
k1	6.0
k2	9.0
k4	9.0
vv	0.33333

Usage

import tsdynamics as ts

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

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