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723b602 | 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 | import numpy as np
def gene_regulatory_rhs(alpha_val, K_val, b_val, g1_val, g2_val):
"""
Create the right-hand side function for the gene regulatory ODE system.
The system is:
dx/dt = (K * x^(1/alpha))/(b^(1/alpha) + x^(1/alpha)) - gamma1 * x
dy/dt = (K * y^(1/alpha))/(b^(1/alpha) + y^(1/alpha)) - gamma2 * y
"""
def rhs(t, state):
x, y = state
n = 1.0 / alpha_val
if n > 1000:
# Handle very large n (approaching infinity) case
frac_x = K_val if x > b_val else 0.0
frac_y = K_val if y > b_val else 0.0
else:
x_pos, y_pos = max(x, 0.0), max(y, 0.0)
try:
pow_b = np.power(b_val, n)
pow_x = np.power(x_pos, n)
pow_y = np.power(y_pos, n)
frac_x = (K_val * pow_x) / (pow_b + pow_x) if np.isfinite(pow_x) else (K_val if x > b_val else 0.0)
frac_y = (K_val * pow_y) / (pow_b + pow_y) if np.isfinite(pow_y) else (K_val if y > b_val else 0.0)
except Exception:
frac_x, frac_y = (K_val if x > b_val else 0.0), (K_val if y > b_val else 0.0)
return [frac_x - g1_val * x, frac_y - g2_val * y]
return rhs
def lotka_volterra_rhs(a, b, k, m):
"""
Create the right-hand side function for the Lotka-Volterra ODE system.
The system is:
dx/dt = x * (a - b * y)
dy/dt = y * (k * b * x - m)
"""
def rhs(t, state):
x, y = state
return [x * (a - b * y), y * (k * b * x - m)]
return rhs |