Binary Choice Simulator

Monte Carlo simulation of collective decision-making between two options

The binary choice model describes the dynamics of individuals choosing between two alternatives:

$$\frac{dX_i}{dt} = \mu_i \left(N-\sum_{j=1}^2 X_j\right) - \frac{\theta_i X_i}{1+(X_i/k)^m} \quad i = 1, 2$$

This system models competitive dynamics where individuals can switch between two shelters or remain uncommitted.

X_i: Individuals in shelter i

N: Total population

μ_i: Joining rate for shelter i

θ_i: Leaving rate for shelter i

k: Threshold parameter

m: Cooperativity parameter

Population Size (N)

Total number of individuals

Joining Rate (μ₁)

Leaving Rate (θ₁)

Joining Rate (μ₂)

Leaving Rate (θ₂)

Threshold (k)

Critical threshold parameter

Cooperativity (m)

Cooperativity exponent

Simulation Time

Total simulation duration

Realizations

Number of simulation runs

Run simulation to view results