Aggregation Model Simulator

Monte Carlo simulation of collective aggregation behavior

Mathematical Model

The aggregation model describes the dynamics of individuals joining and leaving a shelter:

$$\frac{dX}{dt} = \mu (N-X) - \frac{\theta X}{1+(X/k)^m}$$
Parameters:
X: Number of sheltered individuals
N: Total population
μ: Joining rate
θ: Leaving rate
k: Threshold parameter
m: Cooperativity parameter

Model Parameters

Total number of individuals
Rate of entering the shelter
Rate of leaving the shelter
Critical threshold parameter
Cooperativity exponent

Simulation Settings

Total simulation duration
Number of simulation runs

Time Series Plot

Run simulation to view results