Module for the Follow-the-Leader model¶
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cromosim.ftl.plot_people(L, X, t, data, tgrid, periodicity=True, V_leader=None, speed_fct=None, savefig=False, filename='fig.png', ifig=100, spheresize=300)[source]¶ To plot people and their individual paths
- Parameters
- L: float
width of the domain
- X: numpy array
positions of the individuals
- data: numpy array
coordinates of indviduals at each time
- tgrid: numpy array
temporal discretization
- periodicity: boolean
if true the domain is periodic
- V_leader: function
leader velocity as a function of the time
- speed_fct: function
speed as a function of the distance
- savefig: boolean
writes the figure as a png file if true
- filename: string
png filename used to write the figure
- ifig: int
figure number
- spheresize: int
size of the spheres used to represent the individuals
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cromosim.ftl.update_positions_ftl_order_1(L, X, t, dt, Phi, periodicity=True, V_leader=None)[source]¶ To update the positions according to the follow the leader model (order 1)
- Parameters
- L: float
width of the domain
- X: numpy array
coordinates of the individuals
- t: float
time
- dt: float
time step
- Phi: function
speed as a function of the distance
- periodicity: boolean
if true the domain is periodic
- V_leader: function
leader velocity as a function of the time
- Returns
- Xnew: numpy array
new coordinates of the individuals
- V: numpy array
new velocities of the individuals
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cromosim.ftl.update_positions_ftl_order_2(L, X, U, t, dt, tau, Phi, periodicity=True, V_leader=None)[source]¶ To update the positions according to the follow the leader model (order 2)
- Parameters
- L: float
width of the domain
- X: numpy array
coordinates of the individuals
- U: numpy array
velocities of the individuals
- t: float
time
- dt: float
time step
- tau: float
the actual velocity of an individual relaxes toward the velocity that is associated to the current distance from the person in front of them with a characteristic time tau
- Phi: function
speed as a function of the distance
- periodicity: boolean
if true the domain is periodic
- V_leader: function
leader velocity as a function of the time
- Returns
- Xnew: numpy array
new coordinates of the individuals
- Unew: numpy array
new velocities of the individuals