Vicsek Lab: Predator Avoidance

Module 2: Synchronization and Collective Behaviour

Optional extension

This page is optional. It combines the Vicsek model with the repulsion rule of the Couzin model.

In the Couzin model, avoidance takes absolute priority: if an individual senses another within its zone of repulsion, it turns away and ignores alignment and attraction (Couzin et al. 2002). You can implement a similar rule in the Vicsek model to simulate predator avoidance (Vicsek et al. 1995). The predator can be a fixed point, a random walker, or even the mouse cursor. In all cases, if a boid senses the predator within a certain radius, it will turn directly away from it.

Below is a guide on how to implement this in your Vicsek animation. You can choose to implement one or more types of predators (static, random walk, mouse-following) and compare their effects on the collective behavior of the particles.

Static Predator

The simplest case is a predator fixed at a given position. To implement this:

Set the predator’s position (e.g., xy_pred = np.array([L/2, L/2]) for the center).
In your Vicsek update function, check for boids within the predator radius and set their direction directly away from the predator (as in the Couzin rule).
In your animation, draw the predator as a red circle.

Where to add: - Set xy_pred before the animation loop in your main script. - Pass xy_pred to your Vicsek update at each frame. - Draw the predator in the plotting section (after initializing the axes).

Where to include the code

Set xy_pred before the animation loop: In run_simulation, set xy_pred = np.array([box_size/2, box_size/2]) (or wherever you want the static predator) before entering the animation.
Pass xy_pred to the Vicsek update: In the update_animation function, pass xy_pred as an argument to vicsek_equations.
Draw the predator: After initializing the axes in run_simulation, add the predator circle with circle_predator = plt.Circle(xy_pred, radius_predator, color="red", fill=False) and ax_plane.add_artist(circle_predator).
Update the predator’s position in the plot (if needed): For a static predator, this is only needed once. For moving predators, update circle_predator.set_center(xy_pred) in each animation frame.

Random Walk Predator

To make the predator more dynamic, let it perform a random walk:

At each animation frame, update xy_pred by adding a small random displacement (e.g., xy_pred += np.random.normal(0, step_size, 2)).
Apply periodic boundary conditions to keep the predator in the box.
The avoidance rule for boids remains unchanged.

Where to add: - In your animation update function, before updating the boids, update xy_pred with a random walk step. - Pass the new xy_pred to the Vicsek update. - Update the predator’s position in the plot.

Mouse-Following Predator

For an interactive experience, let the predator follow the mouse:

Use a mouse event callback to update xy_pred to the mouse position whenever the mouse moves over the plot.
The avoidance rule for boids is the same: those within the predator radius turn directly away.

Where to add:

Register a mouse motion callback (e.g., with fig.canvas.mpl_connect('motion_notify_event', on_mouse_move)).
In the callback, update xy_pred to the mouse coordinates if the mouse is over the main plot.
The animation update function will use the current xy_pred as usual.

Integration

In all cases, the predator logic is integrated as follows:

The predator’s position (xy_pred) is set or updated before each Vicsek update.
The Vicsek update function receives xy_pred and applies the Couzin avoidance rule.
The predator is drawn as a red circle in the main plot.
For the mouse-following version, the mouse callback is registered during figure setup.

This modular approach allows you to experiment with different predator behaviors by simply changing how xy_pred is updated, while keeping the avoidance rule and animation structure consistent.

Practice

Option B of Practice: Collective Motion asks you to implement this model in a script named vicsek_predator.py. A reference version is in amlab/collective_motion/vicsek_predator.py.

References

Couzin, Iain D, Jens Krause, Richard James, Graeme D Ruxton, and Nigel R Franks. 2002. “Collective Memory and Spatial Sorting in Animal Groups.” Journal of Theoretical Biology 218 (1): 1–11.

Vicsek, Tamás, András Czirók, Eshel Ben-Jacob, Inon Cohen, and Ofer Shochet. 1995. “Novel Type of Phase Transition in a System of Self-Driven Particles.” Physical Review Letters 75 (6): 1226.

--- title: "Vicsek Lab: Predator Avoidance" subtitle: "Module 2: Synchronization and Collective Behaviour" format: html --- ::: {.callout-tip} ## Optional extension This page is optional. It combines the Vicsek model with the repulsion rule of the Couzin model. ::: In the Couzin model, avoidance takes absolute priority: if an individual senses another within its zone of repulsion, it turns away and ignores alignment and attraction [@couzin2002collective]. You can implement a similar rule in the Vicsek model to simulate predator avoidance [@vicsek1995novel]. The predator can be a fixed point, a random walker, or even the mouse cursor. In all cases, if a boid senses the predator within a certain radius, it will turn directly away from it. Below is a guide on how to implement this in your Vicsek animation. You can choose to implement one or more types of predators (static, random walk, mouse-following) and compare their effects on the collective behavior of the particles. --- ## Static Predator The simplest case is a predator fixed at a given position. To implement this: - Set the predator's position (e.g., `xy_pred = np.array([L/2, L/2])` for the center). - In your Vicsek update function, check for boids within the predator radius and set their direction directly away from the predator (as in the Couzin rule). - In your animation, draw the predator as a red circle. **Where to add:** - Set `xy_pred` before the animation loop in your main script. - Pass `xy_pred` to your Vicsek update at each frame. - Draw the predator in the plotting section (after initializing the axes). ::: {.callout-tip collapse="true"} ## Where to include the code - **Set `xy_pred` before the animation loop**: In `run_simulation`, set `xy_pred = np.array([box_size/2, box_size/2])` (or wherever you want the static predator) before entering the animation. - **Pass `xy_pred` to the Vicsek update**: In the `update_animation` function, pass `xy_pred` as an argument to `vicsek_equations`. - **Draw the predator**: After initializing the axes in `run_simulation`, add the predator circle with `circle_predator = plt.Circle(xy_pred, radius_predator, color="red", fill=False)` and `ax_plane.add_artist(circle_predator)`. - **Update the predator's position in the plot (if needed)**: For a static predator, this is only needed once. For moving predators, update `circle_predator.set_center(xy_pred)` in each animation frame. ::: --- ## Random Walk Predator To make the predator more dynamic, let it perform a random walk: - At each animation frame, update `xy_pred` by adding a small random displacement (e.g., `xy_pred += np.random.normal(0, step_size, 2)`). - Apply periodic boundary conditions to keep the predator in the box. - The avoidance rule for boids remains unchanged. **Where to add:** - In your animation update function, before updating the boids, update `xy_pred` with a random walk step. - Pass the new `xy_pred` to the Vicsek update. - Update the predator's position in the plot. --- ## Mouse-Following Predator For an interactive experience, let the predator follow the mouse: - Use a mouse event callback to update `xy_pred` to the mouse position whenever the mouse moves over the plot. - The avoidance rule for boids is the same: those within the predator radius turn directly away. **Where to add:** - Register a mouse motion callback (e.g., with `fig.canvas.mpl_connect('motion_notify_event', on_mouse_move)`). - In the callback, update `xy_pred` to the mouse coordinates if the mouse is over the main plot. - The animation update function will use the current `xy_pred` as usual. --- ## Integration In all cases, the predator logic is integrated as follows: - The predator's position (`xy_pred`) is set or updated before each Vicsek update. - The Vicsek update function receives `xy_pred` and applies the Couzin avoidance rule. - The predator is drawn as a red circle in the main plot. - For the mouse-following version, the mouse callback is registered during figure setup. This modular approach allows you to experiment with different predator behaviors by simply changing how `xy_pred` is updated, while keeping the avoidance rule and animation structure consistent. --- ## Practice Option B of [Practice: Collective Motion](practice-collective-motion.qmd) asks you to implement this model in a script named `vicsek_predator.py`. A reference version is in [amlab/collective_motion/vicsek_predator.py](../../amlab/collective_motion/vicsek_predator.py).