Augmented FCM for an undersea virtual world

The model combines fish school, shark, and dolphin herd FCMs:

F = F_dolphin + F_shark + F_fish

The actors interact through linked common causal concepts (the larger eats the smaller). The binary output states of this FCM move the actors.

Update equation for position

p(t_n+1) = p(t_n)+Δtv(t_n)

The velocity v(f) does not change at time step At. The FCM finds the direction and magnitude of movement. If the FCM state is “run away” then the velocity is FAST, if “rest” - the velocity is SLOW.

Position updates

The prey choose the direction that maximizes the distance from the predator which chases the prey. When a predator searches for food it swims at random. The augmented FCM encodes limit cycles between the actors.

Example - what happens when the shark is hungry?

Vector representing a hungry shark gives 7-step limit cycle after four transition steps:

1. shark searches for food,

2. finds some fish,

3. chases the fish,

4. eats some of the fish,

5. most fish run away and regroup as school

6. fish rest and eat while the shard rests

7. the shark gets hungry again and searches for fish

Simple FCM:

This rule does not model the effects of different threats.

Nested (or embedded) FCM:

The small survival threat may be a slow-moving predator that has not seen or decided to attack the fish. The large survival threat may be a fast predator such as a barracuda or shark that swims toward the center of the school.

Can the actors learn?

• A static world was modelled so far.

• The actors may change the way they act.

• To implement this feature the FCM have to be adaptive, so that they can learn – changing their causal web in time.

Modelling of schooling behaviour

• The size of the threat is a function of the size, speed, and attack angle of the predator.

• A small threat leads to avoidance behavior.

• Maximize the distance from the predator:

• A large threat causes the fish to evade the predator. The fish try to maximize the minimum distance from the predator