Model of a Firefly Swarm
Model of a Firefly Swarm
Using techniques of swarm modeling, it is possible to make a somewhat unrealistic model of firefly behavior.
Concretely, the following differential equations that describe the velocity change of firefly in a swarm of fireflies are solved in a discrete time-step approximation.
i
n
m(t)=-γ(t)+a(t)+(t)exp-+b(t)-(t)-exp-+
′
v
i
v
i
v
i
n
∑
j,j≠i
v
j
(t)-(t)
r
i
r
j
r
a
n
∑
j,j≠i
r
i
r
j
(t)-(t)
r
i
r
j
α
r
b
(t)-(t)
r
i
r
j
β
r
b
(t)-(t)
r
i
r
j
(t)-(t)
r
i
r
j
r
b
ξ
i
For a swarm of fireflies, the parameters and are the interaction strengths, and are the correlation lengths, α and β are the interaction power laws, is the air resistance, and the random variable is interpreted as wind turbulence.
a
b
r
a
r
b
γ
ξ
i