Model of a Firefly Swarm

trial number

1

modeling parameters:

total flight time

100

time unit size

-1.07

swarm parameters:

number of fireflies

12

swarm evolution parameters:

interaction strength 1

0.66

interaction strength 2

0.34

interaction power law 1

2

interaction power law 2

-2.18

correlation length 1

1.92

correlation length 2

0.82

air resistance

5.48

wind turbulence

2.72

fly path visualization

paths as tubes

tube thickness

-1

firefly light

on/off

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

i

in a swarm of

n

fireflies are solved in a discrete time-step approximation.

m

′

v

i

(t)=-γ

v

i

(t)+a

v

i

(t)+

n

∑

j,j≠i

v

j

(t)exp-



r

i

(t)-

r

j

(t)

r

a

+b

n

∑

j,j≠i

r

i

(t)-

r

j

(t)



r

i

(t)-

r

j

(t)

α

r

b



r

i

(t)-

r

j

(t)

-

β

r

b



r

i

(t)-

r

j

(t)

exp-



r

i

(t)-

r

j

(t)

r

b

+

ξ

i

For a swarm of fireflies, the parameters

a

and

b

are the interaction strengths,

r

a

and

r

b

are the correlation lengths, α and β are the interaction power laws,

γ

is the air resistance, and the random variable

ξ

i

is interpreted as wind turbulence.