Roughgarden's Model Of Agression Model
Roughgarden (1992) has considered a model to minimizing time that maximizes the energy per unit of time for all prey items. Moreover, the average waiting time of appearances of prey within the semicircle of radius r is
1/(∫_0^(r_c)▒aπrdr)
The average pursuit time is the product of integral from 0 to r and the probability that an insect pursuit at distance r times the, 2r/v, for the insect at distance r, namely
∫_0^(r_c)▒〖aπr/(∫_0^(r_c)▒aπrdr) 2r/v dr〗
The total average waiting time( w ) spent to captured per insect is the sum of the average pursuit time and the average waiting time to the appearance of insects, namely w= 1/(∫_0^(r_c)▒aπrdr)+∫_0^(r_c)▒〖aπr/(∫_0^(r_c)▒aπrdr)
1/(∫_0^(r_c)▒aπrdr)
The average pursuit time is the product of integral from 0 to r and the probability that an insect pursuit at distance r times the, 2r/v, for the insect at distance r, namely
∫_0^(r_c)▒〖aπr/(∫_0^(r_c)▒aπrdr) 2r/v dr〗
The total average waiting time( w ) spent to captured per insect is the sum of the average pursuit time and the average waiting time to the appearance of insects, namely w= 1/(∫_0^(r_c)▒aπrdr)+∫_0^(r_c)▒〖aπr/(∫_0^(r_c)▒aπrdr)