Change Language

dx_t/dt=rx_t{1-ax_t-y_t} , y_t=b∫_(0→t)x_sexp(-c(t-s))ds
⇔ dx_t/dt=rx_t{1-ax_t-y_t} , y_t/dt=-cy_t+x_t , y₀=0

The effects of intraspecific competition and waste products are taken into consideration in this model. y_t means the amount of waste at the time t.In this model, the newly created wastes have a stronger effect than the wastes created previously. In other word, there is the cleanup of wastes. This cleanup speed is parameterized as the value of c and the greater value means faster cleanup speed. The a value parameterizes the strength of intraspecific competition.