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Using \ref{equation5}, we can write the differential equation for pollunator species explicitely as follows:  \begin{equation}  \frac{dA_i}{dt} = A_i ( K_a - A_i - \epsilon A_{i+1} - \epsilon A_{i-1} + \alpha^{AP}}{\lambda_i^q} \sum_{j<=i} P_j ) 1<=i<=5 \nonumber   \end{equation}