My questions concerns the stability analysis of the following dynamical system :


$\dfrac{d}{dt} a_{i}(t) = D_{i} + \displaystyle{\sum_{j=1}^{n}L_{ij}a_{j}(t) + \sum_{j=1}^{n}\sum_{k=1}^{n} C_{ijk} a_{j}(t)a_{k}(t)}$

defined for the state variables $[a_1,a_2,...,a_n]^{T}$ with the real numbers
$D_i, L_{ij}, C_{ijk}$ for $i,j,k=1,...,n.$ The coefficients $C_{ijk}$ are assumed to be symmetric in $j$ and $k$ : $C_{ijk}=C_{ikj}$

What are the conditions for the asymptotically stability of this system ?


Thank you.