Nonlinear oscillations in a discrete diffusive neutral logistic equation (Q1362547)

The neutral differential system \[ \begin{aligned}{dN_i(t)\over dt}=&rN_i(t)\Biggl[1- {N_i(t-\tau)+ cN_i'(t-\tau)\over k}\Biggr]-\&rd_1N_i(t)\Biggl[{N_{i+1}(t- \sigma)-2N_i(t-\sigma)+ N_{i-1}(t-\sigma)\over k}\Biggr]+\\+& d_2(N_{i+1}(t)- 2N_i(t)+ N_{i-1}(t)),\qquad 1\leq i\leq n\end{aligned}\tag{1} \] is considered, where \(N_{n+1}(t)= N_1(t)\), \(N_0(t)= N_n(t)\), \(k>0\), \(\tau\), \(\sigma\geq 0\), \(c\), \(r\), \(d_1\), \(d_2\in\mathbb{R}\). The problem of stability and asymptotic stability of the solution \((k,\dots,k)\) of the system (1) is studied.