Positive periodic solution for a neutral delay competitive system
The author considers the neutral delay multispecies ecological competitive system \[ \dot N_i(t)= N_i(t) \left[ r_i(t)- \sum_{j=1}^n a_{ij}(t) N_j(t)- \sum_{j=1}^n b_{ij}(t) N_j(t-\tau_{ij}(t))- \sum_{j=1}^n c_{ij} \dot N_j (t-\sigma_{ij}) \right], \tag{1} \] with initial conditions \[ \dot N_i(s)= \varphi_i(s)\geq 0, \qquad s\in [-\tau,0], \quad \varphi_i(0)> 0, \] \[ \varphi_i\in C([-\tau,0], [0,+\infty))\cap C^1([-\tau,0], [0,+\infty)), \quad i=1,\dots, n, \] where \(a_{ij}, b_{ij}\in C(\mathbb{R},(0,+\infty))\), \(r_i, \tau_{ij}\in C(\mathbb{R},\mathbb{R})\) are \(\omega\)-periodic functions and \(c_{ij}\), \(\sigma_{ij}\) are constants, \(c_{ij}\) are nonnegative. The goal of the author is to derive a set of easily verifiable sufficient conditions for the existence of periodic solutions of (1).
scientific article; zbMATH DE number 2082136
scientific article