Robust interval stability, persistence, and partial stability of Lotka-Volterra systems with time-delay
Consider the Lotka-Volterra system \[ x_i'(t)=x_i(t) \biggl(r_i+ \sum^n_{j=1} (a_{ij}x_j(t)+b_{ij} x_j(t-\tau_j)) \biggr),\qquad i=1,\dots,n \] with uncertain (interval) parameters \(\underline{a}_{ij}\leq a_{ij}\leq \overline{a}_{ij}\), etc. Suppose that there is a unique positive equilibrium \(x^*=(x^*_1,\dots,x^*_n)^\top\), \(x^*_i>0\). Conditions are given for \(x^*\) to be globally stable for any choice of the system parameters from the corresponding invervals. Also, conditions are derived for positiveness of the solutions satisfying \(x_i(0)>0\).
scientific article; zbMATH DE number 892435
scientific article