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Global asymptotic stability in a nonautonomous Lotka-Volterra type system with infinite delay. (English) Zbl 0880.34072
Sufficient conditions for the global asymptotic stability of the solutions of the following Lotka--Volterra type system with infinite delay is established: $$ \multline \dot x_i(t)=b_i(x_i(t)) \Biggl[r_i(t)-a_i(t)x_i(t)+ \sum_{j=1}^n\sum_{l=1}^{l_{ij}}b_{ijl}(t)x_j (t-\tau_{ijl}(t)\\ +\sum_{j=1}^n\int_0^\infty b_{ij}(t,s)x_j(t-s) ds\Biggr],\qquad (i=1,2,\ldots,n).\endmultline$${}.

34K20Stability theory of functional-differential equations
Full Text: DOI
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