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Global attractivity of non-autonomous Lotka-Volterra competition system without instantaneous negative feedback. (English) Zbl 1035.34085

The authors consider the following nonautonomous \(n\)-species Lotka-Volterra competition system with delays \[ dx_i(t)/dt=r_i(t)x_i(t)\left[1-\int_{-\tau_{ii}}^0x_i(t+s)d\nu_{ii}(s)- \sum_{j\neq i}\mu_{ij}\int_{-\tau_{ij}}^0 x_j(t+s)\,d\nu_{ij}(s)\right],\;i=1,2,\dots, n, \] with the initial conditions \[ x_i(t)=\phi_i(t), \quad t\in[-\tau, 0],\quad \phi_i(0)>0, \quad i=1,2,\dots,n, \] with \(\tau=\max\{\tau_{ij}: i,j=1,2,\dots,n\}\). They establish some 3/2-type and \(M\)-matrix-type criteria for the global attractivity of the positive equilibrium of this system.

MSC:

34K20 Stability theory of functional-differential equations
93D25 Input-output approaches in control theory
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