Lotka-Volterra Models: Partial Stability and Partial Ultimate Bounded-Ness

P. Fergola and C. Tenneriello
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P. Fergola: Università di Napoli, Dipartimento di Matematica e Applicazioni “R.Caccioppoli”
C. Tenneriello: Università di Napoli, Dipartimento di Matematica e Applicazioni “R.Caccioppoli”

A chapter in Biomathematics and Related Computational Problems, 1988, pp 283-294 from Springer

Abstract: Abstract Stability and boundedness properties for autonomous and non-autonomous Lotka-Volterra systems with respect to a part only of the state variables have been studied. In the autonomous case sufficient conditions for partial asymptotic stability in the large of partially feasible equilibria have been obtained. In the nonautonomous case, due to the general non equilibrium features, it is interesting to investigate attractivity properties of suitable compact sets in the species space. Such an analysis has been performed for some classes of nonautonomous Lotka-Volterra systems for which we proved results concerning with the partial ultimate boundedness. Some of these results can be viewed as persistence criteria for a part only of the actually present species. The used approach is based on the construction of Lyapunov-like functions whose structure together with the amplitude of the time fluctuations of the parameters influence the shape and the size of the attractivity compact regions.

Keywords: Partial Stability; Volterra Model; Boundedness Property; Coordinate Hyperplane; Feasible Equilibrium (search for similar items in EconPapers)
Date: 1988
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DOI: 10.1007/978-94-009-2975-3_26

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