Differential and Integral Equations

Uniform asymptotic stability of a discontinuous predator-prey model under control via non-autonomous systems theory

E.M. Bonotto, J. Costa Ferreira, and M. Federson

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Abstract

The present paper deals with uniform stability for non-autonomous impulsive systems. We consider a non-autonomous system with impulses in its abstract form and we present conditions to obtain uniform stability, uniform asymptotic stability and global uniform asymptotic stability using Lyapunov functions. Using the results from the abstract theory we present sufficient conditions for a controlled predator-prey model under impulse conditions to be globally uniformly asymptotically stable.

Article information

Source
Differential Integral Equations, Volume 31, Number 7/8 (2018), 519-546.

Dates
First available in Project Euclid: 11 May 2018

Permanent link to this document
https://projecteuclid.org/euclid.die/1526004029

Mathematical Reviews number (MathSciNet)
MR3801823

Zentralblatt MATH identifier
06890403

Subjects
Primary: 34A37: Differential equations with impulses 34A34: Nonlinear equations and systems, general 34D05: Asymptotic properties 92B05: General biology and biomathematics 93C15: Systems governed by ordinary differential equations [See also 34H05]

Citation

Bonotto, E.M.; Costa Ferreira, J.; Federson, M. Uniform asymptotic stability of a discontinuous predator-prey model under control via non-autonomous systems theory. Differential Integral Equations 31 (2018), no. 7/8, 519--546. https://projecteuclid.org/euclid.die/1526004029


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