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A survey on stably dissipative Lotka-Volterra systems with an application to infinite dimensional Volterra equations

Waldyr M. Oliva

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Abstract

For stably dissipative Lotka-Volterra equations the dynamics on the attractor are Hamiltonian and we argue that complex dynamics can occur. We also present examples and properties of some infinite dimensional Volterra systems with applications related with stably dissipative Lotka-Volterra equations. We finish by mentioning recent contributions on the subject.

Article information

Source
Publ. Mat., Volume EXTRA (2014), 421-452.

Dates
First available in Project Euclid: 19 May 2014

Permanent link to this document
https://projecteuclid.org/euclid.pm/1400505243

Mathematical Reviews number (MathSciNet)
MR3211844

Zentralblatt MATH identifier
1312.34087

Subjects
Primary: 34C25: Periodic solutions 34K15

Keywords
Lotka-Volterra stably dissipative systems conservative systems Poisson manifolds reducible systems

Citation

Oliva, Waldyr M. A survey on stably dissipative Lotka-Volterra systems with an application to infinite dimensional Volterra equations. Publ. Mat. EXTRA (2014), 421--452. https://projecteuclid.org/euclid.pm/1400505243


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