Variations on Lyapunov's stability criterion and periodic prey-predator systems

Rafael Ortega; Rafael Ortega

doi:10.3934/era.2021069

Electronic Research Archive

2021, Volume 29, Issue 6: 3995-4008. doi: 10.3934/era.2021069

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Variations on Lyapunov's stability criterion and periodic prey-predator systems

Rafael Ortega

Departamento de Matemática Aplicada, Facultad de Ciencias, Universidad de Granada, 18071 Granada, Spain

Received: 01 June 2021 Published: 07 September 2021
Primary: 34D20, 92D25; Secondary: 34C25

A classical stability criterion for Hill's equation is extended to more general families of periodic two-dimensional linear systems. The results are motivated by the study of mechanical vibrations with friction and periodic prey-predator systems.
- Lyapunov stability,
- asymptotic stability,
- prey-predator,
- coexistence state,
- Turing instability
Citation: Rafael Ortega. Variations on Lyapunov's stability criterion and periodic prey-predator systems[J]. Electronic Research Archive, 2021, 29(6): 3995-4008. doi: 10.3934/era.2021069

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Abstract

A classical stability criterion for Hill's equation is extended to more general families of periodic two-dimensional linear systems. The results are motivated by the study of mechanical vibrations with friction and periodic prey-predator systems.

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