Horseshoes in 3D equations with applications to Lotka–Volterra systems

  • Alfonso Ruiz-Herrera
  • Fabio ZanolinEmail author


We discuss a geometric configuration for a class of homeomorphisms in \({\mathbb{R}^3}\) producing the existence of infinitely many periodic points as well a complex dynamics due to the presence of a topological horseshoe. We also show that such a class of homeomorphisms appears in the classical Lotka–Volterra system.

Mathematics Subject Classification

Primary 34C25 Secondary 37C25 37D45 


Complex dynamics Poincaré’s map Topological horseshoes Periodic solutions Three dimensional predator–prey equations Switching systems 


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Authors and Affiliations

  1. 1.Departamento de Matemática Aplicada IIUniversidade de VigoVigoSpain
  2. 2.Department of Mathematics and Computer ScienceUniversity of UdineUdineItaly

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