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

DOI10.1007/s00030-014-0307-9zbMath1327.34076OpenAlexW2000586915MaRDI QIDQ497408

Alfonso Ruiz-Herrera, Fabio Zanolin

Publication date: 24 September 2015

Published in: NoDEA. Nonlinear Differential Equations and Applications (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1007/s00030-014-0307-9

zbMATH Keywords

periodic solutionsswitching systemscomplex dynamicstopological horseshoesPoincaré's mapthree dimensional predator-prey equations

Mathematics Subject Classification ID

Periodic solutions to ordinary differential equations (34C25) Strange attractors, chaotic dynamics of systems with hyperbolic behavior (37D45) Fixed points and periodic points of dynamical systems; fixed-point index theory; local dynamics (37C25) Complex behavior and chaotic systems of ordinary differential equations (34C28) Nonautonomous smooth dynamical systems (37C60)

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Global stability and oscillations for mosquito population models with diapausing stages ⋮ Chaotic dynamics in three dimensions: a topological proof for a triopoly game model ⋮ Stable and unstable endemic solutions in the seasonally forced SIR epidemic model ⋮ A topological proof of chaos for two nonlinear heterogeneous triopoly game models ⋮ Paradoxical phenomena and chaotic dynamics in epidemic models subject to vaccination

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