Food chain chaos due to Shilnikov’s orbit
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Publication:5706310
DOI10.1063/1.1482255zbMath1080.92518OpenAlexW2028920876WikidataQ73463339 ScholiaQ73463339MaRDI QIDQ5706310
Publication date: 7 November 2005
Published in: Chaos: An Interdisciplinary Journal of Nonlinear Science (Search for Journal in Brave)
Full work available at URL: https://semanticscholar.org/paper/c3b2b1d0441f37500ce8ed32531dc4df1b1a0f14
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Cites Work
- On Shilnikov's homoclinic-saddle-focus theorem
- Persistent unstable equilibria and closed orbits of a singularly perturbed equation
- Singular perturbation of relaxed periodic orbits
- Singular homoclinic bifurcations in tritrophic food chains
- Glucose-induced period-doubling cascade in the electrical activity of pancreatic \(\beta\)-cells
- Quantitative universality for a class of nonlinear transformations
- Bifurcation structure of a three-species food chain model
- Food chain chaos due to junction-fold point
- Belyakov Homoclinic Bifurcations in a Tritrophic Food Chain Model
- Low- and High-Frequency Oscillations in Three-Dimensional Food Chain Systems
- CONSTRUCTING HOMOCLINIC ORBITS AND CHAOTIC ATTRACTORS
- CHAOTIC ATTRACTORS IN ONE-DIMENSION GENERATED BY A SINGULAR SHILNIKOV ORBIT
- ON A POINCARÉ-BIRKHOFF PROBLEM
