Effects of noise on some dynamical models in ecology

DOI10.1007/BF00275681zbMath0626.92021OpenAlexW2053426042WikidataQ44682009 ScholiaQ44682009MaRDI QIDQ581300

Mark Kot, Stephen P. Ellner, William M. Schaffer

Publication date: 1986

Published in: Journal of Mathematical Biology (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1007/bf00275681

zbMATH Keywords

chaosrandom perturbationscorrelation dimension of attractordifferential equations for n speciesdynamics of one-dimensional mapseffects of noise on the invariant measurefinite dimensional flowsreconstruction techniquessingle species difference equationsstable fixed-pointtime series of population abundances

Mathematics Subject Classification ID

Dynamics induced by flows and semiflows (37C10) Ecology (92D40) Additive difference equations (39A10) Strange attractors, chaotic dynamics of systems with hyperbolic behavior (37D45) Stochastic analysis (60H99)

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Cites Work

• Existence and bifurcation of stable equilibrium in two-prey, one-predator communities
• Oscillators with chaotic behavior: An illustration of a theorem by Shil'nikov
• A scaling law: How an attractor's volume depends on noise level
• What can we learn from homoclinic orbits in chaotic dynamics ?
• Local and global behavior near homoclinic orbits
• Is the dimension of chaotic attractors invariant under coordinate changes?
• Bifurcation phenomena near homoclinic systems: A two-parameter analysis
• Measuring the strangeness of strange attractors
• On iterations of \(1-\alpha x^2\) on \((-1,1)\)
• Oscillations and chaos in epidemics: A nonlinear dynamic study of six childhood diseases in Copenhagen, Denmark
• Possible new strange attractors with spiral structure
• Strange attractors in Volterra equations for species in competition
• Regular and stochastic motion
• Quantitative universality for a class of nonlinear transformations
• The influence of noise on the logistic model
• On finite limit sets for transformations on the unit interval
• Persistence of Dynamical Systems under Random Perturbations
• Period Three Implies Chaos
• Stable Orbits and Bifurcation of Maps of the Interval
• Deterministic Nonperiodic Flow
• Feigenbaum universality and the thermodynamic formalism
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