zbMATH — the first resource for mathematics

Examples
Geometry Search for the term Geometry in any field. Queries are case-independent.
Funct* Wildcard queries are specified by * (e.g. functions, functorial, etc.). Otherwise the search is exact.
"Topological group" Phrases (multi-words) should be set in "straight quotation marks".
au: Bourbaki & ti: Algebra Search for author and title. The and-operator & is default and can be omitted.
Chebyshev | Tschebyscheff The or-operator | allows to search for Chebyshev or Tschebyscheff.
"Quasi* map*" py: 1989 The resulting documents have publication year 1989.
so: Eur* J* Mat* Soc* cc: 14 Search for publications in a particular source with a Mathematics Subject Classification code (cc) in 14.
"Partial diff* eq*" ! elliptic The not-operator ! eliminates all results containing the word elliptic.
dt: b & au: Hilbert The document type is set to books; alternatively: j for journal articles, a for book articles.
py: 2000-2015 cc: (94A | 11T) Number ranges are accepted. Terms can be grouped within (parentheses).
la: chinese Find documents in a given language. ISO 639-1 language codes can also be used.

Operators
a & b logic and
a | b logic or
!ab logic not
abc* right wildcard
"ab c" phrase
(ab c) parentheses
Fields
any anywhere an internal document identifier
au author, editor ai internal author identifier
ti title la language
so source ab review, abstract
py publication year rv reviewer
cc MSC code ut uncontrolled term
dt document type (j: journal article; b: book; a: book article)
Chaos in periodically forced discrete-time ecosystem models. (English) Zbl 0964.92044
Summary: Natural populations whose generations are non-overlapping can be modelled by difference equations that describe how the populations evolve in discrete time-steps. These ecosystem models are, in general, nonlinear and contain system parameters that relate to such properties as the intrinsic growth-rate of a species. Typically, the parameters are kept constant. In this study, in order to simulate cyclic effects due to changes in environmental conditions, periodic forcing is applied to system parameters in four specific models, comprising three well-known, single-species models due to May, Moran-Ricker, and Hassell, and also a Maynard Smith predator-prey model. It is found that, in each case, a system that has simple (e.g., periodic) behavior in its unforced state can take on extremely complicated behavior, including chaos, when periodic forcing is applied, dependent on the values of the forcing amplitudes and frequencies. For each model, the application of forcing is found to produce an effective increase in the parameter space over which the system can behave chaotically. Bifurcation diagrams are constructed with the forcing amplitude as the bifurcation parameter, and these are observed to display rich structurc, including chaotic bands with periodic windows, pitch-fork and tangent bifurcations, and attractor crises.
MSC:
92D40Ecology
37N25Dynamical systems in biology
37D45Strange attractors, chaotic dynamics