zbMATH — the first resource for mathematics

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.

a & b logic and
a | b logic or
!ab logic not
abc* right wildcard
"ab c" phrase
(ab c) parentheses
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)
Codimension-two bifurcations of fixed points in a class of discrete prey-predator systems. (English) Zbl 1229.92072
Summary: The dynamic behaviour of a Lotka-Volterra system, described by a planar map, is analytically and numerically investigated. We derive analytical conditions for stability and bifurcation of the fixed points of the system and compute analytically the normal form coefficients for the codimension 1 bifurcation points (flip and Neimark-Sacker), and so establish sub- or supercriticality of these bifurcation points. Furthermore, by using numerical continuation methods, we compute bifurcation curves of fixed points and cycles with periods up to 16 under variation of one and two parameters, and compute all codimension 1 and codimension 2 bifurcations on the corresponding curves. For the bifurcation points, we compute the corresponding normal form coefficients. These quantities enable us to compute curves of codimension 1 bifurcations that branch off from the detected codimension 2 bifurcation points. These curves form stability boundaries of various types of cycles which emerge around codimension 1 and 2 bifurcation points. Numerical simulations confirm our results and reveal further complex dynamical behaviours.
39A28Bifurcation theory (difference equations)
37N25Dynamical systems in biology
65C20Models (numerical methods)
39A60Applications of difference equations