# 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)
Planar competitive and cooperative difference equations. (English) Zbl 0907.39004
The author considers the two-dimensional dynamical system given by $$u_{n +1} =f(u_n) -g(v_n),\ v_{n+1} =f(v_n) -g(u_n), \tag *$$ generated by the map $P(u,v)= (f(u)- g(v), \ f(v)-g(u))$. Assuming that $f$ and $g$ are nondecreasing, $P$ is a competitive map which leaves invariant the diagonal $\Delta= \{(u,v):v=u\}$. General definitions of order relations and competitive and cooperative maps are given and, by an example, it is shown that complicated dynamics can occur for such maps, but for exceptional initial data. This paper focusses on the special class of orientation reversing competitive and cooperative maps. Such maps have relatively simple dynamics. Finally, several applications to two models in population biology are discussed.

##### MSC:
 39A10 Additive difference equations 92D25 Population dynamics (general)
Full Text: