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)
On the stable periodic solutions of a delayed two-species model of facultative mutualism. (English) Zbl 1143.34054

Let a i (·),b i (·)C(R,[0,+)); τ i (·),ρ i (·)C 1 (R,[0,+)); c i (·)C(R,(0,+));r i (·)C(R,R)(i=1,2) be ω-periodic functions. The authors establish sufficient conditions for the existence and globally asymptotic stability of positive periodic solutions for the following two-species system modelling “facultative mutualism”:

y 1 ' (t)=y 1 (t)[r 1 (t)-a 1 (t)y 1 (t)-b 1 (t)y 1 (t-τ 1 (t))+c 1 (t)y 2 (t-ρ 1 (t)))],
y 2 ' (t)=y 2 (t)[r 2 (t)-a 2 (t)y 2 (t)-b 2 (t)y 2 (t-τ 2 (t))+c 2 (t)y 1 (t-ρ 2 (t)))],

where 0 ω r i (t)dt>0(i=1,2)· These results are extended to a more general two-species facultative mutualism system involving multiple delays. Some applications and biological interpretations are discussed.

34K60Qualitative investigation and simulation of models
34K13Periodic solutions of functional differential equations
34K20Stability theory of functional-differential equations
92D25Population dynamics (general)