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)
Dynamics of a non-autonomous ratio-dependent predator-prey system. (English) Zbl 1032.34044

The authors consider the Lotka-Volterra-type predator-prey model with Holling type-II functional response

x ' =x[a(t)-b(t)x]-c(t)xy m(t)y+x,y ' =y[-d(t)+f(t)x m(t)y+x],

where, instead of the traditional prey-dependent functional response x m+x, the functional response is x/y m+x/y is given, which is a ratio-dependent response. Assume that a,b,c,d,f,m are bounded continuous functions. Some properties such as positive invariance, permanence, nonpersistence and globally asymptotic stability for the given system are discussed. If a,b,c,d,f,m are periodic or almost-periodic, the existence, uniqueness and stability of a positive periodic solution or a positive almost-periodic solution are also investigated. The methods used in this paper are comparison method, coincidence degree theory and Lyapunov function.


MSC:
34D05Asymptotic stability of ODE
92D25Population dynamics (general)
34C25Periodic solutions of ODE
34C29Averaging method