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)
Effects of optimal antipredator behavior of prey on predator-prey dynamics: The role of refuges. (English) Zbl 0945.92021

Summary: The influence of optimal antipredator behavior of prey on predator-prey dynamics in a two-patch environment is studied. One patch represents an open habitat while the other is a refuge for prey. It is assumed that prey maximize their fitness measured by the instantaneous per capita growth rate. In each patch population dynamics is described by the Lotka-Volterra time continuous model. The refuge is characterized by its protectiveness which is inversely related to the predation risk for prey, and the dependence of population dynamics on protectiveness is studied.

It is shown that adaptive behavior of prey changes qualitative properties of the underlying Lotka-Volterra model due to the appearance of a bounded attractor. Adaptive prey behavior does not lead to a stable equilibrium but to the reduction of population fluctuations. Dynamic consequences of a limited carrying capacity of the refuge are also considered. Low refuge carrying capacity leads to stability of predator-prey dynamics while stability is lost when the carrying capacity of the refuge is high. Lastly, it is shown that optimal antipredator behavior of prey leads to persistence and reduction of oscillations in population densities.

MSC:
92D40Ecology
37N25Dynamical systems in biology
92D25Population dynamics (general)
34D45Attractors
34D99Stability theory of ODE