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### Open Access Journals

DCDS

The logarithmic expansion rate of a positively
invariant set for a $C^1$ endomorphism is shown to equal
the infimum of the Lyapunov exponents for ergodic measures
with support in the invariant set. Using this result, aperiodic
flows of the two torus are shown to have an expansion rate of zero and the effects of
conjugacies on expansion rates are investigated.

MBE

Intraguild predation occurs when one species (the
intraguild predator) predates on and competes with another species
(the intraguild prey). A classic model of this interaction was
introduced by Gary Polis and Robert Holt building on a model of
competing species by Thomas Schoener. A global analysis reveals that
this model exhibits generically six dynamics: extinction of one or
both species; coexistence about a globally stable equilibrium;
contingent exclusion in which the first established species prevents
the establishment of the other species; contingent coexistence in
which coexistence or displacement of the intraguild prey depend on
initial conditions; exclusion of the intraguild prey; and exclusion
of the intraguild predator. Implications for biological control and
community ecology are discussed.

DCDS-B

Let $f:\M\to\M$ be a continuous map of a locally compact metric
space. Models of interacting populations often have a closed
invariant set $\partial \M$ that corresponds to the loss or
extinction of one or more populations. The dynamics of $f$ subject
to bounded random perturbations for which $\partial \M$ is absorbing
are studied. When these random perturbations are sufficiently small,
almost sure absorbtion (i.e. extinction) for all initial conditions
is shown to occur if and only if $M\setminus
\partial M$ contains no attractors for $f$. Applications to evolutionary bimatrix games
and uniform persistence are given. In particular, it shown that
random perturbations of evolutionary bimatrix game dynamics result
in almost sure extinction of one or more strategies.

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