322 research outputs found
Fungi in Danish soils under organic and conventional farming
A multi-soil study was conducted in Denmark including 29 sites, 8 classified as ‘Organic’, 11 as ‘Conventional with manure and synthetic fertilisers’ and 10 as ‘Conventional with synthetic fertilisers’. The variability of fungal abundance within the three farming systems and the long-term effects of different farming systems on fungal propagules in soil were evaluated.
Fungal abundance showed large variations within all three farming systems and this variability reduced the possibility to obtain general conclusions on fungal composition in soils under different farming systems. This was illustrated by the results on total propagule numbers of filamentous fungi and yeasts. Penicillium spp. and Gliocladium roseum were more abundant under organic than conventional farming, while Trichoderma spp. were most abundant in conventionally farmed soils with synthetic fertilisers. These results were not altered after adjusting for possible differences in basic soil properties like total-C and N, extractable P, CEC, base saturation and soil density. The paper discusses whether the differences in fungal abundance are characteristics of a farming system itself or associated with certain management factors being more prevalent in one farming system than the other
Spiralling dynamics near heteroclinic networks
There are few explicit examples in the literature of vector fields exhibiting
complex dynamics that may be proved analytically. We construct explicitly a
{two parameter family of vector fields} on the three-dimensional sphere
\EU^3, whose flow has a spiralling attractor containing the following: two
hyperbolic equilibria, heteroclinic trajectories connecting them {transversely}
and a non-trivial hyperbolic, invariant and transitive set. The spiralling set
unfolds a heteroclinic network between two symmetric saddle-foci and contains a
sequence of topological horseshoes semiconjugate to full shifts over an
alphabet with more and more symbols, {coexisting with Newhouse phenonema}. The
vector field is the restriction to \EU^3 of a polynomial vector field in
\RR^4. In this article, we also identify global bifurcations that induce
chaotic dynamics of different types.Comment: change in one figur
On Takens' Last Problem: tangencies and time averages near heteroclinic networks
We obtain a structurally stable family of smooth ordinary differential
equations exhibiting heteroclinic tangencies for a dense subset of parameters.
We use this to find vector fields -close to an element of the family
exhibiting a tangency, for which the set of solutions with historic behaviour
contains an open set. This provides an affirmative answer to Taken's Last
Problem (F. Takens (2008) Nonlinearity, 21(3) T33--T36). A limited solution
with historic behaviour is one for which the time averages do not converge as
time goes to infinity. Takens' problem asks for dynamical systems where
historic behaviour occurs persistently for initial conditions in a set with
positive Lebesgue measure.
The family appears in the unfolding of a degenerate differential equation
whose flow has an asymptotically stable heteroclinic cycle involving
two-dimensional connections of non-trivial periodic solutions. We show that the
degenerate problem also has historic behaviour, since for an open set of
initial conditions starting near the cycle, the time averages approach the
boundary of a polygon whose vertices depend on the centres of gravity of the
periodic solutions and their Floquet multipliers.
We illustrate our results with an explicit example where historic behaviour
arises -close of a -equivariant vector field
Dense heteroclinic tangencies near a Bykov cycle
This article presents a mechanism for the coexistence of hyperbolic and
non-hyperbolic dynamics arising in a neighbourhood of a Bykov cycle where
trajectories turn in opposite directions near the two nodes --- we say that the
nodes have different chirality. We show that in the set of vector fields
defined on a three-dimensional manifold, there is a class where tangencies of
the invariant manifolds of two hyperbolic saddle-foci occur densely. The class
is defined by the presence of the Bykov cycle, and by a condition on the
parameters that determine the linear part of the vector field at the
equilibria. This has important consequences: the global dynamics is
persistently dominated by heteroclinic tangencies and by Newhouse phenomena,
coexisting with hyperbolic dynamics arising from transversality. The
coexistence gives rise to linked suspensions of Cantor sets, with hyperbolic
and non-hyperbolic dynamics, in contrast with the case where the nodes have the
same chirality.
We illustrate our theory with an explicit example where tangencies arise in
the unfolding of a symmetric vector field on the three-dimensional sphere
Global bifurcations close to symmetry
Heteroclinic cycles involving two saddle-foci, where the saddle-foci share
both invariant manifolds, occur persistently in some symmetric differential
equations on the 3-dimensional sphere. We analyse the dynamics around this type
of cycle in the case when trajectories near the two equilibria turn in the same
direction around a 1-dimensional connection - the saddle-foci have the same
chirality. When part of the symmetry is broken, the 2-dimensional invariant
manifolds intersect transversely creating a heteroclinic network of Bykov
cycles.
We show that the proximity of symmetry creates heteroclinic tangencies that
coexist with hyperbolic dynamics. There are n-pulse heteroclinic tangencies -
trajectories that follow the original cycle n times around before they arrive
at the other node. Each n-pulse heteroclinic tangency is accumulated by a
sequence of (n+1)-pulse ones. This coexists with the suspension of horseshoes
defined on an infinite set of disjoint strips, where the first return map is
hyperbolic. We also show how, as the system approaches full symmetry, the
suspended horseshoes are destroyed, creating regions with infinitely many
attracting periodic solutions
The Discrete Markus-Yamabe Problem for Symmetric Planar Polynomial Maps
We probe deeper into the Discrete Markus-Yamabe Question for polynomial
planar maps and into the normal form for those maps which answer this question
in the affirmative. Furthermore, in a symmetric context, we show that the only
nonlinear equivariant polynomial maps providing an affirmative answer to the
Discrete Markus-Yamabe Question are those possessing Z2 as their group of
symmetries. We use this to establish two new tools which give information about
the spectrum of a planar polynomial map
Global Saddles for Planar Maps
We study the dynamics of planar diffeomorphisms having a unique fixed point
that is a hyperbolic local saddle. We obtain sufficient conditions under which
the fixed point is a global saddle. We also address the special case of
-symmetric maps, for which we obtain a similar result for
homeomorphisms. Some applications to differential equations are also given
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