1,015 research outputs found
Families of piecewise linear maps with constant Lyapunov exponent
We consider families of piecewise linear maps in which the moduli of the two
slopes take different values. In some parameter regions, despite the variations
in the dynamics, the Lyapunov exponent and the topological entropy remain
constant. We provide numerical evidence of this fact and we prove it
analytically for some special cases. The mechanism is very different from that
of the logistic map and we conjecture that the Lyapunov plateaus reflect
arithmetic relations between the slopes.Comment: 26 pages, 13 figure
Emergence of hierarchical networks and polysynchronous behaviour in simple adaptive systems
We describe the dynamics of a simple adaptive network. The network
architecture evolves to a number of disconnected components on which the
dynamics is characterized by the possibility of differently synchronized nodes
within the same network (polysynchronous states). These systems may have
implications for the evolutionary emergence of polysynchrony and hierarchical
networks in physical or biological systems modeled by adaptive networks.Comment: 4 pages, 4 figure
Developing the evidence base for adult social care practice: The NIHR School for Social Care Research
In a foreword to 'Shaping the Future of Care Together', Prime Minister Gordon Brown says that a care and support system reflecting the needs of our times and meeting our rising aspirations is achievable, but 'only if we are prepared to rise to the challenge of radical reform'. A number of initiatives will be needed to meet the challenge of improving social care for the growing older population. Before the unveiling of the green paper, The National Institute for Health Research (NIHR) announced that it has provided 15m pounds over a five-year period to establish the NIHR School for Social Care Research. The School's primary aim is to conduct or commission research that will help to improve adult social care practice in England. The School is seeking ideas for research topics, outline proposals for new studies and expert advice in developing research methods
Imperfect Homoclinic Bifurcations
Experimental observations of an almost symmetric electronic circuit show
complicated sequences of bifurcations. These results are discussed in the light
of a theory of imperfect global bifurcations. It is shown that much of the
dynamics observed in the circuit can be understood by reference to imperfect
homoclinic bifurcations without constructing an explicit mathematical model of
the system.Comment: 8 pages, 11 figures, submitted to PR
Combinatorics of linear iterated function systems with overlaps
Let be points in , and let
be a one-parameter family of similitudes of : where
is our parameter. Then, as is well known, there exists a
unique self-similar attractor satisfying
. Each has
at least one address , i.e.,
.
We show that for sufficiently close to 1, each has different
addresses. If is not too close to 1, then we can still have an
overlap, but there exist 's which have a unique address. However, we
prove that almost every has addresses,
provided contains no holes and at least one proper overlap. We
apply these results to the case of expansions with deleted digits.
Furthermore, we give sharp sufficient conditions for the Open Set Condition
to fail and for the attractor to have no holes.
These results are generalisations of the corresponding one-dimensional
results, however most proofs are different.Comment: Accepted for publication in Nonlinearit
Unstable dimension variability, heterodimensional cycles, and blenders in the border-collision normal form
Chaotic attractors commonly contain periodic solutions with unstable
manifolds of different dimensions. This allows for a zoo of dynamical phenomena
not possible for hyperbolic attractors. The purpose of this Letter is to
demonstrate these phenomena in the border-collision normal form. This is a
continuous, piecewise-linear family of maps that is physically relevant as it
captures the dynamics created in border-collision bifurcations in diverse
applications. Since the maps are piecewise-linear they are relatively amenable
to an exact analysis and we are able to explicitly identify parameter values
for heterodimensional cycles and blenders. For a one-parameter subfamily we
identify bifurcations involved in a transition through unstable dimension
variability. This is facilitated by being able to compute periodic solutions
quickly and accurately, and the piecewise-linear form should provide a useful
test-bed for further study
Assessing the influence of one astronomy camp over 50 years
The International Astronomical Youth Camp has benefited thousands of lives
during its 50-year history. We explore the pedagogy behind this success, review
a survey taken by more than 300 previous participants, and discuss some of the
challenges the camp faces in the future.Comment: 10 pages, 4 figure
Oscillatory bubbles induced by geometrical constraint
International audienc
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