Reconstructing attractors with autoencoders
Chaos An Interdisciplinary Journal of Nonlinear Science,
Journal Year:
2025,
Volume and Issue:
35(1)
Published: Jan. 1, 2025
We
propose
a
method
based
on
autoencoders
to
reconstruct
attractors
from
recorded
footage,
preserving
the
topology
of
underlying
phase
space.
provide
theoretical
support
and
test
with
(i)
footage
temperature
stream
function
fields
involved
in
Lorenz
atmospheric
convection
problem
(ii)
time
series
obtained
by
integrating
Rössler
equations.
Language: Английский
The applicability limits of the lowest-order substitute model for a cantilever beam system hard-impacting a moving base
Chaos An Interdisciplinary Journal of Nonlinear Science,
Journal Year:
2025,
Volume and Issue:
35(1)
Published: Jan. 1, 2025
This
paper
examines
the
circumstances
under
which
a
one-degree-of-freedom
approximate
system
can
be
employed
to
predict
dynamics
of
cantilever
beam
comprising
an
elastic
element
with
significant
mass
and
concentrated
embedded
at
its
end,
impacting
moving
rigid
base.
A
reference
model
was
constructed
using
finite
method,
lowest-order
proposed
that
could
useful
in
engineering
practice
for
rapidly
ascertaining
system,
particularly
predicting
both
periodic
chaotic
motions.
The
number
elements
determined
based
on
calculated
values
natural
frequencies,
were
found
correspond
frequencies
derived
from
application
analytical
formulas.
precision
parameter
identification
outcomes
yielded
by
substitute
validated
through
calculation
regions
stable
solutions
Peterka
method.
Subsequently,
qualitative
quantitative
limits
model's
applicability
determined.
delineated
utilization
Lyapunov
exponents
characteristics
associated
energy
dissipation
due
impacts
average
per
excitation
period.
These
provide
foundation
introduction
global
distance
measures
dynamic
behavior
diverse
systems
within
specified
range
control
parameter.
Language: Английский
Exact reduction of synchronized systems in higher-dimensional spaces
Chaos An Interdisciplinary Journal of Nonlinear Science,
Journal Year:
2025,
Volume and Issue:
35(2)
Published: Feb. 1, 2025
Exact
reduction
by
partial
integration
has
been
extensively
investigated
for
the
Kuramoto
model
means
of
Watanabe–Strogatz
transform.
This
is
simplest
higher-dimensional
reductions
that
apply
to
a
hierarchy
models
in
spaces
any
dimension,
including
Riccati
systems.
Linear
fractional
transformations
enable
system
equations
be
expressed
an
equivalent
matrix
form,
where
variables
can
regarded
as
time-evolution
operators.
allows
us
perform
exact
at
each
node,
which
reduces
single
equation,
associated
operator
acts
over
all
nodes.
group-theoretical
properties,
element
SU(1,1)∼SO(2,1)
model,
and
SO(d,1)
on
unit
sphere
Sd−1.
Parameterization
group
elements
using
subgroup
properties
leads
further
number
solved
also
provides
explicit
formulas
mappings
sphere,
generalize
Möbius
map
S1.
dimensional
applies
another
class
much
less-studied
with
cubic
nonlinearities,
governing
again
transformed
into
form
map.
node
proceeds
before,
now
lies
SL(d,R).
The
formulation
solutions
terms
exponential
trajectories
asymptotically
approach
fixed
points.
As
examples,
we
investigate
partially
integrable
combined
pairwise
higher-order
interactions.
Language: Английский