Physical review. E,
Journal Year:
2023,
Volume and Issue:
108(6)
Published: Dec. 21, 2023
The
reservoir
computing
approach
utilizes
a
time
series
of
measurements
as
input
to
high-dimensional
dynamical
system
known
reservoir.
However,
the
relies
on
sampling
random
matrix
define
its
underlying
layer,
which
leads
numerous
hyperparameters
that
need
be
optimized.
Here,
we
propose
nonlocally
coupled
pendulum
model
with
higher-order
interactions
novel
reservoir,
requires
no
matrices
and
fewer
hyperparameters.
We
use
Bayesian
optimization
explore
hyperparameter
space
within
minimal
number
iterations
train
pendulums
reproduce
chaotic
attractors,
simplifies
complicated
optimization.
illustrate
effectiveness
our
technique
Lorenz
Hindmarsh-Rose
neuronal
model,
calculate
Pearson
correlation
coefficients
between
Hausdorff
metrics
in
phase
space.
demonstrate
contribution
by
analyzing
interaction
different
configurations
prediction
performance,
well
computations
largest
Lyapunov
exponents.
chimera
state
is
found
most
effective
regime
for
prediction.
findings,
where
present
new
structure,
offer
potential
applications
design
high-performance
modeling
dynamics
physical
systems.
Physical review. E,
Journal Year:
2024,
Volume and Issue:
109(2)
Published: Feb. 12, 2024
Chimera
states
are
dynamical
where
regions
of
synchronous
trajectories
coexist
with
incoherent
ones.
A
significant
amount
research
has
been
devoted
to
studying
chimera
in
systems
identical
oscillators,
nonlocally
coupled
through
pairwise
interactions.
Nevertheless,
there
is
increasing
evidence,
also
supported
by
available
data,
that
complex
composed
multiple
units
experiencing
many-body
interactions
can
be
modeled
using
higher-order
structures
beyond
the
paradigm
classic
networks.
In
this
work
we
investigate
whether
phase
appear
framework,
focusing
on
a
topology
solely
involving
many-body,
nonlocal,
and
nonregular
interactions,
hereby
named
nonlocal
$d$-hyperring,
$(d+1)$
being
order
We
present
theory
paradigmatic
Stuart-Landau
oscillators
as
node
dynamics,
show
emerge
variety
different
coupling
functions.
For
comparison,
that,
when
``flattened''
ones,
behavior
weaker
more
elusive.
Physical review. E,
Journal Year:
2025,
Volume and Issue:
111(2)
Published: Feb. 6, 2025
In
recent
studies,
it
has
been
established
that
higher-order
interactions
in
coupled
oscillators
can
induce
a
process
from
continuous
to
explosive
phase
transition.
this
study,
we
identify
transition,
termed
the
stepwise
characterized
by
emergence
of
multiple
critical
plateaus
globally
frequency-weighted
pendulum
model.
This
transition
bridges
and
transitions,
arising
delicate
balance
between
attractive
repulsive
pairwise
interactions.
Specifically,
occurs
when
coupling
is
moderate,
neither
large
nor
small,
while
remain
repulsive.
Our
analysis
shows
stronger
necessitate
weaker
interactions,
leading
partial
frequency
locking
among
triggering
We
construct
an
analytical
framework
using
self-consistent
equations
provide
approximation
steady-state
behavior.
study
uncovers
alternative
pathway
desynchronization,
provides
additional
insights
into
transitions
dynamical
networks.
Chaos An Interdisciplinary Journal of Nonlinear Science,
Journal Year:
2025,
Volume and Issue:
35(5)
Published: May 1, 2025
Most
previous
studies
on
eigenspectral
analysis
of
synchronization
have
focused
static
multilayer
networks
with
pairwise
interactions.
In
this
work,
we
extend
the
to
time-varying
higher-order
Specifically,
consider
two
types
connections,
namely,
multiplex
and
interconnected
networks.
For
networks,
analytically
derive
eigenspectra
for
an
arbitrary
number
layers
Our
results
show
that
stronger
interlayer
coupling
accelerates
supra-diffusion
process
suppresses
multistable
regions,
while
interactions
further
reduce
critical
threshold
required
process,
fostering
bistability
facilitating
emergence
chimera
states.
We
numerically
verify
using
a
two-layer
coupled
pendulum
network.
interactions,
find
high-frequency
switching
between
links
disrupts
synchronization,
whereas
low-frequency
allows
emerge
layers.
Under
high
frequency,
increasing
probability
has
minimal
influence
patterns.
Parameter-space
reveals
conditions
under
which
states
or
disappear,
highlighting
interplay
intralayer
couplings.
Analysis
based
master
stability
function
confirms
becomes
stable
once
surpasses
threshold.
Chaos An Interdisciplinary Journal of Nonlinear Science,
Journal Year:
2023,
Volume and Issue:
33(9)
Published: Sept. 1, 2023
We
investigate
the
impact
of
contrarians
(via
negative
coupling)
in
multilayer
networks
phase
oscillators
having
higher-order
interactions.
report
that
framework
facilitates
synchronization
onset
pairwise
coupling
regime.
The
multilayering
strength
governs
and
nature
transition,
whereas
interactions
dictate
backward
critical
coupling.
Specifically,
system
does
not
synchronize
below
a
value
strength.
analytical
calculations
using
mean-field
Ott-Antonsen
approach
agree
with
simulations.
results
presented
here
may
be
useful
for
understanding
emergent
behaviors
real-world
complex
systems
interactions,
such
as
brain
social
system.
