Discrete and Continuous Dynamical Systems,
Journal Year:
2024,
Volume and Issue:
44(9), P. 2660 - 2683
Published: Jan. 1, 2024
We
provide
a
well-posedness
theory
for
class
of
nonlocal
continuity
equations
on
co-evolving
graphs.
describe
the
connection
among
vertices
through
an
edge
weight
function
and
we
let
it
evolve
in
time,
coupling
its
dynamics
with
graph.
This
is
relevant
applications
to
opinion
transportation
networks.
Existence
uniqueness
suitably
defined
solutions
obtained
by
exploiting
Banach
fixed-point
theorem.
consider
different
time
scales
evolution
function:
faster
slower
than
flow
The
former
leads
graphs
whose
functions
depend
nonlocally
density
configuration
at
vertices,
while
latter
induces
static
Furthermore,
prove
discrete-to-continuum
limit
PDEs
under
study
as
number
converges
infinity.
Physical review. E,
Journal Year:
2025,
Volume and Issue:
111(1)
Published: Jan. 29, 2025
The
quest
to
understand
relationships
in
networks
across
scientific
disciplines
has
intensified.
However,
the
optimal
network
architecture
remains
elusive,
particularly
for
complex
information
processing.
Therefore,
we
investigate
how
and
specific
structures
form
efficiently
solve
distinct
tasks
using
a
framework
of
performance-dependent
evolution,
leveraging
reservoir
computing
principles.
Our
study
demonstrates
that
task-specific
minimal
obtained
through
this
consistently
outperform
generated
by
alternative
growth
strategies
Erdős-Rényi
random
networks.
Evolved
exhibit
unexpected
sparsity
adhere
scaling
laws
node-density
space
while
showcasing
distinctive
asymmetry
input
readout
node
distribution.
Consequently,
propose
heuristic
quantifying
task
complexity
from
performance-dependently
evolved
networks,
offering
valuable
insights
into
evolutionary
dynamics
structure-function
relationship.
findings
advance
fundamental
understanding
process-specific
evolution
shed
light
on
design
optimization
processing
mechanisms,
notably
machine
learning.
Published
American
Physical
Society
2025
Chaos An Interdisciplinary Journal of Nonlinear Science,
Journal Year:
2024,
Volume and Issue:
34(2)
Published: Feb. 1, 2024
Synchronization
holds
a
significant
role,
notably
within
chaotic
systems,
in
various
contexts
where
the
coordinated
behavior
of
systems
plays
pivotal
and
indispensable
role.
Hence,
many
studies
have
been
dedicated
to
investigating
underlying
mechanism
synchronization
systems.
Networks
with
time-varying
coupling,
particularly
those
blinking
proven
essential.
The
reason
is
that
such
coupling
schemes
introduce
dynamic
variations
enhance
adaptability
robustness,
making
them
applicable
real-world
scenarios.
This
paper
introduces
novel
adaptive
wherein
adapts
dynamically
based
on
most
influential
variable
exhibiting
average
disparity.
To
ensure
an
equitable
selection
effective
at
each
time
instance,
difference
normalized
synchronous
solution’s
range.
Due
this
selection,
enhancement
expected
be
observed.
hypothesis
assessed
networks
identical
encompassing
Lorenz,
Rössler,
Chen,
Hindmarsh–Rose,
forced
Duffing,
van
der
Pol
results
demonstrated
substantial
improvement
when
employing
applying
normalization
process.
Chaos An Interdisciplinary Journal of Nonlinear Science,
Journal Year:
2024,
Volume and Issue:
34(2)
Published: Feb. 1, 2024
A
class
of
adaptation
functions
is
found
for
which
a
synchronous
mode
with
different
number
phase
clusters
exists
in
network
oscillators
triadic
couplings.
This
implemented
fairly
wide
range
initial
conditions
and
the
maximum
four.
The
joint
influence
coupling
strength
parameters
on
synchronization
has
been
studied.
desynchronization
transition
under
variation
parameter
occurs
abruptly
begins
highest-frequency
oscillator,
spreading
hierarchically
to
all
other
elements.
European Journal of Applied Mathematics,
Journal Year:
2025,
Volume and Issue:
unknown, P. 1 - 44
Published: Jan. 6, 2025
Abstract
Many
science
phenomena
are
modelled
as
interacting
particle
systems
(IPS)
coupled
on
static
networks.
In
reality,
network
connections
far
more
dynamic.
Connections
among
individuals
receive
feedback
from
nearby
and
make
changes
to
better
adapt
the
world.
Hence,
it
is
reasonable
model
myriad
real-world
co-evolutionary
(or
adaptive)
networks
.
These
used
in
different
areas
including
telecommunication,
neuroscience,
computer
science,
biochemistry,
social
well
physics,
where
Kuramoto-type
have
been
widely
interaction
a
set
of
oscillators.
this
paper,
we
propose
rigorous
formulation
for
limits
sequence
Kuramoto
oscillators
heterogeneous
networks,
which
both
positive
negative
dynamics
We
show
under
mild
conditions,
mean
field
limit
(MFL)
exists
converges
MFL.
Such
MFL
described
by
solutions
generalised
Vlasov
equation.
treat
graph
signed
measures,
motivated
recent
work
[Kuehn,
Xu.
equations
digraph
JDE,
339
(2022),
261–349].
comparison
recently
emerging
works
MFLs
IPS
non-co-evolutionary
(i.e.,
or
time-dependent
independent
IPS),
our
seems
first
rigorously
address
model.
The
approach
based
generalisation
hybrid
system
ODEs
measure
differential
parametrised
vertex
variable,
together
with
an
analogue
variation
parameters
formula
,
Neunzert’s
in-cell-particle
method
developed
Chaos An Interdisciplinary Journal of Nonlinear Science,
Journal Year:
2025,
Volume and Issue:
35(1)
Published: Jan. 1, 2025
Synaptic
plasticity
plays
a
fundamental
role
in
neuronal
dynamics,
governing
how
connections
between
neurons
evolve
response
to
experience.
In
this
study,
we
extend
network
model
of
θ-neuron
oscillators
include
realistic
form
adaptive
plasticity.
place
the
less
tractable
spike-timing-dependent
plasticity,
employ
recently
validated
phase-difference-dependent
rules,
which
adjust
coupling
strengths
based
on
relative
phases
oscillators.
We
explore
two
distinct
implementations
plasticity:
pairwise
updates
individual
and
global
applied
mean
strength.
derive
mean-field
approximation
assess
its
accuracy
by
comparing
it
simulations
across
various
stability
regimes.
The
synchrony
system
is
quantified
using
Kuramoto
order
parameter.
Through
bifurcation
analysis
calculation
maximal
Lyapunov
exponents,
uncover
interesting
phenomena
such
as
bistability
chaotic
dynamics
via
period-doubling
boundary
crisis
bifurcations.
These
behaviors
emerge
direct
result
are
absent
systems
without
Earth System Dynamics,
Journal Year:
2025,
Volume and Issue:
16(1), P. 189 - 214
Published: Jan. 28, 2025
Abstract.
How
do
social
networks
tip?
A
popular
theory
is
that
a
small
minority
can
trigger
population-wide
change.
This
aligns
with
the
Pareto
principle,
semi-quantitative
law
which
suggests
that,
in
many
systems,
80
%
of
effects
arise
from
20
causes.
In
context
transition
to
net-zero
emissions,
this
vital
be
critical
instigator
tipping,
process
rapidly
change
norms.
work,
we
asked
whether
effect
observed
systems
by
conducting
literature
review,
placing
focus
on
norm
diffusion
and
complex
contagion
via
networks.
By
analysing
simulation
empirical
results
tipping
events
across
disciplines
large
parametric
space,
identified
consistent
patterns
studies
key
factors
help
or
hinder
tipping.
We
show
evidence
supporting
point
near
25
total
population
within
our
compiled
dataset.
Near
mass,
observe
high
likelihood
for
event,
where
majority
quickly
adopts
new
Our
findings
illustrate
slight
variations
between
modelling
results,
average
points
at
24
27
%,
respectively.
Additionally,
range
masses
possible;
these
values
lie
10
43
%.
These
indicate
potential,
but
not
inevitability,
rapid
certain
susceptible
populations
contexts.
Finally,
provide
practical
guidance
facilitating
difficult
changes
(1)
leveraging
trusted
community
structures
building
mass
clustered
(particularly
%–43
threshold
range),
(2)
adapting
strategies
based
type
context,
(3)
targeting
groups
moderate
preferences
network
positions
–
avoiding
reliance
highly
central
well-connected
individuals
enable
endogenous
spread.
Proceedings of the Royal Society A Mathematical Physical and Engineering Sciences,
Journal Year:
2025,
Volume and Issue:
481(2306)
Published: Jan. 1, 2025
Estimating
the
outcome
of
a
given
dynamical
process
from
structural
features
is
key
unsolved
challenge
in
network
science.
This
goal
hampered
by
difficulties
associated
with
nonlinearities,
correlations
and
feedbacks
between
structure
dynamics
complex
systems.
In
this
work,
we
develop
an
approach
based
on
machine
learning
algorithms
that
provides
important
step
towards
understanding
relationship
networks.
particular,
it
allows
us
to
estimate
outbreak
size
disease
starting
single
node,
as
well
degree
synchronicity
system
made
up
Kuramoto
oscillators.
We
show
which
topological
are
for
estimation
provide
ranking
importance
metrics
much
higher
accuracy
than
previously
done.
For
epidemic
propagation,
k-core
plays
fundamental
role,
while
synchronization,
betweenness
centrality
accessibility
measures
most
related
state
oscillator.
all
networks,
find
random
forests
can
predict
or
synchronization
high
accuracy,
indicating
role
spreading
process.
Our
general
be
applied
almost
any
dynamic
running
Also,
our
work
applying
methods
unravel
patterns
emerge
networked
