Chaos An Interdisciplinary Journal of Nonlinear Science,
Journal Year:
2024,
Volume and Issue:
34(6)
Published: June 1, 2024
Adaptive
dynamical
networks
are
network
systems
in
which
the
structure
co-evolves
and
interacts
with
state
of
nodes.
We
study
an
adaptive
changes
on
a
slower
time
scale
relative
to
fast
dynamics
identify
phenomenon
we
refer
as
recurrent
chaotic
clustering
(RACC),
chaos
is
observed
slow
scale,
while
exhibits
regular
dynamics.
Such
further
characterized
by
long
(relative
scale)
regimes
frequency
clusters
or
frequency-synchronized
dynamics,
interrupted
jumps
between
these
regimes.
also
determine
parameter
values
where
intervals
show
that
such
robust
parameters
initial
conditions.
Journal of Neural Engineering,
Journal Year:
2023,
Volume and Issue:
20(2), P. 026003 - 026003
Published: March 7, 2023
Abstract
Objective.
While
brain
stimulation
therapies
such
as
deep
for
Parkinson’s
disease
(PD)
can
be
effective,
they
have
yet
to
reach
their
full
potential
across
neurological
disorders.
Entraining
neuronal
rhythms
using
rhythmic
has
been
suggested
a
new
therapeutic
mechanism
restore
neurotypical
behaviour
in
conditions
chronic
pain,
depression,
and
Alzheimer’s
disease.
However,
theoretical
experimental
evidence
indicate
that
also
entrain
at
sub-
super-harmonics,
far
from
the
frequency.
Crucially,
these
counterintuitive
effects
could
harmful
patients,
example
by
triggering
debilitating
involuntary
movements
PD.
We
therefore
seek
principled
approach
selectively
promote
close
frequency,
while
avoiding
preventing
entrainment
super-harmonics.
Approach.
Our
open-loop
selective
entrainment,
dithered
stimulation,
consists
adding
white
noise
period.
Main
results.
theoretically
establish
ability
of
given
rhythm,
verify
its
efficacy
simulations
uncoupled
neural
oscillators,
networks
coupled
oscillators.
Furthermore,
we
show
implemented
neurostimulators
with
limited
capabilities
toggling
within
finite
set
frequencies.
Significance.
Likely
implementable
variety
existing
devices,
dithering-based
enable
therapies,
well
neuroscientific
research
exploiting
modulate
higher-order
entrainment.
Chaos An Interdisciplinary Journal of Nonlinear Science,
Journal Year:
2025,
Volume and Issue:
35(1)
Published: Jan. 1, 2025
We
investigate
the
dynamics
of
adaptive
Kuramoto
model
with
slow
adaptation
in
continuum
limit,
N→∞.
This
is
distinguished
by
dense
multistability,
where
multiple
states
coexist
for
same
system
parameters.
The
underlying
cause
this
multistability
that
some
oscillators
can
lock
at
different
phases
or
switch
between
locking
and
drifting
depending
on
their
initial
conditions.
identify
new
states,
such
as
two-cluster
states.
To
simplify
analysis,
we
introduce
an
approximate
reduction
via
row-averaging
coupling
matrix.
derive
a
self-consistency
equation
reduced
present
stability
diagram
illustrating
effects
positive
negative
adaptation.
Our
theoretical
findings
are
validated
through
numerical
simulations
large
finite
system.
Comparisons
previous
work
highlight
significant
influence
synchronization
behavior.
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
Frontiers in Cellular Neuroscience,
Journal Year:
2024,
Volume and Issue:
18
Published: March 14, 2024
Neural
interactions
in
the
brain
are
affected
by
transmission
delays
which
may
critically
alter
signal
propagation
across
different
regions
both
normal
and
pathological
conditions.
The
effect
of
interaction
on
dynamics
generic
neural
networks
has
been
extensively
studied
theoretical
computational
models.
However,
role
development
oscillatory
basal
ganglia
(BG)
Parkinson's
disease
(PD)
is
overlooked.
Journal of Statistical Mechanics Theory and Experiment,
Journal Year:
2024,
Volume and Issue:
2024(11), P. 113501 - 113501
Published: Nov. 6, 2024
Abstract
The
study
of
adaptive
dynamics,
involving
many
degrees
freedom
on
two
separated
timescales,
one
for
fast
changes
state
variables
and
another
the
slow
adaptation
parameters
controlling
former’s
dynamics
is
crucial
understanding
feedback
mechanisms
underlying
evolution
learning.
We
present
a
path-integral
approach
à
la
Martin–Siggia–Rose-De
Dominicis–Janssen
to
analyse
non-equilibrium
phase
transitions
in
such
dynamical
systems.
As
an
illustration,
we
apply
our
framework
gene-regulatory
networks
under
dynamic
genotype-phenotype
map:
phenotypic
variations
are
shaped
by
stochastic
gene-expression
coupled
slowly
evolving
distribution
genotypes,
each
encoded
network
structure.
establish
that
this
map,
genotypes
corresponding
reciprocal
coherent
loops
selected
within
intermediate
range
environmental
noise,
leading
robustness.
Network Neuroscience,
Journal Year:
2024,
Volume and Issue:
8(3), P. 883 - 901
Published: Jan. 1, 2024
Generalized
epileptic
attacks,
which
exhibit
widespread
disruption
of
brain
activity,
are
characterized
by
recurrent,
spontaneous,
and
synchronized
bursts
neural
activity
that
self-initiate
self-terminate
through
critical
transitions.
Here
we
utilize
the
general
framework
explosive
synchronization
(ES)
from
complex
systems
science
to
study
role
network
structure
resource
dynamics
in
generation
propagation
seizures.
We
show
a
combination
constraint
adaptive
coupling
Kuramoto
oscillator
model
can
reliably
generate
seizure-like
across
different
topologies,
including
biologically
derived
mesoscale
mouse
network.
The
model,
coupled
with
novel
algorithm
for
tracking
seizure
propagation,
provides
mechanistic
insight
into
transition
state
its
dependence
on
resources;
identifies
key
areas
may
be
involved
initiation
spatial
seizure.
though
minimal,
efficiently
recapitulates
several
experimental
theoretical
predictions
more
models
makes
experimentally
testable
predictions.
Neurobiology of Disease,
Journal Year:
2024,
Volume and Issue:
199, P. 106565 - 106565
Published: June 14, 2024
Subthalamic
deep
brain
stimulation
(DBS)
robustly
generates
high-frequency
oscillations
known
as
evoked
resonant
neural
activity
(ERNA).
Recently
the
importance
of
ERNA
has
been
demonstrated
through
its
ability
to
predict
optimal
DBS
contact
in
subthalamic
nucleus
patients
with
Parkinson's
disease.
However,
underlying
mechanisms
are
not
well
understood,
and
previous
modelling
efforts
have
managed
reproduce
wealth
published
data
describing
dynamics
ERNA.
Here,
we
aim
present
a
minimal
model
capable
reproducing
characteristics
slow
date.
We
make
biophysically-motivated
modifications
Kuramoto
fit
parameters
obtained
from
data.
Our
results
demonstrate
that
it
is
possible
(over
hundreds
seconds)
single
neuronal
population,
and,
crucially,
vesicle
depletion
one
key
behind
frequency
decay
our
model.
further
validate
proposed
against
experimental
disease
patients,
where
captures
variations
amplitude
response
variable
frequency,
amplitude,
pulse
bursting.
provide
series
predictions
could
be
subject
future
studies
for
validation.
Chaos An Interdisciplinary Journal of Nonlinear Science,
Journal Year:
2024,
Volume and Issue:
34(11)
Published: Nov. 1, 2024
Natural
and
technological
networks
exhibit
dynamics
that
can
lead
to
complex
cooperative
behaviors,
such
as
synchronization
in
coupled
oscillators
rhythmic
activity
neuronal
networks.
Understanding
these
collective
is
crucial
for
deciphering
a
range
of
phenomena
from
brain
power
grid
stability.
Recent
interest
co-evolutionary
has
highlighted
the
intricate
interplay
between
on
network
with
mixed
time
scales.
Here,
we
explore
behavior
excitable
simple
two
Theta
neurons
adaptive
coupling
without
self-interaction.
Through
combination
bifurcation
analysis
numerical
simulations,
seek
understand
how
level
adaptivity
strength,
a,
influences
dynamics.
We
first
investigate
possible
non-adaptive
limit;
our
reveals
stability
regions
quiescence
spiking
where
frequencies
mode-lock
variety
configurations.
Second,
increase
observe
widening
associated
Arnol’d
tongues,
which
may
overlap
give
room
multi-stable
For
larger
adaptivity,
mode-locked
further
undergo
period-doubling
cascade
into
chaos.
Our
findings
contribute
mathematical
theory
offer
insights
potential
mechanisms
underlying
communication
synchronization.
PLoS Computational Biology,
Journal Year:
2024,
Volume and Issue:
20(12), P. e1012647 - e1012647
Published: Dec. 5, 2024
The
ready
availability
of
brain
connectome
data
has
both
inspired
and
facilitated
the
modelling
whole
activity
using
networks
phenomenological
neural
mass
models
that
can
incorporate
interaction
strength
tract
length
between
regions.
Recently,
a
new
class
model
been
developed
from
an
exact
mean
field
reduction
network
spiking
cortical
cell
with
biophysically
realistic
chemical
synapse.
Moreover,
this
population
dynamics
naturally
electrical
synapses.
Here
we
demonstrate
ability
framework,
when
combined
Human
Connectome
Project,
to
generate
patterns
functional
connectivity
(FC)
type
observed
in
magnetoencephalography
magnetic
resonance
neuroimaging.
Some
limited
explanatory
power
is
obtained
via
eigenmode
description
frequency-specific
FC
patterns,
linear
stability
analysis
steady
state
neigbourhood
Hopf
bifurcation.
However,
direct
numerical
simulations
show
empirical
more
faithfully
recapitulated
nonlinear
regime,
exposes
key
role
gap
junction
coupling
generating
empirically-observed
activity,
associated
their
evolution.
Thereby,
emphasise
importance
maintaining
known
links
biological
reality
developing
multi-scale
dynamics.
As
tool
for
study
dynamic
presented
here
further
provide
suite
C++
codes
efficient,
user
friendly,
simulation
multiple
delayed
interactions.
