Research Square (Research Square),
Год журнала:
2023,
Номер
unknown
Опубликована: Июль 3, 2023
Abstract
We
derive
a
next
generation
neural
mass
model
of
population
quadratic-integrate-and-fire
neurons,
with
slow
adaptation,
and
conductance-based
AMPAR,
GABAR
nonlinear
NMDAR
synapses.
show
that
the
Lorentzian
ansatz
assumption
can
be
satisfied
by
introducing
piece-wise
polynomial
approximation
voltage-dependent
magnesium
block
current.
study
dynamics
resulting
system
for
two
example
cases
excitatory
cortical
neurons
inhibitory
striatal
neurons.
Bifurcation
diagrams
are
presented
comparing
different
dynamical
regimes
as
compared
to
case
linear
currents,
along
sample
comparison
simulation
time
series
demonstrating
possible
oscillatory
solutions.
The
omission
nonlinearity
currents
results
in
shift
range
(and
disappearance)
constant
high
firing
rate
regime,
modulation
amplitude
frequency
power
spectrum
oscillations.
Moreover,
action
is
seen
state-dependent
have
opposite
effects
depending
on
type
involved
level
input
received.
serve
computationally
efficient
building
whole
brain
network
models
investigating
differential
types
synapses
under
neuromodulatory
influence
or
receptor
specific
malfunction.
Chaos An Interdisciplinary Journal of Nonlinear Science,
Год журнала:
2024,
Номер
34(1)
Опубликована: Янв. 1, 2024
We
study
macroscopic
behavior
of
populations
quadratic
integrate-and-fire
neurons
subject
to
non-Gaussian
noises;
we
argue
that
these
noises
must
be
α-stable
whenever
they
are
delta-correlated
(white).
For
the
case
additive-in-voltage
noise,
derive
governing
equation
dynamics
characteristic
function
membrane
voltage
distribution
and
construct
a
linear-in-noise
perturbation
theory.
Specifically
for
recurrent
network
with
global
synaptic
coupling,
theoretically
calculate
observables:
population-mean
firing
rate.
The
theoretical
results
underpinned
by
numerical
simulation
homogeneous
heterogeneous
populations.
possibility
generalization
pseudocumulant
approach
fractional
α
is
examined
both
irrational
rational
α.
This
examination
seemingly
suggests
or
its
modifications
employable
only
integer
values
α=1
(Cauchy
noise)
2
(Gaussian
within
physically
meaningful
range
(0;2].
Remarkably,
analysis
indirectly
revealed
that,
Gaussian
minimal
asymptotically
rigorous
model
reduction
involve
three
pseudocumulants
two-pseudocumulant
an
artificial
approximation.
explains
surprising
gain
accuracy
three-pseudocumulant
models
as
compared
ones
reported
in
literature.
Chaos An Interdisciplinary Journal of Nonlinear Science,
Год журнала:
2024,
Номер
34(5)
Опубликована: Май 1, 2024
Neural
mass
models
are
a
powerful
tool
for
modeling
of
neural
populations.
Such
often
used
as
building
blocks
the
simulation
large-scale
networks
and
whole
brain.
Here,
we
carry
out
systematic
bifurcation
analysis
model
basic
motif
various
circuits,
system
two
populations,
an
excitatory,
inhibitory
ones.
We
describe
scenarios
emergence
complex
collective
behavior,
including
chaotic
oscillations
multistability.
also
compare
dynamics
exact
microscopic
show
that
their
agreement
may
be
far
from
perfect.
The
discrepancy
can
interpreted
action
so-called
shot
noise
originating
finite-size
effects.
This
lead
to
blurring
or
even
turn
its
attractors
into
metastable
states
between
which
switches
recurrently.
Chaos An Interdisciplinary Journal of Nonlinear Science,
Год журнала:
2025,
Номер
35(2)
Опубликована: Фев. 1, 2025
We
report
the
effect
of
nonlinear
bias
frequency
collective
oscillations
sin-coupled
phase
oscillators
subject
to
individual
asymmetric
Cauchy
noises.
The
noise
asymmetry
makes
Ott–Antonsen
ansatz
inapplicable.
argue
that,
for
all
stable
non-Gaussian
noises,
tail
is
not
only
possible
(in
addition
trivial
shift
distribution
median)
but
also
generic
in
many
physical
and
biophysical
setups.
For
theoretical
description
effect,
we
develop
a
mathematical
formalism
based
on
circular
cumulants.
derivation
rigorous
asymptotic
results
can
be
performed
this
basis
seems
infeasible
traditional
terms
moments
(the
Kuramoto–Daido
order
parameters).
entrainment
oscillator
frequencies
by
global
reported
detail.
accuracy
low-dimensional
cumulant
reductions
validated
with
high-accuracy
“exact”
solutions
calculated
continued
fraction
method.
Physical review. E,
Год журнала:
2024,
Номер
109(1)
Опубликована: Янв. 4, 2024
In
this
article
we
focus
on
the
study
of
collective
dynamics
neural
networks.
The
analysis
two
recent
models
coupled
``next-generation''
mass
allows
us
to
observe
different
global
mean
large
populations.
These
describe
all-to-all
networks
quadratic
integrate-and-fire
spiking
neurons.
addition,
one
these
considers
influence
synaptic
adaptation
mechanism
macroscopic
dynamics.
We
show
how
both
are
related
through
a
parameter
and
evolution
when
switching
from
model
other
by
varying
that
parameter.
Interestingly,
have
detected
three
main
dynamical
regimes
in
models:
R\"ossler-type
(funnel
type),
bursting-type,
spiking-like
(oscillator-type)
This
result
opens
question
which
regime
is
most
suitable
for
realistic
simulations
shows
possibility
emergence
chaotic
very
weak.
Journal of Computational Neuroscience,
Год журнала:
2024,
Номер
52(3), С. 207 - 222
Опубликована: Июль 5, 2024
Abstract
We
derive
a
next
generation
neural
mass
model
of
population
quadratic-integrate-and-fire
neurons,
with
slow
adaptation,
and
conductance-based
AMPAR,
GABAR
nonlinear
NMDAR
synapses.
show
that
the
Lorentzian
ansatz
assumption
can
be
satisfied
by
introducing
piece-wise
polynomial
approximation
voltage-dependent
magnesium
block
current.
study
dynamics
resulting
system
for
two
example
cases
excitatory
cortical
neurons
inhibitory
striatal
neurons.
Bifurcation
diagrams
are
presented
comparing
different
dynamical
regimes
as
compared
to
case
linear
currents,
along
sample
comparison
simulation
time
series
demonstrating
possible
oscillatory
solutions.
The
omission
nonlinearity
currents
results
in
shift
range
(and
disappearance)
constant
high
firing
rate
regime,
modulation
amplitude
frequency
power
spectrum
oscillations.
Moreover,
action
is
seen
state-dependent
have
opposite
effects
depending
on
type
involved
level
input
received.
serve
computationally
efficient
building
whole
brain
network
models
investigating
differential
types
synapses
under
neuromodulatory
influence
or
receptor
specific
malfunction.
Physical review. E,
Год журнала:
2024,
Номер
110(2)
Опубликована: Авг. 20, 2024
Continuous
rate-based
neural
networks
have
been
widely
applied
to
modeling
the
dynamics
of
cortical
circuits.
However,
neurons
in
brain
exhibit
irregular
spiking
activity
with
complex
correlation
structures
that
cannot
be
captured
by
mean
firing
rate
alone.
To
close
this
gap,
we
consider
a
framework
for
activity,
called
moment
network,
which
naturally
generalizes
models
second-order
moments
and
can
accurately
capture
statistics
networks.
We
propose
an
efficient
numerical
method
allows
rapid
evaluation
mappings
neuronal
activations
without
solving
underlying
Fokker-Planck
equation.
This
simulation
coupled
interactions
variability
large-scale
circuits
while
retaining
advantage
analytical
tractability
continuous
models.
demonstrate
how
network
explain
range
phenomena
including
diverse
Fano
factor
quenched
disorder
emergence
oscillatory
excitation-inhibition
delay.
Communications in Nonlinear Science and Numerical Simulation,
Год журнала:
2024,
Номер
131, С. 107844 - 107844
Опубликована: Янв. 12, 2024
In
this
work,
we
introduce
a
novel
reduced
order
model
technique,
based
on
the
Proper
Orthogonal
Decomposition
method,
for
dynamical
systems
with
multiple
timescales.
The
main
ideas
are
to
retain
structure
of
original
model,
which
is
lost
in
POD
procedure,
while
producing
competitive
reduction
number
equations
and
computational
time,
determine
best
system
automatically,
via
data-driven
analysis
data.
For
these
techniques,
present
some
numerical
tests
various
behaviors
three
different
neural
network
models
timescales,
support
use
new
methods.
