Dynamic behavior of a two-mass nonlinear fractional-order vibration system
Frontiers in Physics,
Год журнала:
2024,
Номер
12
Опубликована: Сен. 4, 2024
The
two-mass
nonlinear
vocal
cord
vibration
system
(VCVS)
serves
as
a
mechanical
representation
of
the
fundamental
vocalization
process.
Traditional
models
VCVS,
which
are
based
on
integer-order
dynamics,
often
overlook
impact
memory
effects.
To
address
this
limitation
and
enhance
accuracy
simulations,
study
incorporates
effects
vibrations
by
integrating
Grunwald–Letnikov
fractional
derivative
into
VCVS
framework.
Initially,
high-precision
computational
scheme
is
formulated
for
fractional-order
VCVS.
Subsequently,
model
undergoes
comprehensive
series
numerical
simulations
to
investigate
its
dynamic
characteristics.
findings
reveal
that
dynamics
exhibit
significantly
higher
complexity
compared
conventional
models,
with
emergence
novel
chaotic
behaviors
were
previously
unobserved.
Язык: Английский
Numerical simulation of chaotic dynamics in a fractional-order vibration model with Grünwald-Letnikov fractional derivative
Networks and Heterogeneous Media,
Год журнала:
2025,
Номер
20(2), С. 625 - 647
Опубликована: Янв. 1, 2025
Язык: Английский
Hopf bifurcation in a predator-prey model under fuzzy parameters involving prey refuge and fear effects
AIMS Mathematics,
Год журнала:
2024,
Номер
9(9), С. 23945 - 23970
Опубликована: Янв. 1, 2024
<p>In
ecology,
the
most
significant
aspect
is
that
interactions
between
predators
and
prey
are
extremely
complicated.
Numerous
experiments
have
shown
both
direct
predation
fear
induced
in
by
presence
of
lead
to
a
reduction
density
predator-prey
interactions.
In
addition,
suitable
shelter
can
effectively
stop
from
attacking
as
well
support
persistence
population.
There
has
been
less
exploration
effects
not
only
but
also
refuge
factors
on
dynamics
predator
this
paper,
we
unveil
several
conclusions
about
system
with
fuzzy
parameters,
considering
cost
two
species
effect
one
predator.
As
first
step
investigation,
boundedness
non-negativity
solutions
put
forward.
Using
Jocabian
matrix
Lyapunov
function
methods,
further
analyze
existence
stability
available
equilibria
Hopf
bifurcation,
parameter
bifurcation
observed
applying
normal
form
theory.
Finally,
numerical
simulations
help
us
better
understand
model,
which
some
interesting
chaotic
phenomena
exhibited.</p>
Язык: Английский
Innovative analysis to the time-fractional q-deformed tanh-Gordon equation via modified double Laplace transform method
Open Physics,
Год журнала:
2024,
Номер
22(1)
Опубликована: Янв. 1, 2024
Abstract
In
this
study,
we
introduce
an
efficient
analysis
of
a
new
equation,
termed
the
time-fractional
q
q
-deformed
tanh-Gordon
equation
(TGE),
which
is
fractional
form
TGE
that
was
recently
introduced
by
Ali
and
Alharbi.
This
represents
significant
advancement
in
field
mathematical
physics,
due
to
its
applications
many
fields
including
superconductivity
fiber
optics.
It
has
condensed
matter
physics
modeling
physical
systems
exhibit
violated
symmetries.
We
investigate
using
Caputo
derivative
capture
non-local
memory
effects,
means
they
can
take
into
account
entire
history
function
rather
than
just
current
value.
Notably,
not
been
previously
solved
form,
making
our
approach
pioneering
analysis.
solve
utilizing
modified
double
Laplace
transform
method,
considered
semi-analytical
technique
combines
with
Adomian
polynomials
enable
us
extract
nonlinear
terms.
method
renowned
for
efficacy
handling
differential
equations;
evident
from
results
obtained
tables
comparing
analytical
solution
approximate
obtained,
as
well
calculating
absolute
error
between
them.
examine
existence
uniqueness
Schaefer’s
fixed-point
theorem.
Different
graphs
2D
3D
are
presented
clarify
effect
different
parameters
on
behavior
solution,
specially
operator
deformation
parameter
.
Язык: Английский
Dynamical Behavior of the Fractional BBMB Equation on Unbounded Domain
Fractal and Fractional,
Год журнала:
2024,
Номер
8(7), С. 383 - 383
Опубликована: Июнь 28, 2024
The
fractional-order
Benjamin-Bona-Mahony-Burgers
(BBMB)
equation
is
a
generalization
of
the
classical
BBMB
equation.
It’s
dynamic
behaviors
much
more
complex
than
that
corresponding
integer-order
main
purpose
this
paper
to
explore
equations
by
using
Fourier
spectral
method.
Firstly,
numerical
solution
compared
with
exact
solution.
It
proved
proposed
method
effective
and
high
precision
for
solving
spatial
fractional
order
Then,
some
dynamical
are
obtained
present
method,
novel
fractal
waves
on
unbounded
domain
shown.
Язык: Английский
Fourier spectral method for the fractional-in-space coupled Whitham–Broer–Kaup equations on unbounded domain
Open Physics,
Год журнала:
2024,
Номер
22(1)
Опубликована: Янв. 1, 2024
Abstract
Due
to
the
nonlocality
of
fractional
derivatives,
numerical
methods
for
solving
nonlinear
Whitham–Broer–Kaup
(WBK)
equations
are
time-consuming
and
tedious.
Therefore,
it
is
a
research
hotspot
explore
solution
fractional-order
WBK
equation.
The
main
goal
this
study
provide
an
efficient
method
fractional-in-space
coupled
on
unbounded
domain
discover
some
novel
anomalous
transmission
behaviors.
First,
compared
with
exact
determine
validity
proposed
large
time-spatial
domain.
Then,
waves
propagation
equation
numerically
simulated,
influence
different
derivatives
wave
researched.
Some
behaviors
shown.
Язык: Английский
Numerical simulation and theoretical analysis of pattern dynamics for the fractional-in-space Schnakenberg model
Frontiers in Physics,
Год журнала:
2024,
Номер
12
Опубликована: Сен. 11, 2024
Effective
exploration
of
the
pattern
dynamic
behaviors
reaction–diffusion
models
is
a
popular
but
difficult
topic.
The
Schnakenberg
model
famous
system
that
has
been
widely
used
in
many
fields,
such
as
physics,
chemistry,
and
biology.
Herein,
we
explore
stability,
Turing
instability,
weakly
non-linear
analysis
model;
further,
dynamics
fractional-in-space
was
simulated
numerically
based
on
Fourier
spectral
method.
patterns
under
different
parameters,
initial
conditions,
perturbations
are
shown,
including
target,
bar,
dot
patterns.
It
found
not
only
splits
spreads
from
bar
to
spot
also
forms
broken
connections
pattern.
effects
fractional
Laplacian
operator
shown.
In
most
cases,
diffusion
rate
higher
than
integer
model.
By
comparing
with
methods
literature,
it
were
consistent
results
obtained
other
numerical
indicating
method
can
be
effectively
Some
novel
demonstrated.
Язык: Английский