Research Square (Research Square),
Journal Year:
2022,
Volume and Issue:
unknown
Published: Sept. 12, 2022
Abstract
This
paper
investigates
the
bursting
oscillations
of
a
externally
and
parametrically
forced
Rayleigh-Duffing
oscillator,
in
which
three
intermittent
types
one
normal
type,
namely
“supHopf/supHopf-supHopf/supHopf”
bursting,
“fold/Homoclinic-Homoclinic/supHopf”
“fold/Homoclinic-supHopf/supHopf”
“fold/Homoclinic”
are
analyzed
respectively.
Recognizing
excitations
as
slow-varying
state
variables,
corresponding
autonomous
system
can
be
exhibited
bifurcation
characteristics
is
briefly
investigated,
particular,
Homoclinic
by
means
Melnikov
criterion.
shows
that
dynamical
behaviors
excited
oscillator
touchy
to
chosen
parameters,
different
parameter
conditions
lead
distinct
structures
result
trajectory
approaching
stable
attractors
appearance
forms.
Our
study
increases
variousness
deepens
cognition
generation
mechanism
dynamics.
Lastly,
accuracy
analysis
presented
this
fully
vindicated
numerical
simulations.
Journal of Nonlinear Science,
Journal Year:
2024,
Volume and Issue:
34(3)
Published: April 11, 2024
Abstract
We
study
pairs
of
symmetrically
coupled,
identical
Lengyel-Epstein
oscillators,
where
the
coupling
can
be
through
both
fast
and
slow
variables.
find
a
plethora
strong
symmetry
breaking
rhythms,
in
which
two
oscillators
exhibit
qualitatively
different
oscillations,
their
amplitudes
differ
by
as
much
an
order
magnitude.
Analysis
folded
singularities
coupled
system
shows
that
key
node,
located
off
axis,
is
primary
mechanism
responsible
for
breaking.
Passage
neighborhood
this
node
result
splitting
between
one
constrained
to
remain
small
amplitude,
while
other
makes
large-amplitude
oscillation
or
mixed-mode
oscillation.
The
analysis
also
reveals
organizing
center
parameter
space,
undergoes
asymmetric
canard
explosion,
oscillator
exhibits
sequence
limit
cycle
canards,
over
interval
values
centered
at
explosion
point,
executes
amplitude
oscillations.
Other
impact
properties
rhythms.
contrast
these
rhythms
with
are
close
symmetric
states,
such
in-phase
anti-phase
In
addition
we
mediates
transition
from
small-amplitude,
oscillations
large-amplitude,
SIAM Journal on Applied Dynamical Systems,
Journal Year:
2023,
Volume and Issue:
22(2), P. 1383 - 1422
Published: June 26, 2023
.In
this
paper,
we
use
geometric
singular
perturbation
theory
and
blowup
as
our
main
technical
tool
to
study
the
mixed-mode
oscillations
(MMOs)
that
occur
in
two
coupled
FitzHugh–Nagumo
units
with
symmetric
repulsive
coupling.
In
particular,
demonstrate
MMOs
model
are
not
due
generic
folded
singularities,
but
rather
singularities
at
a
cusp
–
fold
of
critical
manifold.
Using
blowup,
determine
number
small-amplitude
(SAOs)
analytically,
showing–-as
for
nodes–-that
they
determined
by
Weber
equation
ratio
eigenvalues.
We
also
show
undergoes
saddle-node
bifurcation
desingularized
reduced
problem,
which–-although
resembling
(type
II)
level–-also
occurs
on
cusp,
fold.
is
associated
emergence
an
invariant
cylinder,
onset
SAOs,
well
SAOs
increasing
amplitude.
relate
findings
numerical
computations
find
excellent
agreement.Keywordsmixed-mode
oscillationscuspfolded
singularitiescanardsblowupgeometric
theoryMSC
codes34C1534D1537E17
The European Physical Journal Plus,
Journal Year:
2023,
Volume and Issue:
138(12)
Published: Dec. 16, 2023
Abstract
In
this
study,
we
explore
the
emergence
of
amplitude-modulated
bursting
in
a
multi-frequency
excited
Liénard
system.
Our
investigation
reveals
that
system
exhibits
distinct
patterns
for
lower
damping
value
and
varying
forcing
frequencies
Conversely,
higher
with
frequencies,
intricate
accompanied
by
variety
oscillations.
The
discrete
arise
as
consequence
dynamic
interplay
slowly
multiple
frequency
within
To
gain
deeper
understanding
these
dynamics,
conduct
comprehensive
stability
bifurcation
analysis.
Furthermore,
to
validate
our
findings,
perform
numerical
simulations
corroborate
results
through
real-time
hardware
circuit
experiment.
This
interdisciplinary
approach
provides
valuable
insights
into
behavior
under
excitation,
shedding
light
on
its
complex
dynamical
characteristics.
