Physica Scripta,
Journal Year:
2023,
Volume and Issue:
99(1), P. 015204 - 015204
Published: Dec. 6, 2023
Abstract
Multiple
timescale
effects
can
be
reflected
bursting
oscillations
in
many
classical
nonlinear
oscillators.
In
this
work,
we
are
concerned
about
the
induced
by
two
damped
Helmholtz-Rayleigh-Duffing
oscillator
(written
as
DHRDO
for
short)
excited
slow-changing
parametrical
and
external
forcings.
By
using
trigonometric
function
variation
authenticating
slow
excitations
a
slowly
varying
state
variable,
time-varying
rewritten
new
time-invariant
system.
Then,
critical
conditions
of
some
typical
bifurcations
presented
bifurcation
theory.
With
help
analyses,
six
patterns,
i.e.,
‘Hopf/Hopf-Hopf/Hopf’
bursting,
‘fold/Homoclinic-Hopf/Hopf’
‘fold/Homoclinic/Hopf’
‘Hopf/fold/Homoclinic/Hopf’
‘Hopf/Homoclinic/Homoclinic/Hopf’
‘Hopf/Homoclinic/Hopf-Hopf/Homoclinic/Hopf’
explored
slow/fast
decomposition
method
other
techniques.
Our
findings
provide
different
forms
oscillation
modes
well
patterns.
addition,
use
numerical
simulation
to
prove
correctness
theoretical
analyses.
Mathematics,
Journal Year:
2023,
Volume and Issue:
11(7), P. 1690 - 1690
Published: April 1, 2023
In
this
paper,
the
bursting
oscillation
phenomenon
in
coupled
systems
with
two
time
scales
is
introduced.
Firstly,
several
types
of
bifurcation
are
briefly
introduced:
fold
bifurcation,
Hopf
limit
cycle
homoclinic
etc.
The
oscillations
system
excitation
terms
and
delay
considered.
Secondly,
some
simple
introduced,
such
as
fold/fold
bursting,
fold/supHopf
subHopf/subHopf
fold/LPC
Hopf/LPC
fold/homoclinic
Hopf/homoclinic
At
same
time,
also
has
complex
oscillations,
asymmetric
delayed
hysteresis
loop,
Finally,
practical
applications
dynamic
vibration
absorbers
nonlinear
energy
harvesting
technology,
Physica Scripta,
Journal Year:
2023,
Volume and Issue:
98(11), P. 115216 - 115216
Published: Sept. 25, 2023
Abstract
The
study
of
bursting
oscillations
induced
by
frequency-domain
multiscale
effect
is
one
the
key
scientific
issues
in
theoretical
analysis
circuit
systems.
In
this
paper,
we
explore
mechanism
a
van
der
Pol-Duffing-Jerk
oscillator
with
slow-changing
parametric
and
external
periodic
excitations.
Three
typical
modes,
namely,
left-right
symmetric
‘subHopf/fold
limit
cycle’
bursting,
origin
‘fold/fold
‘fold/subHopf/fold
are
presented.
slowly
changing
excitation
treated
as
generalized
state
variable
to
analyze
influence
on
critical
manifolds
equilibria
bifurcations.
conditions
fold
Hopf
bifurcations
computed
using
bifurcation
theory,
two
structures
obtained
according
position
different
curves.
Based
analysis,
investigate
appearance
dynamicalal
evolutions
variation
amplitude.
It
pointed
that
not
only
but
also
distance
between
points
can
affect
patterns.
We
find
directions
trajectories
types
sensitive
values
Furthermore,
reveal
overlapping
(
θ
,
x
)-plane
onto
corresponding
structures.
Numerical
simulations
presented
prove
correctness
our
study.
