In
this
work,
we
present
a
new
4-D
highly
chaotic
two-scroll
system
with
hyperbola
of
equilibrium
points.
The
mathematical
model
the
is
obtained
by
modifying
dynamics
Sprott-C
(1994).
First,
study
dynamic
properties
such
as
phase
portraits,
Lyapunov
exponents,
Kaplan-Yorke
dimension,
and
Since
has
infinitely
many
number
points,
it
hidden
attractors.
Next,
carry
out
bifurcation
analysis
using
diagrams
exponents.
We
also
investigate
offset-boosting
control
system.
Furthermore,
demonstrate
presence
multistability
coexisting
attractors
in
newly
introduced
Finally,
design
an
electronic
circuit
for
MultiSim
14.2,
which
useful
practical
applications
proposed
Chaos An Interdisciplinary Journal of Nonlinear Science,
Год журнала:
2025,
Номер
35(4)
Опубликована: Апрель 1, 2025
The
discrete
memristive
chaotic
system
is
characterized
by
discontinuous
phase
trajectories.
To
address
the
limitations
of
ideal
integer-order
memristor
model,
which
fails
to
accurately
reflect
characteristics
practical
devices,
this
study
introduces
a
Grunwald–Letnikov
type
quadratic
trivariate
fractional
model
enhance
nonlinearity
and
memory
properties
memristors.
Simultaneously,
it
demonstrated
that
our
satisfies
essential
generalized
memristor.
Based
on
newly
proposed
memristor,
new
four-dimensional
hyperchaotic
constructed
coupling
non-uniform,
incommensurate-order
This
advances
structure
existing
systems
provides
more
flexible
strategy
for
optimizing
effects.
dynamical
behaviors
are
analyzed
using
attractor
diagrams,
bifurcation
Lyapunov
exponent
spectra,
permutation
entropy
complexity.
Numerical
simulation
results
show
can
exhibit
larger
region,
higher
complexity,
rich
multistable
behaviors,
such
as
coexistence
infinitely
symmetric
attractors
enhanced
offset.
Additionally,
impact
parameter
system’s
behavior
revealed,
with
order
serving
tunable
control
variable
dynamically
reconfigures
paths
needed,
thereby
enabling
transitions
between
hyperchaotic,
chaotic,
non-chaotic
states.
Furthermore,
circuit
was
designed
validate
numerical
results.
Chaos Theory and Applications,
Год журнала:
2024,
Номер
6(2), С. 144 - 151
Опубликована: Май 25, 2024
In
the
present
work,
an
interesting
mini-review
of
hidden
attractors
in
dynamical
systems
with
associated
nonlinear
functions
is
carried
out.
Chaotic
often
possess
due
to
their
inherent
complexity.
These
can
arise
various
mathematical
models,
such
as
Lorenz
system,
Rössler
or
Chua's
circuit.
The
identification
and
comprehension
broaden
our
understanding
complex
provide
new
directions
for
future
study
technological
development.
discovery
characterization
chaotic
have
profound
implications
scientific
disciplines,
including
physics,
biology,
engineering.
Chaos An Interdisciplinary Journal of Nonlinear Science,
Год журнала:
2024,
Номер
34(11)
Опубликована: Ноя. 1, 2024
The
memory
effects
of
the
memristors
in
nonlinear
systems
make
generate
complicated
dynamics,
which
inspires
development
applications
memristors.
In
this
article,
model
discrete
memristive
with
generalized
Ohm’s
law
is
introduced,
where
classical
a
linear
relationship
between
voltage
and
current,
relationship.
To
illustrate
rich
dynamics
model,
dynamical
behavior
three
types
maps
memristances
investigated,
cubic
function
representing
kind
used,
simplified
characteristic
famous
tunnel
diode.
existence
attractors
one
or
two
positive
Lyapunov
exponents
(corresponding
to
chaotic
hyperchaotic
dynamics)
obtained,
coexistence
(infinitely)
many
observable.
A
hardware
device
constructed
implement
these
analog
signals
are
experimentally
acquired.
Chaos An Interdisciplinary Journal of Nonlinear Science,
Год журнала:
2024,
Номер
34(11)
Опубликована: Ноя. 1, 2024
In
recent
years,
the
introduction
of
memristors
in
discrete
chaotic
map
has
attracted
much
attention
due
to
its
enhancement
complexity
and
controllability
maps,
especially
fields
secure
communication
random
number
generation,
which
have
shown
promising
applications.
this
work,
a
three-dimensional
memristive
hyperchaotic
(3D-DMCHM)
based
on
cosine
memristor
is
constructed.
First,
we
analyze
fixed
points
their
stability,
showing
that
can
either
linear
point
or
none
at
all,
stability
depends
parameters
initial
state
map.
Then,
phase
diagrams,
bifurcation
Lyapunov
exponents,
timing
attractor
basins
are
used
complex
dynamical
behaviors
3D-DMCHM,
revealing
3D-DMCHM
enters
into
through
period-doubling
path,
some
special
phenomena
such
as
multi-layer
differentiation,
multi-amplitude
control,
offset
boosting
also
observed.
particular,
with
change
conditions,
there
exists
an
only
homogeneous
hidden
attractors
mixed
coexistence
attractors.
Finally,
confirmed
high
tests
successfully
implemented
it
using
digital
signal
processing
circuit,
demonstrating
hardware
feasibility.
