Mathematics,
Journal Year:
2024,
Volume and Issue:
12(24), P. 3948 - 3948
Published: Dec. 15, 2024
Cryptography
is
one
of
the
most
important
branches
information
security.
ensures
secure
communication
and
data
privacy,
it
has
been
increasingly
applied
in
healthcare
related
areas.
As
a
significant
cryptographic
method,
Hill
cipher
attracted
attention
from
experts
scholars.
To
enhance
security
traditional
(THC)
expand
its
application
medical
image
encryption,
novel
dynamic
with
Arnold
scrambling
technique
(DHCAST)
proposed
this
work.
Unlike
THC,
DHCAST
uses
time-varying
matrix
as
secret
key,
which
greatly
increases
new
successfully
images
encryption.
In
addition,
method
employs
Zeroing
Neural
Network
(ZNN)
decryption
to
find
inversion
key
(TVIKM).
order
efficiency
ZNN
for
solving
TVIKM,
fuzzy
zeroing
neural
network
(NFZNN)
model
constructed,
convergence
robustness
NFZNN
are
validated
by
both
theoretical
analysis
experiment
results.
Simulation
experiments
show
that
time
about
0.05
s,
while
(TZNN)
2
means
speed
400
times
TZNN
model.
Moreover,
Peak
Signal
Noise
Ratio
(PSNR)
Number
Pixel
Change
Rate
(NPCR)
algorithm
reach
9.51
99.74%,
respectively,
effectively
validates
excellent
encryption
quality
attack
prevention
ability.
Chaos An Interdisciplinary Journal of Nonlinear Science,
Journal Year:
2025,
Volume and Issue:
35(1)
Published: Jan. 1, 2025
Memristors
are
commonly
used
to
introduce
various
chaotic
systems
and
can
be
enhance
their
characteristics.
However,
due
the
strict
construction
conditions
of
Hamiltonian
systems,
there
has
been
limited
research
on
development
memristive
conservative
(MHCCSs).
In
this
work,
a
method
for
constructing
three-terminal
memristors
is
proposed,
incorporated
into
system,
resulting
in
class
n-D
MHCCS.
Based
method,
we
model
4D
MHCCS
as
standard
detailed
dynamic
analysis.
The
analysis
reveals
that
exhibits
complex
behaviors,
including
conservativeness,
symmetry,
chaos
depending
parameters,
extreme
multistability,
under
wide
parameter
range.
shows
not
only
retains
favorable
characteristics
system
but
also
more
nonlinear
dynamics
incorporation
memristors,
thereby
further
enhancing
its
Furthermore,
pseudo-random
number
generator
based
excellent
randomness
terms
NIST
test.
Finally,
physical
realizability
verified
through
Field
Programmable
Gate
Array
experiments.
This
study
demonstrates
constructed
MHCCSs
good
entropy
source
applied
embedded
secure
communication,
cryptographic
generator.
Fractal and Fractional,
Journal Year:
2025,
Volume and Issue:
9(2), P. 115 - 115
Published: Feb. 13, 2025
Memristor-based
fractional-order
chaotic
systems
can
record
information
from
the
past,
present,
and
future,
describe
real
world
more
accurately
than
integer-order
systems.
This
paper
proposes
a
novel
memristor
model
verifies
its
characteristics
through
pinched
loop
(PHL)
method.
Subsequently,
new
memristive
Hopfield
neural
network
(4D-FOMHNN)
is
introduced
to
simulate
induced
current,
accompanied
by
Caputo’s
definition
of
fractional
order.
An
Adomian
decomposition
method
(ADM)
employed
for
system
solution.
By
varying
parameters
order
4D-FOMHNN,
rich
dynamic
behaviors
including
transient
chaos,
coexistence
attractors
are
observed
using
methods
such
as
bifurcation
diagrams
Lyapunov
exponent
analysis.
Finally,
proposed
FOMHNN
implemented
on
field-programmable
gate
array
(FPGA),
oscilloscope
observation
results
consistent
with
MATLAB
numerical
simulation
results,
which
further
validate
theoretical
analysis
provide
basis
application
in
field
encryption.
Mathematics,
Journal Year:
2025,
Volume and Issue:
13(2), P. 201 - 201
Published: Jan. 9, 2025
In
this
paper,
we
first
design
the
corresponding
integration
algorithm
and
matlab
program
according
to
Gauss–Legendre
principle.
Then,
select
Lorenz
system,
Duffing
hidden
attractor
chaotic
system
Multi-wing
for
dynamics
analysis.
We
apply
integral
Runge–Kutta
solution
of
dissipative
systems
time
analyze
compare
differences
between
two
algorithms.
propose
a
basin
attraction
estimation
method
based
on
Lyapunov
exponent
decision
criterion
method.
This
can
better
obtain
region
distinguish
pseudo-attractor,
which
provides
new
way
Finally,
use
FPGA
technology
realize
four
algorithm.
Mathematics,
Journal Year:
2025,
Volume and Issue:
13(5), P. 726 - 726
Published: Feb. 24, 2025
In
comparison
with
dissipative
chaos,
conservative
chaos
is
better
equipped
to
handle
the
risks
associated
reconstruction
of
phase
space
due
absence
attractors.
This
paper
proposes
a
novel
five-dimensional
(5D)
memristive
hyperchaotic
system
(CMHS),
by
incorporating
memristors
into
four-dimensional
(4D)
chaotic
(CCS).
We
conducted
comprehensive
analysis,
using
Lyapunov
exponent
diagrams,
bifurcation
portraits,
equilibrium
points,
and
spectral
entropy
maps
thoroughly
verify
system’s
properties.
The
exhibited
characteristics
such
as
hyperchaos
multi-stability
over
an
ultra-wide
range
parameters
initial
values,
accompanied
transient
quasi-periodic
phenomena.
Subsequently,
pseudorandom
sequences
generated
new
were
tested
demonstrated
excellent
performance,
passing
all
tests
set
National
Institute
Standards
Technology
(NIST).
final
stage
research,
image-encryption
application
based
on
5D
CMHS
was
proposed.
Through
security
feasibility
algorithm
confirmed.
Physical review. E,
Journal Year:
2025,
Volume and Issue:
111(3)
Published: March 3, 2025
Although
neuron
models
have
been
well
studied
for
their
rich
dynamics
and
biological
properties,
limited
research
has
done
on
the
complex
geometries
that
emerge
from
basins
of
attraction
basin
boundaries
multistable
systems.
In
this
paper,
we
investigate
geometrical
properties
strange
attractors,
four-dimensional
basins,
fractal
an
asymmetrically
electrically
coupled
system
two
identical
nonchaotic
Rulkov
neurons.
We
discover
a
quasimultistability
in
emerging
existence
chaotic
spiking-bursting
pseudo-attractor,
classify
quantify
system's
attraction,
which
are
found
to
geometries.
Using
method
uncertainty
exponents,
also
find
exhibits
extreme
final
state
sensitivity,
results
dynamical
could
important
applications
neurobiology.
Mathematics,
Journal Year:
2024,
Volume and Issue:
13(1), P. 128 - 128
Published: Dec. 31, 2024
In
contrast
to
previous
research
that
has
primarily
focused
on
distance
synchronization
of
states
in
chaotic
systems,
shape
emphasizes
the
geometric
attractors
two
systems.
Diverging
from
existing
work
synchronization,
this
paper
introduces
application
adaptive
control
methods
achieve
asymptotic
for
first
time.
By
designing
an
controller
using
proposed
rule,
response
system
under
is
able
attain
with
drive
system.
This
method
capable
achieving
models
parameters
requiring
estimation
both
and
The
approach
remains
effective
even
presence
uncertainties
model
parameters.
presents
relevant
theorems
proofs,
simulation
results
demonstrate
effectiveness
synchronization.
Due
pseudo-random
nature
systems
their
extreme
sensitivity
initial
conditions,
which
make
them
suitable
information
encryption,
a
novel
channel-integrated
image
encryption
scheme
proposed.
leverages
generate
sequences,
are
then
used
shuffling,
scrambling,
diffusion
processes.
Simulation
experiments
algorithm
achieves
exceptional
performance
terms
correlation
metrics
entropy,
competitive
value
7.9971.
Robustness
further
validated
through
key
space
analysis,
yielding
10210×2512,
as
well
visual
tests,
including
center
edge
cropping.
confirm
context
encryption.