Complex Variables and Elliptic Equations,
Journal Year:
2024,
Volume and Issue:
unknown, P. 1 - 33
Published: Oct. 21, 2024
A
diffusive
phytoplankton–zooplankton–fish
model
with
toxin
and
Crowley–Martin
functional
response
is
considered.
By
the
global
bifurcation
theorem
fixed
point
index
theory,
existence
multiplicity
of
coexistence
states
are
discussed.
Secondly,
we
investigate
from
a
double
eigenvalue
by
virtue
Lyapunov–Schmidt
procedure
implicit
function
theorem.
Then,
effect
large
k,
which
measures
magnitude
interference
among
zooplankton,
studied
means
combination
perturbation
theory
topological
degree
theory.
The
results
indicate
that
if
k
enough,
this
system
has
only
unique
asymptotically
stable
state
provided
properly
small
maximal
growth
rates
phytoplankton
fish
suitably
large.
Furthermore,
extinction
permanence
time-dependent
determined
comparison
principle.
Finally,
make
some
numerical
simulations
to
validate
complement
theoretical
analysis
exhibit
critical
role
toxin,
spatial
diffusion
zooplankton
in
dynamics.
findings
suggest
spatiotemporal
dynamics
systems
richer
more
complex,
have
significant
effects
on
species.
Fractal and Fractional,
Journal Year:
2024,
Volume and Issue:
8(5), P. 264 - 264
Published: April 27, 2024
In
order
to
stop
and
reverse
land
degradation
curb
the
loss
of
biodiversity,
United
Nations
2030
Agenda
for
Sustainable
Development
proposes
combat
desertification.
this
paper,
a
fractional
vegetation–water
model
in
an
arid
flat
environment
is
studied.
The
pattern
behavior
much
more
complex
than
that
integer
order.
We
study
stability
Turing
instability
system,
as
well
Hopf
bifurcation
α,
obtain
region
parameter
space.
According
amplitude
equation,
different
types
stationary
mode
discoveries
can
be
obtained,
including
point
patterns
strip
patterns.
Finally,
results
numerical
simulation
theoretical
analysis
are
consistent.
find
some
novel
fractal
environment.
When
diffusion
coefficient,
d,
changes
other
parameters
remain
unchanged,
structure
from
stripes
spots.
parameter,
β,
changes,
becomes
stable
not
easy
destroy.
research
provide
new
ideas
prevention
control
desertification
vegetation
Mathematical Methods in the Applied Sciences,
Journal Year:
2024,
Volume and Issue:
unknown
Published: Sept. 11, 2024
In
semiarid
areas,
the
positive
feedback
effect
of
vegetation
and
soil
moisture
plays
an
indispensable
role
in
water
absorption
process
plant
roots.
addition,
can
absorb
through
nonlocal
interaction
Therefore,
this
article,
we
consider
how
interactions
between
cross‐diffusion
delay
affect
growth.
Through
mathematical
analysis,
conditions
for
occurrence
Turing
pattern
water–vegetation
model
are
obtained.
Meanwhile,
using
multi‐scale
analysis
method,
amplitude
equation
near
bifurcation
boundary
is
By
analyzing
stability
equation,
appearance
patterns
such
as
stripes,
hexagons,
mixtures
stripes
hexagons
determined.
Some
numerical
simulations
given
to
illustrate
analytical
results,
especially
evolution
processes
depicted
under
different
parameters.
Mathematical Biosciences & Engineering,
Journal Year:
2024,
Volume and Issue:
21(3), P. 4521 - 4553
Published: Jan. 1, 2024
<abstract><p>The
vegetation
pattern
generated
by
aeolian
sand
movements
is
a
typical
type
of
patterns
in
arid
and
semi-arid
areas.
This
paper
presents
vegetation-sand
model
with
nonlocal
interaction
characterized
an
integral
term
kernel
function.
The
instability
the
Turing
was
analyzed
conditions
stable
occurrence
were
obtained.
At
same
time,
multiple
scales
method
applied
to
obtain
amplitude
equations
at
critical
value
bifurcation.
spatial
distributions
under
different
delays
obtained
numerical
simulation.
results
revealed
that
biomass
increased
as
intensity
decreased
or
distance
increased.
We
demonstrated
between
crucial
mechanism
for
forming
patterns,
which
provides
theoretical
basis
preserving
restoring
vegetation.</p></abstract>
Applicable Analysis,
Journal Year:
2024,
Volume and Issue:
unknown, P. 1 - 29
Published: July 7, 2024
In
this
paper,
we
have
proposed
a
reaction-diffusion
SIRS
epidemic
model
with
general
incidence
function
f(S,I)
in
spatially
heterogeneous
environment.
For
model,
derive
the
basic
reproduction
number
R0
and
establish
results
of
threshold
dynamics
respect
to
R0.
Specifically,
disease-free
equilibrium
is
globally
asymptotically
stable
when
R0<1,
while
disease
persists
if
R0>1.
Especially,
under
homogeneous
condition,
admits
unique
steady
state,
which
some
assumptions
Finally,
take
Beddington-DeAngelis-type
perform
numerical
simulations
illustrate
solutions
as
parameters
are
varied.
Communications on Pure & Applied Analysis,
Journal Year:
2024,
Volume and Issue:
23(3), P. 356 - 382
Published: Jan. 1, 2024
In
this
paper,
a
diffusive
mussel-algae
model
subject
to
Neumann
boundary
conditions
is
considered.
The
main
criteria
for
the
stability
and
instability
of
constant
steady-state
solutions
are
presented.
Then,
by
maximum
principle,
Hölder
inequality
Poincar$
\acute{e}
$
inequality,
priori
estimates
some
characters
positive
given
nonexistence
non-constant
corresponding
elliptic
system
investigated.
Moreover,
bifurcations
at
both
simple
double
eigenvalues
intensively
particular,
implicit
function
theorem
techniques
space
decomposition
used
get
local
structure
from
eigenvalues.
Next,
our
analysis
focuses
on
providing
specific
that
can
determine
bifurcation
direction
extend
global
one.
Finally,
numerical
results
presented
provide
support
complement
theoretical
findings.
More
specifically,
under
various
parameters,
evolution
processes
in
spatial
patterns
illustrated.
