International Journal of Bifurcation and Chaos,
Год журнала:
2024,
Номер
34(05)
Опубликована: Апрель 1, 2024
In
this
paper,
we
investigate
the
spatiotemporal
dynamics
in
a
diffusive
two-species
system
with
taxis
term
and
general
functional
response,
which
means
directional
movement
of
one
species
upward
or
downward
other
one.
The
stability
positive
equilibrium
existences
Turing
bifurcation,
Turing–Hopf
bifurcation
Turing–Turing
are
investigated.
An
algorithm
for
calculating
normal
form
induced
by
another
parameter
is
derived.
Furthermore,
apply
our
theoretical
results
to
cooperative
Lotka–Volterra
predator–prey
prey-taxis.
For
system,
stable
becomes
unstable
taxis-driven
instability,
impossible
without
taxis.
prey-taxis,
dynamical
classification
near
point
clearly
described.
Near
point,
there
spatially
inhomogeneous
steady-state
solution,
homogeneous/nonhomogeneous
periodic
solution
pattern
transitions
from
state
Discrete and Continuous Dynamical Systems - B,
Год журнала:
2023,
Номер
29(1), С. 426 - 458
Опубликована: Июнь 2, 2023
In
this
paper,
a
water-vegetation
model
with
the
infiltration
feedback
effect
is
considered.
Firstly,
through
linear
stability
analysis,
we
get
parameter
area
where
Turing
instability
can
occur.
Next,
by
maximum
principle,
priori
estimates
for
positive
steady-state
solutions
are
obtained
and
sufficient
conditions
nonexistence
of
nonconstant
solution
given.
Moreover,
bifurcations
at
both
simple
double
eigenvalues
analyzed
separately.
We
establish
global
structure
bifurcation
from
condition
to
determine
direction.
For
case
eigenvalues,
techniques
space
decomposition
implicit
function
theorem
used.
Finally,
verify
supplement
theoretical
analysis
results
numerical
simulations.
Mathematical Methods in the Applied Sciences,
Год журнала:
2024,
Номер
unknown
Опубликована: Сен. 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.
Chaos An Interdisciplinary Journal of Nonlinear Science,
Год журнала:
2024,
Номер
34(11)
Опубликована: Ноя. 1, 2024
Inappropriate
human
activities
contribute
to
the
degradation
of
ecosystems
in
arid
or
semi-arid
regions.
Therefore,
emphasizing
importance
strategies
for
restoring
vegetation
these
areas
cannot
be
overstated.
However,
there
has
been
insufficient
research
on
how
develop
effective
restoration
at
minimal
cost.
This
paper
addresses
this
gap
by
studying
optimizing
spatiotemporal
distribution
through
local
and
boundary
controls
can
reduce
level
desertification
pattern
structures,
thereby
facilitating
recovery
land
vegetation.
The
results
indicate
that
depends
proportion
number
activity
areas,
with
a
trade-off
between
them.
Furthermore,
consistent
conclusions
were
obtained
circular
regions,
demonstrating
robustness
approach
shapes.
aims
offer
new
insights
into
prevention
catastrophic
ecosystem
changes
from
perspective
optimal
control.
Journal of Applied Analysis & Computation,
Год журнала:
2023,
Номер
14(1), С. 473 - 505
Опубликована: Дек. 4, 2023
In
order
to
understand
the
mechanism
of
water
uptake
by
vegetation,
we
propose
a
vegetation-water
model
with
nonlocal
effect
which
is
characterised
delay
strong
kernel
in
this
paper.
By
mathematical
analysis,
condition
producing
steady
pattern
obtained.
Furthermore,
amplitude
equation
determines
type
Turing
obtained
nonlinear
analysis
method.
The
corresponding
vegetation
and
evolution
process
under
different
intensity
roots
are
given
numerical
simulations.
results
show
that
as
increases,
isolation
degree
increases
indicates
robustness
ecosystem
decreases.
Besides,
reveal
diffusion
coefficient
change
structure
is:
stripe
pattern$
\rightarrow
$mixed
$spot
pattern.
Our
effects
on
distribution,
provide
theoretical
basis
for
study
vegetation.
Results in Physics,
Год журнала:
2023,
Номер
53, С. 106926 - 106926
Опубликована: Сен. 11, 2023
Allee
effect,
as
one
of
the
research
hotspots
in
ecology
and
conservation
biology,
extremely
easily
affects
distribution
population
space,
especially
for
low-density
population.
In
ecosystem,
spatial
predator
is
more
vulnerable
to
effect
since
density
always
smaller
than
that
prey,
but
relevant
attention
paid
it
few.
this
paper,
we
establish
analyze
a
predator–prey
system
incorporating
on
Theoretically,
use
multi-scale
analysis
derive
amplitude
equation
obtain
different
Turing
patterns
under
intensities
effect.
Numerically,
verify
theoretical
results.
We
also
find
growth
rate
significantly
inhibited
time
reaching
equilibrium
tends
be
slower
with
increase
intensity
within
certain
limits.
More
interestingly,
discovered
extent
stable
although
may
lead
complex
dynamic
behaviors.
Our
results
help
better
understand
species
invasion
nature
ecology.
