Mathematical Medicine and Biology A Journal of the IMA,
Journal Year:
2024,
Volume and Issue:
41(1), P. 53 - 80
Published: Feb. 29, 2024
Abstract
Altay
Prefecture,
a
typical
arid
region
in
northwestern
China,
has
experienced
the
climate
transition
from
warming-drying
to
warming-wetting
since
1980s
and
attracted
widespread
attention.
Nonetheless,
it
is
still
unclear
how
change
influenced
distribution
of
vegetation
this
region.
In
paper,
reaction–diffusion
model
climate–vegetation
system
proposed
study
impact
(precipitation,
temperature
carbon
dioxide
concentration)
on
patterns
Prefecture.
Our
results
indicate
that
tendency
growth
Prefecture
improved
gradually
1985
2010.
Under
current
conditions,
increase
precipitation
pattern
structures,
eventually
coverage
tends
be
uniform.
Moreover,
we
found
there
exists
an
optimal
where
spot
structure
remains
stable.
Furthermore,
concentration
induces
transition.
Based
four
scenarios
Coupled
Model
Intercomparison
Project
Phase
6
(CMIP6),
used
power
law
range
(PLR)
predict
scenario
for
sustainable
development
ecosystem
Discrete and Continuous Dynamical Systems - B,
Journal Year:
2023,
Volume and Issue:
29(1), P. 426 - 458
Published: June 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.
Chaos An Interdisciplinary Journal of Nonlinear Science,
Journal Year:
2024,
Volume and Issue:
34(11)
Published: Nov. 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.
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.
Chaos An Interdisciplinary Journal of Nonlinear Science,
Journal Year:
2025,
Volume and Issue:
35(3)
Published: March 1, 2025
The
localized
patterns
observed
with
a
spatiotemporal
oscillatory
background
in
the
experiment
are
believed
to
emerge
due
bistability
of
supercritical
Turing-Hopf
modes.
However,
branching
origin
these
remains
unclear.
In
this
paper,
we
explore
formation
local
near
subcritical
bifurcation
point
using
Gray-Scott
model
as
an
example.
By
employing
multiple
scales
analysis
method,
derive
amplitude
equation
coupling
both
time
and
space,
demonstrating
that
special
pattern
can
persist
even
under
bifurcation.
Through
numerical
continuation
analysis,
reveal
originate
from
new
branch
on
homoclinic
snaking.
Our
findings
provide
insights
into
complex
offer
reasonable
explanation
for
perspective
higher-order
bifurcations.
Results in Physics,
Journal Year:
2023,
Volume and Issue:
53, P. 106926 - 106926
Published: Sept. 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.
