Stationary and Oscillatory patterned solutions in three-compartment reaction–diffusion systems: Theory and application to dryland ecology
Chaos Solitons & Fractals,
Год журнала:
2024,
Номер
186, С. 115287 - 115287
Опубликована: Июль 23, 2024
This
work
aims
at
elucidating
the
conditions
under
which
stationary
and
oscillatory
periodic
patterns
may
emerge
in
a
class
of
one-dimensional
three-compartments
reaction–diffusion
models
where
one
interacting
species
does
not
undergo
any
spatial
dispersal.
To
this
purpose,
linear
stability
analysis
is
firstly
employed
to
deduce
system
undergoes
Turing
or
wave
instability
as
well
extract
information
on
main
features
that
characterize
corresponding
patterned
solutions
onset.
Then,
multiple-scale
weakly
nonlinear
carried
out
describe
time
evolution
pattern
amplitude
close
bifurcation
thresholds
above-mentioned
instabilities.
Finally,
provide
quantitative
estimation
most
relevant
features,
an
illustrative
example
context
dryland
ecology
addressed.
It
deals
with
generalization
Klausmeier
vegetation
model
for
flat
arid
environments
describes
interaction
among
biomass,
soil
water
toxic
compounds.
Numerical
simulations
are
also
used
corroborate
theoretical
findings
gain
some
useful
insights
into
ecological
response
ecosystems
variable
environmental
conditions.
Язык: Английский
Prediction of vegetation pattern evolution in arid ecosystems using 3D-Var data assimilation
Chaos An Interdisciplinary Journal of Nonlinear Science,
Год журнала:
2025,
Номер
35(5)
Опубликована: Май 1, 2025
In
arid
regions,
ecosystems
are
fragile,
and
vegetation
exhibits
high
sensitivity
to
changes
in
climatic
conditions.
Vegetation
patterns–non-uniform
macroscopic
structures
formed
by
through
temporal
spatial
self-organization–serve
as
critical
indicators
of
an
ecosystem’s
adaptive
capacity,
post-disturbance
resilience,
early
warning
signals
ecosystem
degradation.
Investigating
the
formation
mechanisms
patterns
using
reaction–diffusion
(RD)
models
represents
a
vital
approach
deciphering
evolution
dynamics,
with
significant
implications
for
protecting
ecosystems.
However,
heterogeneous
steady-state
solutions
RD
systems,
such
Turing
patterns,
often
reside
multistable
regions.
This
implies
that
minute
variations
initial
conditions
may
lead
markedly
divergent
outcomes.
When
distribution
data
imprecise,
predictions
trends
distributions
given
position
become
highly
sensitive
errors—a
case
where
“minor
discrepancies
input
yield
vastly
results.”
study
applies
three-dimensional
variational
assimilation
method
model
coupling
vegetation,
soil
moisture,
surface
water
dynamics
The
results
demonstrate
incorporating
modest
amount
observational
can
substantially
enhance
model’s
predictive
accuracy
trajectories.
Язык: Английский
Pattern dynamics of a vegetation-water model with saturated effect and diffusion feedback
Physica A Statistical Mechanics and its Applications,
Год журнала:
2025,
Номер
unknown, С. 130676 - 130676
Опубликована: Май 1, 2025
Язык: Английский
Sustainable management of predatory fish affected by an Allee effect through marine protected areas and taxation
Mathematical Biosciences,
Год журнала:
2024,
Номер
373, С. 109220 - 109220
Опубликована: Май 24, 2024
Язык: Английский
Bifurcation analysis of a Leslie-type predator–prey system with prey harvesting and group defense
Frontiers in Physics,
Год журнала:
2024,
Номер
12
Опубликована: Июнь 19, 2024
In
this
paper,
we
investigate
a
Leslie-type
predator–prey
model
that
incorporates
prey
harvesting
and
group
defense,
leading
to
modified
functional
response.
Our
analysis
focuses
on
the
existence
stability
of
system’s
equilibria,
which
are
essential
for
coexistence
predator
populations
maintenance
ecological
balance.
We
identify
maximum
sustainable
yield,
critical
factor
achieving
Through
thorough
examination
positive
equilibrium
stability,
determine
conditions
initial
values
promote
survival
both
species.
delve
into
dynamics
by
analyzing
saddle-node
Hopf
bifurcations,
crucial
understanding
system
transitions
between
various
states.
To
evaluate
bifurcation,
calculate
first
Lyapunov
exponent
offer
quantitative
assessment
stability.
Furthermore,
explore
Bogdanov–Takens
(BT)
co-dimension
2
scenario,
employing
universal
unfolding
technique
near
cusp
point.
This
method
simplifies
complex
reveals
trigger
such
bifurcations.
substantiate
our
theoretical
findings,
conduct
numerical
simulations,
serve
as
practical
validation
predictions.
These
simulations
not
only
confirm
results
but
also
showcase
potential
predicting
real-world
scenarios.
in-depth
contributes
nuanced
within
interactions
advances
field
modeling.
Язык: Английский
Effective detection of early warning signal with power spectrum in climate change system
Chaos Solitons & Fractals,
Год журнала:
2024,
Номер
187, С. 115409 - 115409
Опубликована: Авг. 22, 2024
Язык: Английский
Bifurcations analysis and pattern formation in a plant-water model with nonlocal grazing
Nonlinear Dynamics,
Год журнала:
2024,
Номер
unknown
Опубликована: Окт. 17, 2024
Язык: Английский
Evolution of Turing patterns of a predator–prey system with variable carrying capacity and harvesting
Chaos Solitons & Fractals,
Год журнала:
2024,
Номер
191, С. 115790 - 115790
Опубликована: Дек. 5, 2024
Язык: Английский
Dynamic patterns in herding predator–prey system: Analyzing the impact of inertial delays and harvesting
Chaos An Interdisciplinary Journal of Nonlinear Science,
Год журнала:
2024,
Номер
34(12)
Опубликована: Дек. 1, 2024
This
study
expands
traditional
reaction–diffusion
models
by
incorporating
hyperbolic
dynamics
to
explore
the
effects
of
inertial
delays
on
pattern
formation.
The
kinetic
system
considers
a
harvested
predator–prey
model
where
predator
and
prey
populations
gather
in
herds.
Diffusion
are
subsequently
introduced.
Theoretical
frameworks
establish
conditions
for
stability,
revealing
that
delay
notably
alters
diffusion-induced
instabilities
Hopf
bifurcations.
inclusion
narrows
stability
region
wave
instability,
which
cannot
arise
two-variable
spatiotemporal
without
inertia.
Computational
simulations
demonstrate
Turing
lead
diverse
spatial
patterns.
highlights
initial
influence
generating
distinct
patterns
based
different
values,
while
other
remain
unaffected.
Additionally,
patterns,
such
as
hot
spots,
cold
stripes,
observed
within
region.
impact
harvesting
is
also
examined,
showing
increased
efforts
can
shift
systems
between
unstable
uniform
states.
findings
provide
practical
implications
ecological
modeling,
offering
insights
into
how
practices
affect
formation
natural
populations.
Язык: Английский
Spatiotemporal fluctuation induces Turing pattern formation in the chemical Brusselator
Mathematical Methods in the Applied Sciences,
Год журнала:
2024,
Номер
unknown
Опубликована: Окт. 8, 2024
Chemical
reactions
are
embedded
in
spatiotemporal
fluctuations
instead
of
a
constant
environment.
Here,
we
aimed
to
assess
reaction–diffusion
(RD)
with
dichotomous
noise‐controlling
system
parameters
the
Brusselator
and
examine
effect
these
on
dynamic
behavior
chemical
reactions.
By
performing
multiscale
perturbation
analysis,
demonstrated
that
correlated
noise
can
broaden
Turing
region
even
if
molecular
memory
(autocorrelation
time)
exists.
However,
for
small
noise,
short‐term
promotes
instability.
The
instability
is
determined
by
strength,
which
belongs
optimal
diffusion
coefficient
fixed.
pattern
selection
stability
also
governed
character
amplitude
equation,
entire
shifts
right
phase
space
perturbation.
Finally,
numerical
simulations
validate
theoretical
derivation
amplify
formation
maintain
distinct
patterns.
Язык: Английский