Travelling pulses on three spatial scales in a Klausmeier-type vegetation-autotoxicity model
Nonlinearity,
Journal Year:
2024,
Volume and Issue:
37(9), P. 095008 - 095008
Published: July 18, 2024
Abstract
Reaction-diffusion
models
describing
interactions
between
vegetation
and
water
reveal
the
emergence
of
several
types
patterns
travelling
wave
solutions
corresponding
to
structures
observed
in
real-life.
Increasing
their
accuracy
by
also
considering
ecological
factor
known
as
autotoxicity
has
lead
more
involved
supporting
existence
complex
dynamic
patterns.
In
this
work,
we
include
an
additional
carrying
capacity
for
biomass
a
Klausmeier-type
vegetation-water-autotoxicity
model,
which
induces
presence
two
asymptotically
small
parameters:
ɛ
,
representing
usual
scale
separation
vegetation-water
models,
δ
directly
linked
autotoxicity.
We
construct
three
separate
homoclinic
pulse
based
on
different
scaling
regimes
involving
with
without
so-called
superslow
plateau
.
The
relative
ordering
parameters
significantly
influences
phase
space
geometry
underlying
construction
solutions.
complement
analysis
numerical
continuation
constructed
solutions,
demonstrate
(and
stability)
direct
simulation
full
partial
differential
equation
model.
Language: Английский
Deformations of acid-mediated invasive tumors in a model with Allee effect
Journal of Mathematical Biology,
Journal Year:
2025,
Volume and Issue:
90(6)
Published: May 5, 2025
Abstract
We
consider
a
Gatenby–Gawlinski-type
model
of
invasive
tumors
in
the
presence
an
Allee
effect.
describe
construction
bistable
one-dimensional
traveling
fronts
using
singular
perturbation
techniques
different
parameter
regimes
corresponding
to
tumor
interfaces
with,
or
without,
acellular
gap.
By
extending
front
as
planar
interface,
we
perform
stability
analysis
long
wavelength
perturbations
transverse
direction
propagation
and
derive
simple
criterion
for
two
spatial
dimensions.
In
particular
find
that
general
gap
indicates
transversal
instability
associated
front,
which
can
lead
complex
interfacial
dynamics
such
development
finger-like
protrusions
and/or
invasion
speeds.
Language: Английский