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
Journal of Mathematical Biology,
Год журнала:
2022,
Номер
86(1)
Опубликована: Дек. 17, 2022
Abstract
Spatiotemporal
patterns
of
vegetation
are
a
ubiquitous
feature
semi-arid
ecosystems.
On
sloped
terrain,
occur
as
stripes
perpendicular
to
the
contours.
Field
studies
report
contrasting
long-term
dynamics
between
different
observation
sites;
some
observe
slow
uphill
migration
bands
while
stationary
patterns.
In
this
paper,
we
show
that
long-range
seed
dispersal
provides
mechanism
enables
occurrence
both
migrating
and
We
utilise
nonlocal
PDE
model
in
which
is
accounted
for
by
convolution
term.
The
represents
periodic
travelling
waves
numerical
continuation
shows
almost
stable
if
distances
sufficiently
large.
use
perturbation
theory
approach
obtain
analytical
confirmation
existence
patterned
solutions
provide
biological
interpretation
phenomenon.
International Journal of Bifurcation and Chaos,
Год журнала:
2023,
Номер
33(01)
Опубликована: Янв. 1, 2023
In
this
paper,
we
investigate
the
spatiotemporal
dynamics
of
Sel’kov–Schnakenberg
system.
The
stability
positive
constant
steady
state
is
studied
by
linear
theory.
Hopf
bifurcation
and
Turing–Hopf
are
generated
varying
two
parameters
in
model.
normal
form
near
singularity
calculated
to
explore
complex
Finally,
numerical
simulations
carried
out
verify
theoretical
results.
Our
results
show
that
system
exhibits
singularity,
including
existence
inhomogeneous
states,
homogeneous
periodic
solutions
solutions.
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
