Over
the
last
two
decades,
tipping
points
have
become
a
hot
topic
due
to
devastating
consequences
that
they
may
on
natural
and
human
systems.
Tipping
are
typically
associated
with
system
bifurcation
when
external
forcing
crosses
critical
level,
causing
an
abrupt
transition
alternative,
often
less
desirable,
state.
The
main
message
of
this
review
is
rate
change
in
arguably
even
greater
relevance
human-dominated
anthropocene,
but
rarely
examined
as
potential
sole
mechanism
for
points.
Thus,
we
address
related
phenomenon
rate-induced
tipping:
instability
occurs
varies
across
some
rate,
usually
without
crossing
any
bifurcations.
First,
explain
expect
tipping.
Then,
use
three
illustrating
examples
differing
complexity
highlight
universal
generic
properties
range
Earth System Dynamics,
Journal Year:
2023,
Volume and Issue:
14(3), P. 669 - 683
Published: June 14, 2023
Abstract.
Over
the
last
2
decades,
tipping
points
in
open
systems
subject
to
changing
external
conditions
have
become
a
topic
of
heated
scientific
debate
due
devastating
consequences
that
they
may
on
natural
and
human
systems.
Tipping
are
generally
believed
be
associated
with
system
bifurcation
at
some
critical
level
conditions.
When
across
level,
undergoes
an
abrupt
transition
alternative,
often
less
desirable,
state.
The
main
message
this
paper
is
rate
change
arguably
even
greater
relevance
human-dominated
Anthropocene
but
rarely
examined
as
potential
sole
mechanism
for
points.
Thus,
we
address
related
phenomenon
rate-induced
tipping:
instability
occurs
when
vary
faster,
or
sometimes
slower,
than
rate,
usually
without
crossing
any
levels
(bifurcations).
First,
explain
expect
tipping.
Then,
use
three
illustrative
distinctive
examples
differing
complexity
highlight
universal
generic
properties
range
Physical review. E,
Journal Year:
2024,
Volume and Issue:
110(4)
Published: Oct. 4, 2024
Statistical
physics
and
dynamical
systems
theory
are
key
tools
to
study
high-impact
geophysical
events
such
as
temperature
extremes,
cyclones,
thunderstorms,
geomagnetic
storms,
many
others.
Despite
the
intrinsic
differences
between
these
events,
they
all
originate
temporary
deviations
from
typical
trajectories
of
a
system,
resulting
in
well-organized,
coherent
structures
at
characteristic
spatial
temporal
scales.
While
statistical
extreme
value
analysis
techniques
capable
providing
return
times
probabilities
occurrence
certain
not
apt
account
for
their
underlying
physics.
Their
focus
is
compute
probability
that
large
or
small
with
respect
some
specific
observable
(e.g.,
temperature,
precipitation,
solar
wind),
rather
than
relate
rare
phenomena
anomalous
regimes.
This
paper
outlines
this
knowledge
gap,
presenting
related
challenges,
new
formalisms
briefly
commenting
on
how
stochastic
approaches
tailored
can
help
advance
understanding.
Proceedings of the Royal Society A Mathematical Physical and Engineering Sciences,
Journal Year:
2025,
Volume and Issue:
481(2311)
Published: April 1, 2025
We
study
rate-induced
phase-tipping
(RP-tipping)
between
two
stable
limit
cycles
of
a
birhythmic
oscillator.
say
that
such
an
oscillator
RP-tips
when
time
variation
input
parameter
preserves
the
bistability
but
induces
transitions
from
one
cycle
to
other,
causing
abrupt
changes
in
amplitude
and
frequency
oscillations.
Crucially,
these
occur
when:
rate
change
is
certain
interval
bounded
by
critical
rate(s)
,
system
phases
cycle.
focus
on
illustrative
examples:
van
der
Pol
Decroly–Goldbeter
glycolysis
model,
each
subjected
monotone
non-monotone
shifts
their
parameters.
explain
RP-tipping
terms
properties
autonomous
frozen
system,
including
phase
partial
basin
instability
along
path
traced
changing
input.
show
can
as
irreversible
one-way
transition
or
series
cycles.
Finally,
we
present
diagrams
showing
combinations
magnitude
oscillation
give
rise
this
genuine
non-autonomous
instability.
Abstract.
Over
the
last
two
decades,
tipping
points
have
become
a
hot
topic
due
to
devastating
consequences
that
they
may
on
natural
and
human
systems.
Tipping
are
typically
associated
with
system
bifurcation
when
external
forcing
crosses
critical
level,
causing
an
abrupt
transition
alternative,
often
less
desirable,
state.
The
main
message
of
this
review
is
rate
change
in
arguably
even
greater
relevance
human-dominated
anthropocene,
but
rarely
examined
as
potential
sole
mechanism
for
points.
Thus,
we
address
related
phenomenon
rate-induced
tipping:
instability
occurs
varies
across
some
rate,
usually
without
crossing
any
bifurcations.
First,
explain
expect
tipping.
Then,
use
three
illustrating
examples
differing
complexity
highlight
universal
generic
properties
range
bioRxiv (Cold Spring Harbor Laboratory),
Journal Year:
2023,
Volume and Issue:
unknown
Published: Sept. 17, 2023
Abstract
Atmospherically
rising
temperature
and
CO
2
impact
all
freshwater
systems,
including
groundwater.
Increasing
leads
to
more
intense
weathering
of
silicate
rocks.
Here,
we
tested
whether
the
increased
levels,
weathering,
or
rather
increasing
temperature,
impacted
on
fauna
prokaryotes
in
groundwater
ecosystem.
We
conducted
analyses
separately
for
deep,
i.e.
secluded,
shallow,
quaternary
aquifers
which
exchange
with
surface
intensely.
Organism
abundances
relative
composition
did
not
correlate
levels.
While
many
organisms
rely
silica,
contrast,
found
negative
correlations
between
silica
fauna.
The
increases
over
time,
temporal
trends,
also
partly
correlated
negatively
organisms.
hypothesize
that
unexpected
are
direct
effects,
but
indirectly
indicate
communities
do
adapt
rapidly
enough
changes.
This
jeopardizes
future
drinking
water
production
relies
self-cleaning
ecosystem
services
Abstract.
Over
the
last
two
decades,
tipping
points
have
become
a
hot
topic
due
to
devastating
consequences
that
they
may
on
natural
and
human
systems.
Tipping
are
typically
associated
with
system
bifurcation
when
external
forcing
crosses
critical
level,
causing
an
abrupt
transition
alternative,
often
less
desirable,
state.
The
main
message
of
this
review
is
rate
change
in
arguably
even
greater
relevance
human-dominated
anthropocene,
but
rarely
examined
as
potential
sole
mechanism
for
points.
Thus,
we
address
related
phenomenon
rate-induced
tipping:
instability
occurs
varies
across
some
rate,
usually
without
crossing
any
bifurcations.
First,
explain
expect
tipping.
Then,
use
three
illustrating
examples
differing
complexity
highlight
universal
generic
properties
range
Abstract.
Over
the
last
two
decades,
tipping
points
have
become
a
hot
topic
due
to
devastating
consequences
that
they
may
on
natural
and
human
systems.
Tipping
are
typically
associated
with
system
bifurcation
when
external
forcing
crosses
critical
level,
causing
an
abrupt
transition
alternative,
often
less
desirable,
state.
The
main
message
of
this
review
is
rate
change
in
arguably
even
greater
relevance
human-dominated
anthropocene,
but
rarely
examined
as
potential
sole
mechanism
for
points.
Thus,
we
address
related
phenomenon
rate-induced
tipping:
instability
occurs
varies
across
some
rate,
usually
without
crossing
any
bifurcations.
First,
explain
expect
tipping.
Then,
use
three
illustrating
examples
differing
complexity
highlight
universal
generic
properties
range
Abstract.
Over
the
last
two
decades,
tipping
points
have
become
a
hot
topic
due
to
devastating
consequences
that
they
may
on
natural
and
human
systems.
Tipping
are
typically
associated
with
system
bifurcation
when
external
forcing
crosses
critical
level,
causing
an
abrupt
transition
alternative,
often
less
desirable,
state.
The
main
message
of
this
review
is
rate
change
in
arguably
even
greater
relevance
human-dominated
anthropocene,
but
rarely
examined
as
potential
sole
mechanism
for
points.
Thus,
we
address
related
phenomenon
rate-induced
tipping:
instability
occurs
varies
across
some
rate,
usually
without
crossing
any
bifurcations.
First,
explain
expect
tipping.
Then,
use
three
illustrating
examples
differing
complexity
highlight
universal
generic
properties
range
bioRxiv (Cold Spring Harbor Laboratory),
Journal Year:
2023,
Volume and Issue:
unknown
Published: Dec. 8, 2023
Abstract
Predator-prey
systems
often
feature
periodic
population
cycles.
In
an
empirical
system
with
a
heritable
prey
defence
trait,
ecological
oscillations
were
previously
shown
to
cause
evolution
of
on
the
timescale
this
paper,
we
develop
eco-evolutionary
mathematical
model
comprising
partial
differential
equations
investigate
evolutionary
dynamics
during
We
reveal
that
cycles
induce
mean
trait.
contrast
existing
continuum
modelling
frameworks,
our
allows
for
individual
variability.
show
select
increased
variability
close
transition
from
stable
oscillatory
states.
also
requires
both
high
efficiency
and
low
cost
highlight
more
information
trade-offs
between
is
required.
Abstract.
Over
the
last
two
decades,
tipping
points
have
become
a
hot
topic
due
to
devastating
consequences
that
they
may
on
natural
and
human
systems.
Tipping
are
typically
associated
with
system
bifurcation
when
external
forcing
crosses
critical
level,
causing
an
abrupt
transition
alternative,
often
less
desirable,
state.
The
main
message
of
this
review
is
rate
change
in
arguably
even
greater
relevance
human-dominated
anthropocene,
but
rarely
examined
as
potential
sole
mechanism
for
points.
Thus,
we
address
related
phenomenon
rate-induced
tipping:
instability
occurs
varies
across
some
rate,
usually
without
crossing
any
bifurcations.
First,
explain
expect
tipping.
Then,
use
three
illustrating
examples
differing
complexity
highlight
universal
generic
properties
range
