In general
Although this may appear to be an esoteric and unusual behavior, it is exhibited by very simple systems: for example, a ball placed at the crest of a hill might roll into any of several valleys depending on slight differences in initial position.
The butterfly effect is a common trope in fiction when presenting scenarios involving time travel and with "what if" scenarios where one storyline diverges at the moment of a seemingly minor event resulting in two significantly different outcomes.
wikipedia.org
Butterfly Effect: History and Theory

Almost 10% of Europe's butterflies face extinction
Hundreds of butterflies, beetles and dragonflies are at risk of extinction across Europe with almost one-third of 435 butterfly species in decline, scientists have warned.
The loss of habitat caused by intensive farming, climate change, forest fires and the expansion of tourism is threatening with extinction 14% of dragonflies, 11% of saproxylic beetles and 9% of butterflies within Europe, according to the European red list report for the European commission.
"When talking about threatened species, people tend to think of larger, more charismatic creatures such as pandas or tigers, but we mustn't forget that the small species on our planet are just as important," said Jane Smart of the International Union for Conservation of Nature (IUCN), the conservation group which produced the report.
"Butterflies, for instance, play a hugely pivotal role as pollinators in the ecosystems in which they live."
Many of the endangered insect species live in southern Europe where increasingly hot, dry summers combined with irrigation and water extraction is causing wetland habitats to dry up.
The Madeiran large white butterfly is listed as critically endangered on the red list, which reviews the status of 6,000 European species including mammals, reptiles and plants. But the butterfly may already be extinct because it has not been seen on the island of Madeira for 20 years.
The Macedonian grayling butterfly is critically endangered because quarrying is reducing its habitat while other endangered species include the Danube clouded yellow, the violet copper and the Canary Islands large white. Only 4% of Europe's butterfly species, which include 142 unique to the continent, are increasing in number.
Martin Warren, co-author of the butterfly section of the report and chief executive of UK charity, Butterfly Conservation, said the insects were being hit by the loss of grassland habitats due to both intensification of agriculture and recent abandonment of traditional farming land in Europe.
"In the 1950s and 60s we had massive losses of habitat in the UK, and it is still going on to a lesser extent, but in Europe big changes have been going on in the last five to 10 years," said Warren. We lost a lot of our flower-rich meadows in the 50s and 60s, while they are losing theirs at a rate of knots now."
The large blue butterfly, a rare conservation success after it was reintroduced in Devon and Somerset after it became extinct in the UK in 1979, is endangered throughout Europe, declining in every country where it occurs apart from the UK.
Other struggling species, such as the Duke of Burgundy and the Lulworth skipper, which both suffered their worst ever year in the UK last summer, are in decline in many countries across the continent.
Intensification of agriculture is destroying habitat in some areas, while flower and insect-rich pastures in many mountain regions in the Alps and Pyrenees are being abandoned and falling into a poor condition because livestock farming is not financially viable.
Warren called for more support for traditional farming systems to help insects such as butterflies, which he said were very good indicators of changes to the environment.
Saproxylic beetles, which depend on decaying wood in forests and play a crucial role in recycling nutrients, were assessed for the first time on the red list.
Logging, changing woodland management practices and a declining number of mature trees are threatening species such as the violet click beetle. Almost 11%, 46 of 431 species studied, are at risk of being lost to Europe and 7% are threatened with global extinction. A further 13% are listed as "near threatened" in Europe.
Almost a quarter of 137 dragonfly species assessed, including 18 species not found anywhere else in the world, were found to be at risk of extinction or "near threatened". Last year, a new dragonfly centre opened in the UK in a bid to reverse a trend of decline that has seen one-third of British species facing extinction.
Jason Mraz - Butterfly (Live, 2008)
Jason Mraz - Butterfly
I'm taking a moment just imaginin' that I'm dancin' with you
I'm your pole and all you're wearing is your shoes
You got soul, you know what to do to turn me on until I write a song about you
And you have your own engaging style
And you've got the knack to vivify
And you make my slacks a little tight, you may unfasten them if you like
That's if you crash and spend the night
But you don't fold, you don't fade
You've got everything you need, especially me
Sister you've got it all
You make the call to make my day
In your message say my name
Your talk is all the talk, sister you've got it all
Curl your upper lip up and let me look around
Ride your tongue along your bottom lip and bite down
And bend your back and ask those hips if I can touch
Because they're the perfect jumping off point of getting closer to your
Butterfly
Well you float on by
Oh kiss me with your eyelashes tonight
Or Eskimo your nose real close to mine
And let's mood the lights and finally make it right
But you don't fold, you don't fade, you've got everything you need
Especially me
Sister you've got it all
You make the call to make my day
In your message say my name
Your talk is all the talk sister you've got it all
You've got it all, you've got it all, you've got it all [2x]
You've got it all, you've got it all
Doll I need to see you pull your knee socks up
Let me feel you upside down, slide in, slide out, slide over here
Climb into my mouth now child
Butterfly, well you landed on my mind
Dammit you landed on my ear and then you crawled inside
And now I see you perfectly behind closed eyes
I wanna fly with you and I don't wanna lie to you
Cause I, cause I can't recall a better day
Sun coming to shine on the occasion
You're an open-minded lady
You've got it all
And I never forget a face
Except for maybe my own,
I have my days
But let's face the fact here, it's you who's got it all
You know that fortune favors the brave
Well let me get paid while I make you breakfast
The rest is up to you, you make the call
You make the call to make my day
In your message say my name
Your talk is all the talk, sister you've got it all
I can't recall a better day
Sun comin' to shine on the occasion
You're a sophisticated lady, oh
You've got it all, you've got it all, you've got it all [3x]
You've got it all, you've got it all.
You've got it all
You've got it all
You gotta gotta gotta got it all
Butterfly, baby, well you've got it all
Smashing Pumpkins - Bullet with Butterfly Wings (Video)
Smashing Pumpkins
"Believe it or not, the original riff from this song came to me during one of the Siamese Dream recording sessions. Somewhere, I have a tape of us from 1993 endlessly playing the 'world is a vampire' part over and over. But it wasn't until a year and a half later that I finished the song, writing the 'rat in the cage' part on an acoustic guitar at the BBC studios in London on the same day that 'Landslide' was recorded." -BC (Guitar World 1/97)
The world is a vampire, sent to drain
secret destroyers, hold you up to the flames
and what do i get, for my pain
betrayed desires, and a piece of the game
even though i know-i suppose i'll show
all my cool and cold-like old job
despite all my rage i am still just a rat in a cage
then someone will say what is lost can never be saved
despite all my rage i am still just a rat in a cage
now i'm naked, nothing but an animal
but can you fake it, for just one more show
and what do you want, i want to change
and what have you got
when you feel the same
even though i know-i suppose i'll show
all my cool and cold-like old job
despite all my rage i am still just a rat in a cage
then someone will say what is lost can never be saved
despite all my rage i am still just a rat in a cage
tell me i'm the only one
tell me there's no other one
jesus was an only son
tell me i'm the chosen one
jesus was an only son for you
despite all my rage i am still just a rat in a cage
and i still believe that i cannot be saved
http://billycorgan.livejournal.com/
Crazy Town - Butterfly
Come come my lady
you're my butterfly
Sugar.baby (X2)
Such a sexy,sexy pretty little thing
Fierce nipple pierce you got me sprung with your tongue ring
and I ain't gonna lie cause your loving gets me high
So to keep you by my side there's nothing that I won't try
Butterflies in her eyes and looks to kill
Time is passing I'm asking could this be real
Cause I can't sleep I can't hold still
The only thing I really know is she got sex appeal
I can feel too much is never enough
You're always there to lift me up
When these times get rough I was lost Now I'm found
Ever since you've been around
You're the women that I want
So yo, I'm putting it down.
CHORUS
I don't deserve you unless it's some kind of hidden message
to show me life is precious
Then I guess it's true
To tell truth, I really never knew
T'll I met you I was lost and confused
Twisted and used up
Knew a better life existed but thought that I missed it
My lifestyle's wild I was living like a wild child
Trapped on a short leash paroled the police files
And yo. what' s happening now?
I see the sun breaking shining through dark clouds
and a vision of you standing out in a crowd.
CHORUS
Hey sugar momma, come and dance with me
The smartest thing you ever did was take a chance with me
So, what ever tickles your fancy
Girls who you knew like Sid and Nancy
So sexy....almost evil Talkin' about butterflies in my head
I used to think happy endings were only in the books I read but
you made me feel alive when I was almost dead
You filled that empty space with the love I used to chase
and as far as I can see it don't get better than this
So butterfly, here is a song and it's sealed with a kiss
and a thank you miss.