Excitable Systems
Aron Wolinetz
Who am I?
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PhD student at the CUNY Graduate Center
Masters from Lehman College (almost)
B.S. in Real Estate from Baruch College
Husband
Father
Not much
else
Lets have some fun!
What should we play?
• LETS PLAY AIR-TO-GROUND
ACTIONS!!!
• WOULDN’T YOU PREFER A NICE GAME
OF CHESS?
• LETS PLAY AIR-TO-GROUND
ACTIONS!!!
• What do we need?
– Paper airplanes
– Rules
– Ruthlessness
Simple Paper Airplane
Air-to-Ground Actions Rules
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First create a squadron
Then wait for an attack
Finally launch an attack of your own
Build a new squadron
Wait for an attack
Launch an attack
Etc etc
Additional Rules
• A squadron consists of five planes
• You must build your entire squadron, before
you may attack.
• You may only attack, right after being attacked
• When you attack, you may attack anyone you
choose
• No points for hitting ME
LETS ROCK ! ! !
What we might have seen?
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Nothing? Mayhem? Chaos?
People crying? Collateral damage?
Waves of attacks followed by lulls?
Lets call the lulls
between waves…
Refractory time
Refractory time
• Every EXCITABLE SYSTEM needs it
• Before the Refractory time has elapsed, a new
wave cannot begin or propagate.
• Ever try flushing the toilet
before the tank fills up?
Did it work?
Excitable Systems
• Lets do the Wave!
• Successive groups of
spectators briefly stand,
yell, and raise their arms.
Immediately upon stretching to full height,
the spectator returns to the usual seated
position. (Wikipedia)
What are excitable systems?
Excitable media can be defined as a system
formed by segments or elemental cells, each
of which has the following properties:
• A well defined steady state (or rest state)
• A threshold for excitation
• An excitation that only a function of the system and
independent of the stimulus.
• A refractory period following excitation
• A diffusive coupling with near neighbors (in space )
They can be: Physical, biological, mechanical, electrical,
mathematical, chemical, … and they can lead to chaos.
What else is an excitable system?
Example: Forest fires
Good example to understand refractory period and
collision between waves. (not solitons)
Problem: very long wave length, even longer refractory period
One more example?
• Dominos falling
• Refractory Period?
• Set them back up 
Cool… but why are we learning this?
• This is exactly the way the heart works
• Electrical signal starts at (SA node).
• Propagates around
the heart
• Refractory period
• Repeat as necessary
To the cellular level
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Outside is positive, Inside is negative
𝑁𝑎+ is outside, wants to get in
𝐾 + is inside and wants to get out
Pumps work to push 𝑁𝑎+ out and 𝐾 + in
Add some stimulus!!!
• Some voltage opens a sodium channel
allowing 𝑁𝑎+ to flood into the cell
• Causing a voltage spike that stimulates its
neighbors
Phew… That was exhausting
• A 𝐾 + slower reacting channel opens to allow
the voltage to equalize
• Cell goes into a Refractory Period when pumps
reset the 𝑁𝑎+ and 𝐾 + levels to the resting
state.
• Look familiar? -->
Neural is similar to Cardiac
ETC… ETC… ETC… till your dying breath
Thank You