Excitable Systems AronWolinetz
Who am I? • 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
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
Air-to-Ground Actions Rules • 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 • Etcetc
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
What we might have seen? • 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 SYSTEMneeds 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 • Outside is positive, Inside is negative • is outside, wants to get in • is inside and wants to get out • Pumps work to push out and in
Add some stimulus!!! • Some voltage opens a sodium channel allowing to flood into the cell • Causing a voltage spike that stimulates its neighbors
Phew… That was exhausting • A slower reacting channel opens to allow the voltage to equalize • Cell goes into a Refractory Period when pumps reset the and levels to the resting state. • Look familiar? -->