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EE48499:EmergentbehaviorinCoupledRing-Oscillators
JoseM.PerroneDr.GaryBernstein
DepartmentofElectricalEngineeringUniversityofNotreDame
SouthBend,[email protected]
Abstract:Similartohowthedevelopmentofsymmetricalandcomplexpatternsfoundin
natureexemplifyemergenceinaphysicalnature,Iwishtostudyemergentbehaviorusing
neuromorphic circuit principles to examine if I canmodel neuron communication using
simpleconfigurationsofcoupledringoscillatorsandhavingthembehaveinuniqueways.
Keywords:Emergentbehavior,neuromorphiccircuitsMaterials:
1. LT-SPICEIVa. MonolithicP-MOSb. MonolithicN-MOSc. VoltageSourced. Wires
2. cmosedu.txt
Introduction
Ourneuronalcircuitsarethefoundationsofwhoweare.Werelyonthemwhether
weareawareof themornot.Theyneed tokeepupwithourdaily tasksandneed tobe
robustenoughtoadapttotheabundantamountofvaryingstimulibeinginputtedfromthe
world outside. In my research I attempt to gain more insight into how to model
neuromorphiccircuitsbylookingforemergentbehaviorincoupledringoscillators.
The description of circuits relating to the human brain can vary. Throughoutmy
researchIcameacrossthreedifferenttypesofcircuitsusedtostudythehumanbrain.The
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first type isequivalent toanelectricalcircuitbuilt inelectronics.Aneuron ismodeledto
describe its electrical properties in a measurable way. This model relates parts of the
neurontopartsofatraditionalelectricalcircuit,suchasbatteriesorcapacitors.Thismodel
iscriticaltolearninghowneuronsuseelectricalsignalstocommunicatewithoneanother.
ThisisthetypeofmodelIamreferringtowhenIbringupneuromorphiccircuits.
Thesecondtypeofcircuitcanbereferredtoasananatomicalcircuit. It iswidely
used in the neuroscience community to study systems, such as themotor systemor the
visual system.This specific typeof circuit hasno relation to a circuit in electronics. It is
simplya convenientway to talkaboutgroupsof interconnectedneurons. For instance, a
basal Ganglio-Thalamocortical circuit, is describing a group of neurons which send
information from the basal ganglia to the thalamus, and then from the thalamus to the
cerebralcortexandnotrelatingspecificpartstocircuitcomponents.
Lastly, the final type of circuit I came across is known as a functional circuit.
Functional circuitsmayormaynotbe referring to the electrical properties of a cell. For
example,aworkingmemorycircuitisatypeoffunctionalcircuit.Onewayoftalkingabout
workingmemoryisbystudyingtheelectricalproperties(thresholdvalue,dischargerate,
spontaneousactivity,etc.)oftheneuronsthatarerelatedtothispartofthebraintotryto
understand how information in thememory is coded and transmitted. This circuit may
thenalsobestudiedbydescribingtheanatomicalconnectionsbetweengroupsofneurons
thatarethoughttoprocessinformationaboutworkingmemory.
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ResultsandDiscussions
Thestartingpointforthisresearchwastoreadthroughseveralpaperstolookfor
potential experiments I could use to model my own research off. After reading a large
amountofpapers,Icameacrossthreepotentialcandidates.Thefirstwasapaperthattried
to link information theoretic (variational) and thermodynamic (Helmholtz) free-energy
formulations of neuronal processing and show how they are fundamentally related [9].
This paper also explained that biological systems will behave in a way that minimizes
changes in Helmholtz free energy and will prefer to move towards a non-equilibrium
steady state that has developed as an evolutionary result. Iwas interested in this paper
because I felt that the emergent behavior found in coupled ring oscillatorswould agree
withthefundamentalbehaviorfoundinnaturethatthispaperemphasizeson.
Thesecondpotentialcandidatewasapaperthatstudiedthebehaviorofamapped
clockoscillator(MCO)asaringdeviceandconsideredthepotentialofitservingasneural
prosthesesfortreatingdynamicdiseasessuchasepilepsy[15].Ifeltthispaper’sapproach
tomodelingneuronalpopulationswouldcorrelatenicelywithmyownresearch.
The thirdpotential candidatewas apaper thatwas recentlypublished inApril of
2016.Thispaperstudiedthebehaviorofmigratingmonarchbutterfliesandwassuccessful
indevelopingamodelofatime-compensatedsuncompassusedbythesebutterflies[10].
Throughspecial integrationofneuronaloscillationstheysuccessfullyenabledcorrections
to southwest and northeast flight. I considered this paper to be a potential candidate
becausetheneuralcircuittheydevelopedinawaystudiedtheemergentbehaviorfoundin
monarch butterflies that allows them to synchronize in a seemingly chaotic system and
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reachtheirdestination,4,000kmaway.
Aftermuchconsideration,Idecidedtodevelopthreeindividualcircuits,whichIcall
“Cells”,thatwouldhaveunrelatedfrequenciesandthenattempttohavethemcommunicate
toproduceanewemergentpatternthatbehavesdifferentlyfromwhentheyarenotlinked
together.
TheprogramthatwaschosentodevelopthesecircuitswasLTSPICE.Thisspecific
programwas chosen because a colleague of mine, Linda Gong, had experience working
withLTSPICEfromaprevioussemesterandwouldbeabletoprovidemewithimportant
resources to help me get started with my simulations. Linda provided me with the
followingsymbols:Singleinverter,3-gateringoscillator,5-gateringoscillator,15-gatering
oscillator, 31-gate ring oscillator and XOR gate. After familiarizing myself with the
parametersinthesymbolsandverifyingthesymbolswereworkingproperly,Idelvedinto
buildingmyfirstcell.
My first cell was built with a 3-gate ring oscillator coupled with a 17-gate ring
oscillatorascanbeseeninFigure1.Inordertocouplethesetwooscillatorssuccessfully,I
needed to use an XOR gate to prevent confusion between the different outputs of the
oscillators.TheXORgatewasfedbytheoutputofthe3-gateringoscillator,theoutputfrom
the15thinverterofthe17-gateringoscillatorandthentheXOR’soutputwasfedintothe
16th inverter. A Pulse function was used as a voltage source in order to start the
oscillations.ThePulsefunctionwassettostartwithaninitialvalueof0volts,andwithan
ONstateset to1.5volts.The functionwasset tohavenodelay, riseor fall time.TheON
timeofthePulsewassetto0.5microseconds.Ispecifiedaperiodof10microsecondsand
5
500cyclestokeepthesimulationfromrunningforever.
I also included a, cmosedu, text file that was provided by Dr. Jacob Baker, a
professor at the University of Nevada. This text file contains parameters for various
componentsoftheMonolithicP-MOSandN-MOSmodels(internalcapacitance,resistance,
etc).FormysimulationIperformedatransientanalysistodeterminehowthecircuitwill
behaveundernon-well-behavedsignals.Bycheckingifmycircuitbecomesunstableunder
certainconditions,Icandetermineitisnotarobustcircuit.Inaddition,IbypassedtheDC
operating point analysis in my transient analysis by including the UIC (to calculate the
initial transient conditions rather than solving for the quiescent operating point)
parameter.
Figure1:“Cell1”3-gateROcoupledwith17-gateRO
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The simulation begins with a transient state and then stabilizes at around 0.6
microseconds.Thefirstinterferencepatternstartsat1.2microsecondsandstopsatabout
2.0 microseconds. Interference patterns will continue to appear about every 1.2
microsecondsandlastforabout0.7microseconds.Figure3showsthedifferentwaveforms
found in Cell 1 in more detail. The center waveform seems to resemble the I-V
characteristicsfoundinacapacitor.
Figure2:SimulationofCell1for5.5microseconds
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Next, Ibuilta largerCellusingthesameproceduresasCell1.Cell2wasdesigned
witha7-gateringoscillatorcoupledwitha33-gateringoscillatorascanbeseeninFigure
4.ThebehaviorofCell2isshowninFigure5.Ascanbeseeninthesimulations,Cell1and
Cell 2 have different behaviors. A transient state is observed in Cell 2, however it has a
largerinterferencesequence.Theinterferencelastsforabout0.2microsecondslongerthan
Cell1.Also,it’sinterferencepatternhasarangeof0voltsto1.5volts,whereasCell1hasa
rangeofroughly1.05volts to1.5volts.Figure6showsthedifferentwaveformsfoundin
Cell2inmoredetail.
Figure3:CloserlookofwaveformsfoundinCell1
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Figure4:“Cell2”7-gateROcoupledwith33-gateRO
Figure5:SimulationofCell2for5.3microseconds
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Finally, Ibuilt the largestCellofall threeusingthesameproceduresasCell1and
Cell 2. Cell 3 was designed with a 17-gate ring oscillator coupled with a 49-gate ring
oscillator as can be seen in Figure 7. The behavior of Cell 3 is shown in Figure 8. As
expected,Cell3behavesdifferentlycomparedtoCell1andCell2.Atransientstateisstill
observedinCell3,howeverit isfarmoredifficulttoobservetheinterferencepattern.To
showtheinterferencepatternIprovidedazoomedincutoutofthefirst2.2microseconds,
shown in Figure9. The interference lasts for about 0.8microseconds. Cell 3 has amuch
largerfrequencycomparedtoCell1andCell2.
Figure6:CloserlookatthewaveformsfoundinCell2
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Figure7:“Cell3”17-gateROcoupledwith49-gateRO
Figure8:SimulationofCell3for5.3microsecondsfor7.3microseconds
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The next objective was to have all three Cell’s communicate with each other. To
accomplishthis,IarrangedaseriesconfigurationofallthreeCell’s.Cell1wasfedintoCell2
andCell2wasfedintoCell3ascanbeseeninFigure10.Ihadsomedifficultyfindingthe
rightparameters touse for thePulse function.After testinga fewdifferentparameters I
foundthesimulationsworkedbestifthefunctionwassettohavealongerONtimethanthe
larger ring-oscillators. The initial and ON state were still set to 0 volts and 1.5 volts
respectivelyandthefunctionwasstillsettohavenodelay,riseorfalltime.However,the
ONtimeofthePulsewassetto1microsecondinsteadof0.5microseconds.Ialsospecified
a period of 2 microseconds and 1000 cycles. The transient analysis was set to 1000
microseconds.
Figure9:SimulationofCell3zoomedinto2.2microseconds
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Thefinalcircuitproducedaninterestingbehavior.AscanbeseeninFigure11,the
circuitexperiencedashortertransientstateandbegantostabilizebelow0volts.Ibelieve
this occurred as a result of inserting signalswithmuch smaller frequencies into signals
with much larger frequencies. The circuit appears to rise above 0 volts at about 1.13
microseconds. A clearer observation of this is shown in Figure 12. In addition, one can
clearly observe to different waveforms throughout the simulation. Figure 12 seems to
resemblemodulationfoundintelecommunications.Theinterferencepatternofthiscircuit
appearstobeginatapproximately1.2microsecondsandlast forabout0.8microseconds.
Figure10:SeriesconfigurationofallthreeCell’s
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AnexampleoftheFouriertransformforthiscircuitisshowninFigure13.Unfortunately,
takingtheFouriertransformofasquarewavewillnothelprevealmuchaboutthecircuit’s
behavior.However, lookingatthefrequencyspectrumofthiscircuitIcandeducethat, in
order to successfully build this kind of circuit, one would have to design a microwave
circuit,duetotheveryshortwavelengthsbeingproduced.
Figure11:Simulationofseriesconfigurationwithall3Cell’s
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Figure12:Closerlookatwaveformsfoundinseriesconfiguration
Figure13:Simulationofseriesconfigurationwithall3Cell’s
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FutureWork Due to time I was not able to test more circuits that would produce interesting
emergentbehavior.Figure14, showsacircuit Iwasworkingonwhere Iwas includinga
pass-gatethatwouldbeswitchedonandoffusinganotherringoscillator. Iwould liketo
getthiscircuitworkingandthenbuildsimilarcircuitsandtestdifferentconfigurationsto
see what sorts of behaviors I may find. My goal for future research would be to find a
potentialmodelthatcanbeimbeddedontoanelectroniccircuitandcanthenbeusedasa
potentialneuralprosthesistohelptreatpatientswithepilepsyortobuildbettercomputer
architectures that resemble more closely to how our own brains compute and transfer
information.
Figure14:17-gateROcoupledwith49-gateROwithpass-gate
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Conclusions
Myresearchwassuccessfulinthat,Iwasabletoobserveemergentbehaviorfound
incoupledringoscillatorsandIwasabletofindsimplebuildingblocksthatcanbeusedto
producemoresymmetricalandcomplexpatterns.Inaddition,Igainedabetterscopeofthe
typeofworkcurrentlybeingdoneinthescientificcommunityandwhatkindschallenges
arebeingfaced.Mygoalsforfutureresearcharetobuildmoresophisticatedneuromorphic
circuitsandtofindnewwaysthatIcanmodelneuralcommunication.
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