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EE48499:EmergentbehaviorinCoupledRing-Oscillators

JoseM.PerroneDr.GaryBernstein

DepartmentofElectricalEngineeringUniversityofNotreDame

SouthBend,INPerronej11@gmail.com

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

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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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