新型神经元模型及生物神经网络模拟实现算法

:(60275023):2004-06-2922520055:1006-9348(2005)05-0179-06,,(,361006):,,,,,,,,,,,:;;;;:TP391.9:AANewModelofBiologicalNeuronandaMathematicalMethodofNeuralNetworkYOUZhi-ning,ZHOUChang-le,ZHANGKe-zhi(DepartmentofComputerScience,ComputerandInformationEngineeringCollegeofXiamenUniversity,XiamenFujian361006,China)ABSTRACT:Accordingtothemaincharacterofsynapseofdendrite,actionpotentialinthecellbodyandaxon,anewmathematicalmodelofneuronisproposedinthispaper.Itisdiscussedhowthemodelisusedtosimulatesomedifferentkindsofneurons.Thismathematicalmodelconsistsofthreepartsthatareformulaofsynapse,formulaofcellbody,formulaofaxon.Asexamples,wetakeshapeofapartofformulaofsynapseaccordingtohomosynapticplasticity.Wetakeshapeofapartofformulaofcellbodyaccordingtochangelawofpotentialsandthresholdfollowingactionpotentials,specialityofin2ternalsourcesneuronandpostinhibitoryreboundsneuron.So,thenetworkbuiltbythismathematicalmodelframeworkofbiologicalneuronwillbeanisomerousnetwork.Hereacomputationmethodofsimulatingbiologicalneuralnetworkispro2posed.Weanalyzeitscomplexity.Itilluminatethatthiscomputationmethodhasgoodcalculability.KEYWORDS:Neuron;Model;Neuralnetwork;Mathematicalmethod;Complexity1,,,,,,[1],,,,,,,,,,,,,,,,2971,[2],,,,([3]),[4],,,,,:xji(t-r)=SYNji(yji(t-r-TFRji),wji,ADDji)(1)xi(t+TACi)=Fi(Ai(t)+Qi(t-tlast)+Nj=1trttastPi(xji(t-r),(t-r))-i(t-tlast,OTHi))(2)yik(t+TACi+TBEik)=AXONik(xi(t+TACi))(3),wjiADDjiTFRjiOTHiTACiTBEik,;wji,Hebb,,;ADDji(homosynapticplasticity);TFRji(yjilast,tjilast,t-r),tlasti([5],),Qii,,Pii;i(t-tlast,OTHi)i();Ai(t)2.1:,(homosynapticplasticity)(facilitation)(potentiation)(depression),,,[3]1SYNji:SYNji=wji3yji(t-r-TFRji)+ADDji,SYN=w3y(t-r-TFR)+ADDADD(,,),1:(facilitation),1)t-0(1I),,ADDtADDt,ADDtADDt0;(1)ADD:ADD=a1t-t-b1+c1(4)2)t-0(1II),,ADDtADDt0,ADDtADDt0;(1)ADD:ADD=a2t-t-b2+c2(5),ADD:ADD=a1t-t-b1+c1t-0(I)c3t-=0a2t-t-b2+c2t-0(II)(6),,t,t,a1a2b1b2c1c2c3ADD,(6)ADD,ADD,ADD:,ADDlast=SYNlast-wlast3ylast,:SYNlastwlastylast,ADDlastt=t-r-TFR-tlast,:t-r-TFR,tlastADDlastADDt(6),t,tlasttnow=tlast+t,tnowtt(6),ADD:,0811([3])2.2[5](2)Qi(t-tlast)i,,2aQi(t-tlast):Qi(t-tlast)=a1(t-tlast)+b10(t-tlast)a2sin(c2(t-tlast)+d2)(t-tlast)+b2(t-tlast)(7),a1b1a2b2c2d22.3,,,(refractory)(absoluterefractoryperiod)(relativerefractoryperiod),[3](2b)(2)i(t-tlast,OTHi):1812a.,[5]b.,[3]c.,[3]d.e.i(t-tlast,OTHi)=€i(t-tlast)-OTHi(8)OTHi,€i(t-tlast),€i(t-tlast):€i=+(t-tlast)tabsth+b(t-tlast)-tabstabs(t-tlast)trelthtrel(t-tlast)(9),tabs,trel,th,b2.4,,(silent),(beat),(burstingneurons),(2)Ai(t):Ai(t)=A1(10)Ai(t)=A2(11)Ai(t)=C1t(T,T+]C2t(T+,(+1)T](12)Ai(t),A1,,,(2d)281Ai(t),A2,,i(t-tlast,OTHi),2dAi(t),C1C2,C1,C2,T,T,2e2.5(postinhibitoryrebound),,2c,(2)i(t-tlast,OTHi)OTHi:OTH=THAi(t)+ml=0Pi(xi(l)(t-tl),(t-rl))C,m=01n0(13):tlasti;t0t1tntlasti,t0t1......tn,tn(4)t,t0t1......tnxi(0)xi(1)......xi(n);TH;C31)AP(id,top,bt,ht);DONE(type,IP,IT,front,behild);INNUM=0;yji(tji):(A)xji(tji+TFRji)=SYNji(yji(tji),wji,ADDjiTFRjixji;(B)(0,xji,(tji+TFRji,j,i)IN(type,IP,IT,front,behild),INNUM=INNUM+1i(Ai(t)0):(A)ti;(B)(1,0,ti,-1,i)IN,INNUM=INNUM+12)INNUM0,;,INNUM=INNUM-1,INITdo,behild,behildi,ITt,doIN,dotype0,doDONE3)AP,id=iht,iht,tlast4)tC=Nj=1trtlastpi(xji(t-r),(t-r))C=0;DONEbehildi:(A)ITr,IPx,D=Pi(x(t-r),(t-r));(B)C=C+D5)tB=Ai(t)+Qi(t-tlast)+C-i(t-tlast,OTHi);6)BB0,;B=0,:(A)Bxi=Fi(B),xit+TACi,(i,xi,t,t+TACi)AP(B)ik:yik(t+TACi+TBEik)=AXONik(xi(t+TACi))xik=SYNik(yik,wik,ADDik),xik(t+TACi+TBEik+TFRik),(xik,(t+TACi+TBEik+TFRik),i,k)IN,INNUM=INNUM+1(C)behildiDONE7)i(Ai(t)0),INtype=1behild=i(k),iti,(1,0,ti,-1,i)IN,INNUM=INNUM-k+18)i,INtype=2behild=i(k),iti,(2,0,ti,-1,i)IN,INNUM=INNUM-k+19)2),,,,4,1)AP,381,id,idid,,htn,APnDONEAP,n,DONEna,,(A)o(a),(B),()IN,IT(B)a(o(alog2a),2),INITdo1,(p)2log2p;,doDONE,DONEi,doi,1;3)APid=iht,DONEi,14),behildi,DONEi,,15)OTH6)(A),AP,DONEi,i,1;(B),l,lIN(p)2llog2p;(C),behildiDONE,DONEi,,1,2)5),,((2log2p)+3),o(log2p);2)6),,((2(l+1)log2p)+4),o(llog2p);m,m((2log2p)+3)+2llog2p+1=2(m+l)log2p+(3m+1),o((m+l)log2p);q,:q(2(m+1)log2p+(3m+1)),o(q(m+l)log2p)o(q(m+l)log2p,q,,m+l,,p,,,log2p,:[1].[M].:,2000.[2],,.[M].:,2002.[3]IB,LK,,.:[M].:,2001.[4]ERKandel,JHSchwartz,TMJessell.[M].:,2003.[5]JG,,,.[M].:,2003.[](1974.4-),(),,,;(1959.11-),(),,,,(),,();(1976.7-),(),,,481