Model Mathematics

Component: output_18

Component: clamp_para

Component: free_para_18

Component: MWC_18

k_C=0.5⁢alpha⁢ⅇV-V08⁢K k_Cminus=0.5⁢alpha⁢ⅇ-V-V08⁢K O=O_0+O_1+O_2+O_3+O_4+O_5+O_6+O_7+O_8 C=C_0+C_1+C_2+C_3+C_4+C_5+C_6+C_7+C_8 norm=C+O P_o=Onorm Q=O_1+2⁢O_2+3⁢O_3+4⁢O_4+5⁢O_5+6⁢O_6+7⁢O_7+8⁢O_8+C_1+2⁢C_2+3⁢C_3+4⁢C_4+5⁢C_5+6⁢C_6+7⁢C_7+8⁢C_88 dQ=dO_1+2⁢dO_2+3⁢dO_3+4⁢dO_4+5⁢dO_5+6⁢dO_6+7⁢dO_7+8⁢dO_8+dC_1+2⁢dC_2+3⁢dC_3+4⁢dC_4+5⁢dC_5+6⁢dC_6+7⁢dC_7+8⁢dC_88

Component: C0_S2

k_i1=k_L k_i2=N⁢k_C k_1i=k_Lminus k_2i=k_Cminus

Component: S1

ddtS_i=k_1i⁢S_1norm-k_i1⁢S_inorm dS_i=k_1i⁢S_1norm-k_i1⁢S_inorm

Component: S2

ddtS_i=k_1i⁢S_1norm+k_2i⁢S_2norm-k_i1+k_i2⁢S_inorm dS_i=k_1i⁢S_1norm+k_2i⁢S_2norm-k_i1+k_i2⁢S_inorm

Component: S3

ddtS_i=k_1i⁢S_1norm+k_2i⁢S_2norm+k_3i⁢S_3norm-k_i1+k_i2+k_i3⁢S_inorm dS_i=k_1i⁢S_1norm+k_2i⁢S_2norm+k_3i⁢S_3norm-k_i1+k_i2+k_i3⁢S_inorm

Component: C_S3

k_i1=k_Cminus⁢i k_i2=k_Lfi k_i3=N-i⁢k_C k_1i=N-i+1⁢k_C k_2i=k_Lminus⁢fi k_3i=i+1⁢k_Cminus

Component: S1

ddtS_i=k_1i⁢S_1norm-k_i1⁢S_inorm dS_i=k_1i⁢S_1norm-k_i1⁢S_inorm

Component: S2

ddtS_i=k_1i⁢S_1norm+k_2i⁢S_2norm-k_i1+k_i2⁢S_inorm dS_i=k_1i⁢S_1norm+k_2i⁢S_2norm-k_i1+k_i2⁢S_inorm

Component: S3

ddtS_i=k_1i⁢S_1norm+k_2i⁢S_2norm+k_3i⁢S_3norm-k_i1+k_i2+k_i3⁢S_inorm dS_i=k_1i⁢S_1norm+k_2i⁢S_2norm+k_3i⁢S_3norm-k_i1+k_i2+k_i3⁢S_inorm

Component: C_S3

k_i1=k_Cminus⁢i k_i2=k_Lfi k_i3=N-i⁢k_C k_1i=N-i+1⁢k_C k_2i=k_Lminus⁢fi k_3i=i+1⁢k_Cminus

Component: S3

ddtS_i=k_1i⁢S_1norm+k_2i⁢S_2norm+k_3i⁢S_3norm-k_i1+k_i2+k_i3⁢S_inorm dS_i=k_1i⁢S_1norm+k_2i⁢S_2norm+k_3i⁢S_3norm-k_i1+k_i2+k_i3⁢S_inorm

Component: C_S3

k_i1=k_Cminus⁢i k_i2=k_Lfi k_i3=N-i⁢k_C k_1i=N-i+1⁢k_C k_2i=k_Lminus⁢fi k_3i=i+1⁢k_Cminus

Component: S3

ddtS_i=k_1i⁢S_1norm+k_2i⁢S_2norm+k_3i⁢S_3norm-k_i1+k_i2+k_i3⁢S_inorm dS_i=k_1i⁢S_1norm+k_2i⁢S_2norm+k_3i⁢S_3norm-k_i1+k_i2+k_i3⁢S_inorm

Component: C_S3

k_i1=k_Cminus⁢i k_i2=k_Lfi k_i3=N-i⁢k_C k_1i=N-i+1⁢k_C k_2i=k_Lminus⁢fi k_3i=i+1⁢k_Cminus

Component: S3

ddtS_i=k_1i⁢S_1norm+k_2i⁢S_2norm+k_3i⁢S_3norm-k_i1+k_i2+k_i3⁢S_inorm dS_i=k_1i⁢S_1norm+k_2i⁢S_2norm+k_3i⁢S_3norm-k_i1+k_i2+k_i3⁢S_inorm

Component: C_S3

k_i1=k_Cminus⁢i k_i2=k_Lfi k_i3=N-i⁢k_C k_1i=N-i+1⁢k_C k_2i=k_Lminus⁢fi k_3i=i+1⁢k_Cminus

Component: S3

ddtS_i=k_1i⁢S_1norm+k_2i⁢S_2norm+k_3i⁢S_3norm-k_i1+k_i2+k_i3⁢S_inorm dS_i=k_1i⁢S_1norm+k_2i⁢S_2norm+k_3i⁢S_3norm-k_i1+k_i2+k_i3⁢S_inorm

Component: C_S3

k_i1=k_Cminus⁢i k_i2=k_Lfi k_i3=N-i⁢k_C k_1i=N-i+1⁢k_C k_2i=k_Lminus⁢fi k_3i=i+1⁢k_Cminus

Component: S3

ddtS_i=k_1i⁢S_1norm+k_2i⁢S_2norm+k_3i⁢S_3norm-k_i1+k_i2+k_i3⁢S_inorm dS_i=k_1i⁢S_1norm+k_2i⁢S_2norm+k_3i⁢S_3norm-k_i1+k_i2+k_i3⁢S_inorm

Component: C_S3

k_i1=k_Cminus⁢i k_i2=k_Lfi k_i3=N-i⁢k_C k_1i=N-i+1⁢k_C k_2i=k_Lminus⁢fi k_3i=i+1⁢k_Cminus

Component: S3

ddtS_i=k_1i⁢S_1norm+k_2i⁢S_2norm+k_3i⁢S_3norm-k_i1+k_i2+k_i3⁢S_inorm dS_i=k_1i⁢S_1norm+k_2i⁢S_2norm+k_3i⁢S_3norm-k_i1+k_i2+k_i3⁢S_inorm

Component: CN_S2

k_i1=k_Cminus⁢N k_i2=k_LfN k_1i=k_C k_2i=k_Lminus⁢fN

Component: S1

ddtS_i=k_1i⁢S_1norm-k_i1⁢S_inorm dS_i=k_1i⁢S_1norm-k_i1⁢S_inorm

Component: S2

ddtS_i=k_1i⁢S_1norm+k_2i⁢S_2norm-k_i1+k_i2⁢S_inorm dS_i=k_1i⁢S_1norm+k_2i⁢S_2norm-k_i1+k_i2⁢S_inorm

Component: S3

ddtS_i=k_1i⁢S_1norm+k_2i⁢S_2norm+k_3i⁢S_3norm-k_i1+k_i2+k_i3⁢S_inorm dS_i=k_1i⁢S_1norm+k_2i⁢S_2norm+k_3i⁢S_3norm-k_i1+k_i2+k_i3⁢S_inorm

Component: O0_S2

k_i1=k_Lminus k_i2=N⁢k_Cf k_1i=k_L k_2i=f⁢k_Cminus

Component: S1

ddtS_i=k_1i⁢S_1norm-k_i1⁢S_inorm dS_i=k_1i⁢S_1norm-k_i1⁢S_inorm

Component: S2

ddtS_i=k_1i⁢S_1norm+k_2i⁢S_2norm-k_i1+k_i2⁢S_inorm dS_i=k_1i⁢S_1norm+k_2i⁢S_2norm-k_i1+k_i2⁢S_inorm

Component: S3

ddtS_i=k_1i⁢S_1norm+k_2i⁢S_2norm+k_3i⁢S_3norm-k_i1+k_i2+k_i3⁢S_inorm dS_i=k_1i⁢S_1norm+k_2i⁢S_2norm+k_3i⁢S_3norm-k_i1+k_i2+k_i3⁢S_inorm

Component: O_S3

k_i1=k_Cminus⁢i⁢f k_i2=k_Lminus⁢fi k_i3=N-i⁢k_Cf k_1i=N-i+1⁢k_Cf k_2i=k_Lfi k_3i=i+1⁢k_Cminus⁢f

Component: S1

ddtS_i=k_1i⁢S_1norm-k_i1⁢S_inorm dS_i=k_1i⁢S_1norm-k_i1⁢S_inorm

Component: S2

ddtS_i=k_1i⁢S_1norm+k_2i⁢S_2norm-k_i1+k_i2⁢S_inorm dS_i=k_1i⁢S_1norm+k_2i⁢S_2norm-k_i1+k_i2⁢S_inorm

Component: S3

ddtS_i=k_1i⁢S_1norm+k_2i⁢S_2norm+k_3i⁢S_3norm-k_i1+k_i2+k_i3⁢S_inorm dS_i=k_1i⁢S_1norm+k_2i⁢S_2norm+k_3i⁢S_3norm-k_i1+k_i2+k_i3⁢S_inorm

Component: O_S3

k_i1=k_Cminus⁢i⁢f k_i2=k_Lminus⁢fi k_i3=N-i⁢k_Cf k_1i=N-i+1⁢k_Cf k_2i=k_Lfi k_3i=i+1⁢k_Cminus⁢f

Component: S3

ddtS_i=k_1i⁢S_1norm+k_2i⁢S_2norm+k_3i⁢S_3norm-k_i1+k_i2+k_i3⁢S_inorm dS_i=k_1i⁢S_1norm+k_2i⁢S_2norm+k_3i⁢S_3norm-k_i1+k_i2+k_i3⁢S_inorm

Component: O_S3

k_i1=k_Cminus⁢i⁢f k_i2=k_Lminus⁢fi k_i3=N-i⁢k_Cf k_1i=N-i+1⁢k_Cf k_2i=k_Lfi k_3i=i+1⁢k_Cminus⁢f

Component: S3

ddtS_i=k_1i⁢S_1norm+k_2i⁢S_2norm+k_3i⁢S_3norm-k_i1+k_i2+k_i3⁢S_inorm dS_i=k_1i⁢S_1norm+k_2i⁢S_2norm+k_3i⁢S_3norm-k_i1+k_i2+k_i3⁢S_inorm

Component: O_S3

k_i1=k_Cminus⁢i⁢f k_i2=k_Lminus⁢fi k_i3=N-i⁢k_Cf k_1i=N-i+1⁢k_Cf k_2i=k_Lfi k_3i=i+1⁢k_Cminus⁢f

Component: S3

ddtS_i=k_1i⁢S_1norm+k_2i⁢S_2norm+k_3i⁢S_3norm-k_i1+k_i2+k_i3⁢S_inorm dS_i=k_1i⁢S_1norm+k_2i⁢S_2norm+k_3i⁢S_3norm-k_i1+k_i2+k_i3⁢S_inorm

Component: O_S3

k_i1=k_Cminus⁢i⁢f k_i2=k_Lminus⁢fi k_i3=N-i⁢k_Cf k_1i=N-i+1⁢k_Cf k_2i=k_Lfi k_3i=i+1⁢k_Cminus⁢f

Component: S3

ddtS_i=k_1i⁢S_1norm+k_2i⁢S_2norm+k_3i⁢S_3norm-k_i1+k_i2+k_i3⁢S_inorm dS_i=k_1i⁢S_1norm+k_2i⁢S_2norm+k_3i⁢S_3norm-k_i1+k_i2+k_i3⁢S_inorm

Component: O_S3

k_i1=k_Cminus⁢i⁢f k_i2=k_Lminus⁢fi k_i3=N-i⁢k_Cf k_1i=N-i+1⁢k_Cf k_2i=k_Lfi k_3i=i+1⁢k_Cminus⁢f

Component: S3

ddtS_i=k_1i⁢S_1norm+k_2i⁢S_2norm+k_3i⁢S_3norm-k_i1+k_i2+k_i3⁢S_inorm dS_i=k_1i⁢S_1norm+k_2i⁢S_2norm+k_3i⁢S_3norm-k_i1+k_i2+k_i3⁢S_inorm

Component: O_S3

k_i1=k_Cminus⁢i⁢f k_i2=k_Lminus⁢fi k_i3=N-i⁢k_Cf k_1i=N-i+1⁢k_Cf k_2i=k_Lfi k_3i=i+1⁢k_Cminus⁢f

Component: S3

ddtS_i=k_1i⁢S_1norm+k_2i⁢S_2norm+k_3i⁢S_3norm-k_i1+k_i2+k_i3⁢S_inorm dS_i=k_1i⁢S_1norm+k_2i⁢S_2norm+k_3i⁢S_3norm-k_i1+k_i2+k_i3⁢S_inorm

Component: ON_S2

k_i1=k_Cminus⁢N⁢f k_i2=k_Lminus⁢fN k_1i=k_Cf k_2i=k_LfN

Component: S1

ddtS_i=k_1i⁢S_1norm-k_i1⁢S_inorm dS_i=k_1i⁢S_1norm-k_i1⁢S_inorm

Component: S2

ddtS_i=k_1i⁢S_1norm+k_2i⁢S_2norm-k_i1+k_i2⁢S_inorm dS_i=k_1i⁢S_1norm+k_2i⁢S_2norm-k_i1+k_i2⁢S_inorm

Component: S3

ddtS_i=k_1i⁢S_1norm+k_2i⁢S_2norm+k_3i⁢S_3norm-k_i1+k_i2+k_i3⁢S_inorm dS_i=k_1i⁢S_1norm+k_2i⁢S_2norm+k_3i⁢S_3norm-k_i1+k_i2+k_i3⁢S_inorm

Component: Para

Component: sPulse_protocol_ms

V=V_actHoldingiftime<t_ssV_actTestiftime≥t_ss∧time<t_act+t_ssV_actHoldingotherwise

Component: dPulse_protocol_ms

V=V_actHoldingiftime<t_cdV_cdiftime≥t_cd∧time<t_cd+T_cdV_actHoldingiftime≥t_cd+T_cd∧time<t_cd+T_cd+t_ssV_actTestiftime≥t_cd+T_cd+t_ss∧time<t_cd+T_cd+t_act+t_ssV_actHoldingotherwise

Component: sPulse_protocol_s

V=V_actHoldingiftime<t_ssV_actTestiftime≥t_ss∧time<t_act+t_ssV_actHoldingotherwise

Component: mPulse_protocol_ms

stimPeriod=t_act+t_intp t=time-t_ss-stimPeriod⁢⌊time-t_ssstimPeriod⌋ V=V_actHoldingiftime<t_ssV_actTestiftime≥t_ss∧t≦t_act∧time≦t_ss+stimPeriod⁢npV_actHoldingotherwise

Component: mPulse_protocol_s

stimPeriod=t_act+t_intp t=time-t_ss-stimPeriod⁢⌊time-t_ssstimPeriod⌋ V=V_actHoldingiftime≦t_ssV_actTestiftime>t_ss∧t≦t_act∧time≦t_ss+stimPeriod⁢npV_actHoldingotherwise

Component: time_ms

Component: time_s