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calum.g Feb22-12 09:45 AM

Non linear ODE system matlab fourier analysis problem
Hello all.

I am studying a system and want to investigate how the frequency of y(3) varies under different conditions. However, my the fft I perform on it tells me the frequency is zero, which must be incorrect. I have tried a stack of things but can't see what the problem is. I'm relatively new to the matlab environment.

The main code:

close all; clear all;
Time control and initial conditions
timeinmin=600; % Time in minutes
tfin=timeinmin*60; % Time in seconds
Initial Levels and system Saturation
totIKK=0.08; % Total IKKn at start
totNFkB=0.08; % Total NFkB cytoplasmic at start
T=1; % Saturation of the system
yint=[totNFkB,0,0,0,0,0,totIKK,0,0,0,0,totIKK,totNFkB,T]; % Initial conditions
[t,y]=ode45(@nfkb,[0 tfin],yint); % calls Model
Extract Data from the ODE
fs = 1; % The sampling freqency in Hz
time = 0:1/fs:tfin; % Define time of interesrt
Datapoints = tfin*fs; % # of Data points being used
yi = interp1(t,y(:,3),time);
%plot(time/60,yi,'o',t/60,y(:,3)) % test to ensure it is working
Fourier Analysis from
NFFT = 2^nextpow2(tfin); % Next power of 2 from length of y
Y = fft(yi,NFFT)/Datapoints;
f = fs/2*linspace(0,1,NFFT/2+1);
% Plot single-sided amplitude spectrum.
title('Single-Sided Amplitude Spectrum of y(t)')
xlabel('Frequency (Hz)')
ylabel('Amplitude - |Y(f)|')
% Get value of frequency
[B,IX] = sort(2*abs(Y(1:NFFT/2+1)));
BFloor=0.1; %BFloor is the minimum amplitude value (ignore small values)
Amplitudes=B(B>=BFloor) %find all amplitudes above the BFloor
Frequencies=f(IX(1+end-numel(Amplitudes):end)) %frequency of the peaks

The ODEs:

function dydt=nfkb(t,y)

The parameters:

kv=3.3; % C:N ratio
kp=0.0006; % Conversion rate of IKKi
ka=0.004; %activation rate of IKK
ki=0.003; % Usage rate of IKK
kda=0.0045; % Deg rate of A20 protein
kbA20=0.0018; % A20 concentration
kc2=0.074; % phosopho of IkB
kc3=0.37; % phospho of IkB-NFkB
kdegpin=0.1; % splitting of Ikb-NFkB due to phospho
ka1=0.5; % nuclear IkB-NFkB formation
kd1=0.0005; % dissisociation of nuclear IkB-NFkB
kdegf=0.0005; % Deg rate of nuclear IkB
kdegc=0.000022; % dissisociation of cyto IkB-NFkB
ki1=0.0026; % nuclear entry of NF-kB
ke1f=52*10^(-6); % nuclear exit of NF-kB
ke1c=0.01; % Transport of IkB-NFkB out of nuc.
ki2=0.00067; % nuclear entry of IkB
ke2=3.35*10^(-4); % Nuclear exit of IkB
h=2; % hill coefficient of IkB transcription
k=0.065; % dissasociation constant for IkB tanscription with NFkB
kitria=1.4*10^(-7); % trans rate of IkB
ktria=0.5; % translation of IkB
kdegtia=0.0003; % Deg rate of IkB RNA
kitra=1.4*10^(-7); % Transcription rate of A20 RNA
ktra=0.5; % transcription rate of A20
kdegta=0.00048; % deg rate of A20 RNA

Thank you in advance for any insights.

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