Nonlinear Biomedical Signal Processing - Dynamic Analysis by Metin Akay

By Metin Akay

That includes present contributions by way of specialists in sign processing and biomedical engineering, this booklet introduces the thoughts, fresh advances, and implementations of nonlinear dynamic research equipment. including quantity I during this sequence, this ebook offers complete assurance of nonlinear sign and picture processing ideas. Nonlinear Biomedical sign Processing: quantity II combines analytical and organic services within the unique mathematical simulation and modeling of physiological platforms. exact discussions of the research of steady-state and dynamic platforms, discrete-time procedure concept, and discrete modeling of continuous-time structures are supplied. Biomedical examples contain the research of the respiration keep watch over approach, the dynamics of cardiac muscle and the cardiorespiratory functionality, and neural firing styles in auditory and imaginative and prescient structures.

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M % % Calculate all the Lyapunov exponents for the Duff ing-Van der Pol oscillator. ;Ol, a(2)=[0;1;0... ;Ol,. . , a(n)=[O;O;O... l; Sigma=zeros(n,3); % Initial conditions x0=[1;0;01; aO=eye(3); x=zeros(3,n); % j=1 (Iteration variable) for j=l:n % Step2: Integrate the nonlinear equation of motion over a % characteristic time scale tau to obtain x(j*tau). , an) for time tau. Dim} x ( : ,j ) =xpoint ; % Step3: Apply Gram-Schmidt re-orthonormalization to the axis vectors. , % % % Appendix 31 Sigma(j,n)=log(norm(a(n)) for i=1:3 aOrth(:,i)=dot(a(:,i),aUnit(:,i))*aUnit(:,i); end for i=1:3 Sigma(j,i)=log(norm(aOrth(:,i),2)); end xO=xpoint; aO=aUnit ; end % Step 5 : Compute the Lyapunov exponents Lyapunov=(l/(n*tau))*sum(Sigma,l); % function [x,a]=IntegrateVDPSystem(xO,aO,tau) % % % % % % % % % % % % % % % % This function integrates the Duffing-Van der Pol equations and the variational equations returning the final result at t ime tau for initial conditions x0 and a0 (3 vectors associated with variational equations ) .

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