ODE_2MDSSM_POLAR

function y = ode_2mDSSM_polar(z, p, data)
        

This function presents vectorized implementation of vector field of reduced dynamics on 2m-dimensional SSMs. Here z is a 2m-dimensinoal state vector and p is parameter vector for excitation frequency and amplitude. All other info such as eigenvalues of master subspace, coefficients of nonlinear terms is included in the structure data. The state vector here is in the form of polar coordinate.

See also: ODE_2MDSSM_CARTESIAN

assert(~isempty(data), 'Structure data in ode_2mDSSM_polar is empty');
% extract data fields
beta   = data.beta;
kappa  = data.kappa;
lamdRe = data.lamdRe;
lamdIm = data.lamdIm;
mFreqs = data.mFreqs;
iNonauto = data.iNonauto;
rNonauto = data.rNonauto;

% rename state and parameter
rho = z(1:2:end-1,:);
th  = z(2:2:end,:);
om   = p(1,:);
epsf = p(2,:);

% autonomous linear part
yrho = lamdRe.*rho;
yth  = lamdIm-mFreqs(:)*om;

% autonomous nonlinear part
m  = numel(mFreqs);
em = eye(m);
for i=1:m
    kappai = kappa{i};
    kappai = full(kappai);
    betai  = beta{i};
    nka = size(kappai,1);
    nbe = numel(betai);
    assert(nka==nbe, 'Size of kappa%d and beta%d does not match',i,i);
    ei = em(i,:);
    for k=1:nka
        ka = kappai(k,:);
        be = betai(k);
        l = ka(1:2:end-1);
        j = ka(2:2:end);
        ang = (l-j-ei)*th;
        rhopower = rho.^((l+j)');
        pdrho = prod(rhopower,1);
        yrho(i,:) = yrho(i,:)+pdrho.*(real(be)*cos(ang)-imag(be)*sin(ang));
        yth(i,:)  = yth(i,:)+pdrho./rho(i,:).*(real(be)*sin(ang)+imag(be)*cos(ang));
    end
end

% nonautonomous leading part
for i=1:numel(iNonauto)
    id = iNonauto(i);
    r  = rNonauto(i);
    r  = epsf*r;
    if data.isbaseForce; r = r.*om.^2; end
    rRe = real(r);
    rIm = imag(r);
    yrho(id,:) = yrho(id,:)+rRe.*cos(th(id,:))+rIm.*sin(th(id,:));
    yth(id,:)  = yth(id,:)-rRe.*sin(th(id,:))./rho(id,:)+rIm.*cos(th(id,:))./rho(id,:);
end

nt = numel(om);
y  = zeros(2*m,nt);
y(1:2:end-1,:) = yrho;
y(2:2:end,:)   = yth;
        

end
        

Published with MATLAB® R2023a