AUTO_ODE_2MDSSM_CARTESIAN

function y = auto_ode_2mDSSM_cartesian(z, data)

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

See also: ODE_2MDSSM_POLAR

assert(~isempty(data), 'Structure data in ode_2mDSSM_cartesian is empty');
% extract data fields
beta   = data.beta;
kappa  = data.kappa;
lamdRe = data.lamdRe;
lamdIm = data.lamdIm;

% rename state and parameter
zRe  = z(1:2:end-1,:);
zIm  = z(2:2:end,:);
zcomp = zRe+1i*zIm; % qs in formulation
zconj = conj(zcomp);

% autonomous linear part
yRe = lamdRe.*zRe-lamdIm.*zIm;
yIm = lamdRe.*zIm+lamdIm.*zRe;

% autonomous nonlinear part
m  = numel(lamdRe);
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);
    for k=1:nka
        ka = kappai(k,:);
        be = betai(k);
        l = ka(1:2:end-1)';
        j = ka(2:2:end)';
        zk = be*prod(zcomp.^l.*zconj.^j,1);
        yRe(i,:) = yRe(i,:)+real(zk);
        yIm(i,:) = yIm(i,:)+imag(zk);
    end
end

nt = size(z,2);
y  = zeros(2*m,nt);
y(1:2:end-1,:) = yRe;
y(2:2:end,:)   = yIm;

end