ODE_aut

Contents

function y = ode_aut(obj, z, p, data)
        

ODE_AUT

This function presents nonvectorized implementation of vector field

where epsilon is a parameter will be applied to damping matrix, and alpha is the parameter will be applied to nonlinearity. We assume there is only one conserved quantity in the system without damping. If the system has other symmetries, this implementation will fail.

if isempty(data)
    error('a data structure with fnl field should be given');
else
    n = obj.system.n;
    nt = size(z,2);
    x  = z(1:n,:);
    xd = z(n+1:2*n,:);

    % linear part
    y1x = xd;
    y1d = obj.system.K*x+repmat(p(1,:),[n,1]).*(obj.system.C*xd); % Kx+Cv

    % nonlinear part
    fnl = data.fnl; % fnl.coeffs and fnl.ind
    numNonlinearTerms = size(fnl.coeffs,2);
    y2 = 0;
    for i=1:numNonlinearTerms
        coeff = repmat(fnl.coeffs(:,i),[1, nt]);
        ind = fnl.ind(i,:);
        % find nonzero exponents
        expind = find(ind);
        s = 1;
        for j=1:numel(expind)
            s = s.*x(expind(j),:).^ind(expind(j));
        end
        s = repmat(s, [n, 1]);
        y2 = y2+coeff.*s;
    end
    y2 = repmat(p(2,:),[n,1]).*y2;
    y = [y1x; -obj.system.M\(y1d+y2)];
end
        

end
        

Published with MATLAB® R2023a