AUTO_PO_SOLVER

Contents

function varargout = auto_po_solver(obj,R_0,oid,t0,p0,coordinates)
        

Autonomous periodic orbit solver

This function solves for the periodic orbit of autonomous dynamics on SSM with given initial guess of periodic orbit {t0,p0}. Here t0 is a time sequence, and p0 are the corresponding sequence of states in either polar or cartesian representation (string in coordinates). For the rest of arguments, lambda is the spectrum of the spectral subspace used for yielding the reduced dynamics R_0

lambda = obj.System.spectrum.Lambda;
lambdaRe = real(lambda);
lambdaIm = imag(lambda);

% check reduced dynamics to see its consistent with reduced dynamics
m     = numel(lambda)/2;
order = numel(R_0);
beta  = cell(m,1); % coefficients - each cell corresponds to one mode
kappa = cell(m,1); % exponants
for k = 2:order
    R = R_0{k};
    coeffs = R.coeffs;
    ind = R.ind;
    if ~isempty(coeffs)
        for i=1:m
            betai = coeffs(2*i-1,:);
            [~,ki,betai] = find(betai);
            kappai = ind(ki,:);
            % check resonant condition
            % assemble terms
            beta{i}  = [beta{i} betai];
            kappa{i} = [kappa{i}; kappai];
        end
    end
end

fdata = struct();
fdata.beta  = beta;
fdata.kappa = kappa;
fdata.lamdRe = lambdaRe(1:2:end-1);
fdata.lamdIm = lambdaIm(1:2:end-1);

ispolar = strcmp(coordinates, 'polar');
fdata.ispolar = ispolar;
if ispolar
    error('autonomous vector field in polar representation is not implemented yet');
else
    odefun = @(z,p) auto_ode_2mDSSM_cartesian(z,fdata);
end
funcs  = {odefun};

prob = coco_prob();
prob = coco_set(prob,'corr','TOL',1e-5);
prob = ode_isol2po(prob, '', funcs{:}, t0, p0);
runid = coco_get_id(oid, 'auto-po');
bd = coco(prob, runid, [], 0);
varargout{1} = bd;
        

end
        

Published with MATLAB® R2023a