SSM_POSWEEPS

SSM_POSWEEPS

Contents

function FRC = SSM_poSweeps(obj,oid,modes,order,epSamp,omRange,varargin)

SSM_POSWEEPS

This function performs a family of continuations of periodic orbits of reduced dynamics. Continuation is performed with varied forcing frequency for each forcing amplitude. The continuation here starts from the guess of an initial solution.

FRC = SSM_POSWEEPS(OBJ,OID,MODES,ORDER,EPSAMPS,OMRANGE, VARARGIN)

FRC: Forced Response Curve data struct

See also: COCO_POSWEEPS, SSM_LVLSWEEPS, SSM_EPSWEEPS

if~isempty( varargin)
    plotfrc = varargin{1};
end

outdof = obj.FRCOptions.outdof;
FRCom  = cell(numel(epSamp),1);

ii = 1;
for ep = epSamp
    oideps = strcat(oid,num2str(ep));
    if obj.System.order == 1
        obj.System.Fext.epsilon = ep;
    else
        obj.System.fext.epsilon = ep;
    end

    FRCom{ii} = FRC_cont_po(obj,oideps,modes,order,omRange);
    ii = ii +1;
end

results extraction

FRCom = horzcat(FRCom{:});

% save results
FRC = struct();
FRC.SSMorder   = order;
FRC.SSMnonAuto = obj.Options.contribNonAuto;
FRC.FRCom = FRCom;
FRC.eps = epSamp;

Visualization of results

if~isempty( varargin)
    if plotfrc
        sweeps_plot(numel(FRCom),FRCom,outdof,order);
    end
else
   sweeps_plot(numel(FRCom),FRCom,outdof,order);
end
        
end
        
function sweeps_plot(numLabs,FRCom,outdof,order)
% Plot FRC in normal coordinates
thm = struct( 'special', {{'SN', 'HB' , 'PD'}});
thm.SN = {'LineStyle', 'none', 'LineWidth', 2, ...
  'Color', 'cyan', 'Marker', 'o', 'MarkerSize', 8, 'MarkerEdgeColor', ...
  'cyan', 'MarkerFaceColor', 'white'};
thm.HB = {'LineStyle', 'none', 'LineWidth', 2, ...
  'Color', 'black', 'Marker', 's', 'MarkerSize', 8, 'MarkerEdgeColor', ...
  'black', 'MarkerFaceColor', 'white'};
thm.PD = {'LineStyle', 'none', 'LineWidth', 2, ...
  'Color', 'green', 'Marker', 's', 'MarkerSize', 8, 'MarkerEdgeColor', ...
  'black', 'MarkerFaceColor', 'white'};



% Plot FRC in system coordinates
% setup legend
legTypes = zeros(numLabs,1); % each entry can be 1/2/3 - all stab/all unstab/mix
for k=1:numLabs
   stab = FRCom{k}.stability;
   if all(stab)
       legTypes(k) = 1;
   elseif all(~stab)
       legTypes(k) = 2;
   else
       legTypes(k) = 3;
   end
end
legDisp = []; % figure with legends displayed
idmix = find(legTypes==3);
if ~isempty(idmix)
    legDisp = [legDisp idmix(1)];
else
    idallstab = find(legTypes==1);
    if ~isempty(idallstab)
        legDisp = [legDisp,idallstab(1)];
    end
    idallunstab = find(legTypes==2);
    if ~isempty(idallunstab)
        legDisp = [legDisp,idallunstab(1)];
    end
end

ndof = numel(outdof);
for i=1:ndof
    % 2D plot
    figure; hold on
    for k=1:numLabs
        om = FRCom{k}.om;
        Aout = FRCom{k}.Aout(i,:);
        stab = FRCom{k}.stability;
        if any(legDisp==k)
            stab_plot(om,Aout,stab,order,'blue');
        else
            stab_plot(om,Aout,stab,order,'blue','nolegends');
        end
        % plot special points
        SNidx = FRCom{k}.SNidx;
        SNfig = plot(om(SNidx),Aout(SNidx),thm.SN{:});
        set(get(get(SNfig,'Annotation'),'LegendInformation'),...
            'IconDisplayStyle','off');
        %HBidx = FRCom{k}.HBidx;
        %HBfig = plot(om(HBidx),Aout(HBidx),thm.HB{:});
        %set(get(get(HBfig,'Annotation'),'LegendInformation'),...
        %    'IconDisplayStyle','off');
    end
    xlabel('$\Omega$','interpreter','latex','FontSize',16);
    zk = strcat('$||z_{',num2str(outdof(i)),'}||_{\infty}$');
    ylabel(zk,'Interpreter','latex');
    set(gca,'FontSize',14);
    grid on, axis tight; legend boxoff;

    % 3D plot
    figure; hold on
    for k=1:numLabs
        om = FRCom{k}.om;
        epsf = FRCom{k}.ep;
        Aout = FRCom{k}.Aout(i,:);
        stab = FRCom{k}.stability;
        if any(legDisp==k)
            stab_plot3(om,epsf,Aout,stab,order);
        else
            stab_plot3(om,epsf,Aout,stab,order,'nolegends');
        end
        % plot special points
        SNidx = FRCom{k}.SNidx;
        SNfig = plot3(om(SNidx),epsf(SNidx),Aout(SNidx),thm.SN{:});
        set(get(get(SNfig,'Annotation'),'LegendInformation'),...
            'IconDisplayStyle','off');
        %HBidx = FRCom{k}.HBidx;
        %HBfig = plot3(om(HBidx),epsf(HBidx),Aout(HBidx),thm.HB{:});
        %set(get(get(HBfig,'Annotation'),'LegendInformation'),...
        %    'IconDisplayStyle','off');
    end
    xlabel('$\Omega$','interpreter','latex','FontSize',16);
    ylabel('$\epsilon$','interpreter','latex','FontSize',16);
    zk = strcat('$||z_{',num2str(outdof(i)),'}||_{\infty}$');
    zlabel(zk,'Interpreter','latex');
    set(gca,'FontSize',14);
    grid on, axis tight; legend boxoff;
    view([-1,-1,1]);
end

end
        
function stab_plot3(x,y,z,S,order,varargin)
% This function is adapted from stab_plot in coco_plot_bd in coco

II  = 1;
EI  = numel(x);
I   = II;
figs = [];
stab = [];
ST = cell(2,1);
%ST{1} = {'ro','MarkerSize', 4};
%ST{2} = {'bo','MarkerSize', 4};
ST{1} = {'b--','LineWidth',1.5};
ST{2} = {'b-','LineWidth',1.5};
while true
  if II>=EI; break; end
  [I, I0] = next_index(EI, S, I, II);
  fig = plot3(x(II:I0), y(II:I0), z(II:I0), ST{S(II)+1}{:});
  figs = [figs fig];
  stab = [stab S(II)+1];
  II = I0;
end

if isempty(varargin)
    Leg = cell(2,1);
    Leg{1} = strcat('SSM-$$\mathcal{O}(',num2str(order),')$$ - unstable');
    Leg{2} = strcat('SSM-$$\mathcal{O}(',num2str(order),')$$ - stable');
    numSegs = numel(figs);
    if numSegs==1
        % add legend
        legend(Leg{stab(1)},'Interpreter','latex');
    else
        legend(Leg{stab(1)},Leg{stab(2)},'Interpreter','latex');
        if numSegs>2
            % remove repetitive legends from option
            for j=3:numSegs
                set(get(get(figs(j),'Annotation'),'LegendInformation'),...
                    'IconDisplayStyle','off');
            end
        end
    end
else
    numSegs = numel(figs);
    for j=1:numSegs
        set(get(get(figs(j),'Annotation'),'LegendInformation'),...
            'IconDisplayStyle','off');
    end
end
end

function [I, I0] = next_index(EI, S, I, II)
while (I<EI && S(II)==S(I)); I=I+1; end
I0 = I;
end


Published with MATLAB® R2023a