How to plot an unstable attractor?





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6












$begingroup$


I'm trying to solve and plot the following in Mathematica:



eqns = {x'[t] == 

    x[t] - y[t] - 

     x[t] (x[t]^2 + y[t]^2) + (x[t] y[t])/Sqrt[x[t]^2 + y[t]^2], 

   y'[t] == 

    x[t] + y[t] - y[t] (x[t]^2 + y[t]^2) - 

     x[t]^2/Sqrt[x[t]^2 + y[t]^2]};

DSolve[eqns, {x, y}, t]


This is supposed to be an example of unstable attractor ODE. However, execution never ends and I don't manage to see the solution of the equation.






plotting differential-equations







share|improve this question











$endgroup$










  • 1




    $begingroup$
    Try using NDSolve instead
    $endgroup$
    – b3m2a1
    May 26 at 20:55


















6












$begingroup$


I'm trying to solve and plot the following in Mathematica:



eqns = {x'[t] == 

    x[t] - y[t] - 

     x[t] (x[t]^2 + y[t]^2) + (x[t] y[t])/Sqrt[x[t]^2 + y[t]^2], 

   y'[t] == 

    x[t] + y[t] - y[t] (x[t]^2 + y[t]^2) - 

     x[t]^2/Sqrt[x[t]^2 + y[t]^2]};

DSolve[eqns, {x, y}, t]


This is supposed to be an example of unstable attractor ODE. However, execution never ends and I don't manage to see the solution of the equation.






plotting differential-equations







share|improve this question











$endgroup$










  • 1




    $begingroup$
    Try using NDSolve instead
    $endgroup$
    – b3m2a1
    May 26 at 20:55














6












6








6


1



$begingroup$


I'm trying to solve and plot the following in Mathematica:



eqns = {x'[t] == 

    x[t] - y[t] - 

     x[t] (x[t]^2 + y[t]^2) + (x[t] y[t])/Sqrt[x[t]^2 + y[t]^2], 

   y'[t] == 

    x[t] + y[t] - y[t] (x[t]^2 + y[t]^2) - 

     x[t]^2/Sqrt[x[t]^2 + y[t]^2]};

DSolve[eqns, {x, y}, t]


This is supposed to be an example of unstable attractor ODE. However, execution never ends and I don't manage to see the solution of the equation.






plotting differential-equations







share|improve this question











$endgroup$




I'm trying to solve and plot the following in Mathematica:



eqns = {x'[t] == 

    x[t] - y[t] - 

     x[t] (x[t]^2 + y[t]^2) + (x[t] y[t])/Sqrt[x[t]^2 + y[t]^2], 

   y'[t] == 

    x[t] + y[t] - y[t] (x[t]^2 + y[t]^2) - 

     x[t]^2/Sqrt[x[t]^2 + y[t]^2]};

DSolve[eqns, {x, y}, t]


This is supposed to be an example of unstable attractor ODE. However, execution never ends and I don't manage to see the solution of the equation.






plotting differential-equations




plotting differential-equations






share|improve this question















share|improve this question













share|improve this question




share|improve this question








edited May 27 at 3:56









user64494

4,2162 gold badges14 silver badges23 bronze badges




4,2162 gold badges14 silver badges23 bronze badges










asked May 26 at 20:48









JavierJavier

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1506 bronze badges











  • 1




    $begingroup$
    Try using NDSolve instead
    $endgroup$
    – b3m2a1
    May 26 at 20:55














  • 1




    $begingroup$
    Try using NDSolve instead
    $endgroup$
    – b3m2a1
    May 26 at 20:55








1




1




$begingroup$
Try using NDSolve instead
$endgroup$
– b3m2a1
May 26 at 20:55




$begingroup$
Try using NDSolve instead
$endgroup$
– b3m2a1
May 26 at 20:55










2 Answers
2






active

oldest

votes


















15














$begingroup$

To visualize a 2D system, I would start with StreamPlot:



vf = {x', y'} /. First@Solve[eqns /. f_[t] :> f, {x', y'}]; (* strip the args *)

StreamPlot[vf, {x, -2, 2}, {y, -2, 2}]


Mathematica graphics



You can use StreamPoints to highlight the structure and Epilog to mark the attractor at $(1,0)$:



ics = {{{Cos[1/5], Sin[1/5]}, Red},

       {{0.5, 0}, Magenta}, {{1.5, 0.}, Magenta}};

StreamPlot[vf, {x, -2, 2}, {y, -2, 2},

 StreamPoints -> {Append[ics, Automatic]},

 Epilog -> {White, EdgeForm[Black], Disk[{1, 0}, 0.03]}]


Mathematica graphics






share|improve this answer









$endgroup$























    5














    $begingroup$

    eqns = {x'[t] == 
    
    x[t] - y[t] - 
    
     x[t] (x[t]^2 + y[t]^2) + (x[t] y[t])/Sqrt[x[t]^2 + y[t]^2], 
    
   y'[t] == 
    
    x[t] + y[t] - y[t] (x[t]^2 + y[t]^2) - 
    
     x[t]^2/Sqrt[x[t]^2 + y[t]^2]};
    
sol = NDSolve[Join[{x[0]==1.5, y[0]==1.5}, eqns], {x, y}, {t, 0, 50}];
    
ParametricPlot[{x[t], y[t]}/.sol//Evaluate, {t, 0, 50}, PlotRange->All]


    enter image description here






    share|improve this answer









    $endgroup$

















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      2 Answers
      2






      active

      oldest

      votes








      2 Answers
      2






      active

      oldest

      votes









      active

      oldest

      votes






      active

      oldest

      votes









      15














      $begingroup$

      To visualize a 2D system, I would start with StreamPlot:



      vf = {x', y'} /. First@Solve[eqns /. f_[t] :> f, {x', y'}]; (* strip the args *)
      
StreamPlot[vf, {x, -2, 2}, {y, -2, 2}]


      Mathematica graphics



      You can use StreamPoints to highlight the structure and Epilog to mark the attractor at $(1,0)$:



      ics = {{{Cos[1/5], Sin[1/5]}, Red},
      
       {{0.5, 0}, Magenta}, {{1.5, 0.}, Magenta}};
      
StreamPlot[vf, {x, -2, 2}, {y, -2, 2},
      
 StreamPoints -> {Append[ics, Automatic]},
      
 Epilog -> {White, EdgeForm[Black], Disk[{1, 0}, 0.03]}]


      Mathematica graphics






      share|improve this answer









      $endgroup$




















        15














        $begingroup$

        To visualize a 2D system, I would start with StreamPlot:



        vf = {x', y'} /. First@Solve[eqns /. f_[t] :> f, {x', y'}]; (* strip the args *)
        
StreamPlot[vf, {x, -2, 2}, {y, -2, 2}]


        Mathematica graphics



        You can use StreamPoints to highlight the structure and Epilog to mark the attractor at $(1,0)$:



        ics = {{{Cos[1/5], Sin[1/5]}, Red},
        
       {{0.5, 0}, Magenta}, {{1.5, 0.}, Magenta}};
        
StreamPlot[vf, {x, -2, 2}, {y, -2, 2},
        
 StreamPoints -> {Append[ics, Automatic]},
        
 Epilog -> {White, EdgeForm[Black], Disk[{1, 0}, 0.03]}]


        Mathematica graphics






        share|improve this answer









        $endgroup$


















          15














          15










          15







          $begingroup$

          To visualize a 2D system, I would start with StreamPlot:



          vf = {x', y'} /. First@Solve[eqns /. f_[t] :> f, {x', y'}]; (* strip the args *)
          
StreamPlot[vf, {x, -2, 2}, {y, -2, 2}]


          Mathematica graphics



          You can use StreamPoints to highlight the structure and Epilog to mark the attractor at $(1,0)$:



          ics = {{{Cos[1/5], Sin[1/5]}, Red},
          
       {{0.5, 0}, Magenta}, {{1.5, 0.}, Magenta}};
          
StreamPlot[vf, {x, -2, 2}, {y, -2, 2},
          
 StreamPoints -> {Append[ics, Automatic]},
          
 Epilog -> {White, EdgeForm[Black], Disk[{1, 0}, 0.03]}]


          Mathematica graphics






          share|improve this answer









          $endgroup$



          To visualize a 2D system, I would start with StreamPlot:



          vf = {x', y'} /. First@Solve[eqns /. f_[t] :> f, {x', y'}]; (* strip the args *)
          
StreamPlot[vf, {x, -2, 2}, {y, -2, 2}]


          Mathematica graphics



          You can use StreamPoints to highlight the structure and Epilog to mark the attractor at $(1,0)$:



          ics = {{{Cos[1/5], Sin[1/5]}, Red},
          
       {{0.5, 0}, Magenta}, {{1.5, 0.}, Magenta}};
          
StreamPlot[vf, {x, -2, 2}, {y, -2, 2},
          
 StreamPoints -> {Append[ics, Automatic]},
          
 Epilog -> {White, EdgeForm[Black], Disk[{1, 0}, 0.03]}]


          Mathematica graphics







          share|improve this answer












          share|improve this answer



          share|improve this answer










          answered May 26 at 22:01









          Michael E2Michael E2

          159k13 gold badges219 silver badges518 bronze badges




          159k13 gold badges219 silver badges518 bronze badges




























              5














              $begingroup$

              eqns = {x'[t] == 
              
    x[t] - y[t] - 
              
     x[t] (x[t]^2 + y[t]^2) + (x[t] y[t])/Sqrt[x[t]^2 + y[t]^2], 
              
   y'[t] == 
              
    x[t] + y[t] - y[t] (x[t]^2 + y[t]^2) - 
              
     x[t]^2/Sqrt[x[t]^2 + y[t]^2]};
              
sol = NDSolve[Join[{x[0]==1.5, y[0]==1.5}, eqns], {x, y}, {t, 0, 50}];
              
ParametricPlot[{x[t], y[t]}/.sol//Evaluate, {t, 0, 50}, PlotRange->All]


              enter image description here






              share|improve this answer









              $endgroup$




















                5














                $begingroup$

                eqns = {x'[t] == 
                
    x[t] - y[t] - 
                
     x[t] (x[t]^2 + y[t]^2) + (x[t] y[t])/Sqrt[x[t]^2 + y[t]^2], 
                
   y'[t] == 
                
    x[t] + y[t] - y[t] (x[t]^2 + y[t]^2) - 
                
     x[t]^2/Sqrt[x[t]^2 + y[t]^2]};
                
sol = NDSolve[Join[{x[0]==1.5, y[0]==1.5}, eqns], {x, y}, {t, 0, 50}];
                
ParametricPlot[{x[t], y[t]}/.sol//Evaluate, {t, 0, 50}, PlotRange->All]


                enter image description here






                share|improve this answer









                $endgroup$


















                  5














                  5










                  5







                  $begingroup$

                  eqns = {x'[t] == 
                  
    x[t] - y[t] - 
                  
     x[t] (x[t]^2 + y[t]^2) + (x[t] y[t])/Sqrt[x[t]^2 + y[t]^2], 
                  
   y'[t] == 
                  
    x[t] + y[t] - y[t] (x[t]^2 + y[t]^2) - 
                  
     x[t]^2/Sqrt[x[t]^2 + y[t]^2]};
                  
sol = NDSolve[Join[{x[0]==1.5, y[0]==1.5}, eqns], {x, y}, {t, 0, 50}];
                  
ParametricPlot[{x[t], y[t]}/.sol//Evaluate, {t, 0, 50}, PlotRange->All]


                  enter image description here






                  share|improve this answer









                  $endgroup$



                  eqns = {x'[t] == 
                  
    x[t] - y[t] - 
                  
     x[t] (x[t]^2 + y[t]^2) + (x[t] y[t])/Sqrt[x[t]^2 + y[t]^2], 
                  
   y'[t] == 
                  
    x[t] + y[t] - y[t] (x[t]^2 + y[t]^2) - 
                  
     x[t]^2/Sqrt[x[t]^2 + y[t]^2]};
                  
sol = NDSolve[Join[{x[0]==1.5, y[0]==1.5}, eqns], {x, y}, {t, 0, 50}];
                  
ParametricPlot[{x[t], y[t]}/.sol//Evaluate, {t, 0, 50}, PlotRange->All]


                  enter image description here







                  share|improve this answer












                  share|improve this answer



                  share|improve this answer










                  answered May 26 at 21:16









                  b3m2a1b3m2a1

                  31.7k3 gold badges64 silver badges184 bronze badges




                  31.7k3 gold badges64 silver badges184 bronze badges


































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