http://www.mapleprimes.com/posts/35891-Rossler-System-Initial-Investigation en-us 2026 Maplesoft, A Division of Waterloo Maple Inc. Maplesoft Document System Wed, 10 Jun 2026 20:58:51 GMT Wed, 10 Jun 2026 20:58:51 GMT The latest comments added to the Post, Rossler system, initial investigation http://www.mapleprimes.com/images/mapleprimeswhite.jpg http://www.mapleprimes.com/posts/35891-Rossler-System-Initial-Investigation http://www.mapleprimes.com/posts/35891-Rossler-System-Initial-Investigation?ref=Feed:MaplePrimes:Rossler system, initial investigation:Comments#comment59699 My post above seems to have lost all it's new-line-carriage-return's. Why would that happen ? I'm sure it looked OK when I posted it earlier ! I'll try again: Here is the Rossler system, one of the simplest examples of 3 dimensional deterministic chaos (under certain conditions according to "params"). Thanks to Doug and Joe for various assists. Comments and critiques most welcome ! restart; interface(displayprecision=10): ross_x:=diff(x(t),t)=-y(t)-z(t): ross_y:=diff(y(t),t)=x(t)+a*y(t): ross_z:=diff(z(t),t)=b+x(t)*z(t)-c*z(t): rossler_sys:=ross_x,ross_y,ross_z; #Find fixed points: sol:=solve({rhs(ross_x)=0,rhs(ross_y)=0,rhs(ross_z)=0},{x(t),y(t),z(t)}): fp_sol:=solve({rhs(ross_x)=0,rhs(ross_y)=0,rhs(ross_z)=0},{x(t),y(t),z(t)}): params:={a=0.32,b=0.3,c=4.5}: fp_sol:=allvalues(eval(fp_sol,params)): fp1:=fp_sol[1];fp2:=fp_sol[2]; #Jacobian: J := frontend(Student:-VectorCalculus:-Jacobian, [map(rhs,[rossler_sys]), [x,y,z](t)], [{`*`,`+`,list},{}]); ev1:=LinearAlgebra[Eigenvalues](eval(J,fp1 union params)); ev2:=LinearAlgebra[Eigenvalues](eval(J,fp2 union params)); # now take a look at the orbits assign(params); DEtools[DEplot3d]({rossler_sys},{x(t),y(t),z(t)},t=50..200,[[x(0)=1,y(0)=1,z(0)=1]],scene=[x(t),y(t),z(t)],stepsize=0.05,thickness=1,linecolor=blue,orientation=[40,120]); #To do: #check eigenvectors #plot poincare return map #plot bifurcation diagram (vary b) #plot 2D or 1D orbits with differing IVPs The latest comments added to the Post, Rossler system, initial investigation 59699 Tue, 26 Jan 2010 10:25:26 Z longrob longrob http://www.mapleprimes.com/posts/35891-Rossler-System-Initial-Investigation?ref=Feed:MaplePrimes:Rossler system, initial investigation:Comments#comment59700 <p>&nbsp;A slight mod to your worksheet to add animation.</p> <p><span><a href="http://www.mapleprimes.com:8080/maplenet/primes/worksheet/221_rossler_animate.mw">View 221_rossler_animate.mw on MapleNet</a> or <a href="http://www.mapleprimes.com/files/221_rossler_animate.mw">Download 221_rossler_animate.mw</a><br /> </span></p> <p>&nbsp;</p> <p>&nbsp;</p> <address>Regards,<br /> Georgios Kokovidis</address> <address>Dr&auml;ger Medical</address> <pre> </pre> The latest comments added to the Post, Rossler system, initial investigation 59700 Tue, 26 Jan 2010 21:33:07 Z gkokovidis gkokovidis http://www.mapleprimes.com/posts/35891-Rossler-System-Initial-Investigation?ref=Feed:MaplePrimes:Rossler system, initial investigation:Comments#comment59701 You should be able to edit the post to fix it. There's an edit button at the bottom. The latest comments added to the Post, Rossler system, initial investigation 59701 Wed, 27 Jan 2010 09:14:22 Z roman_pearce roman_pearce http://www.mapleprimes.com/posts/35891-Rossler-System-Initial-Investigation?ref=Feed:MaplePrimes:Rossler system, initial investigation:Comments#comment59702 <p>Giorgios, the animation doesn't work here (Maple13.01, standard), I haven't looked into it, is a change in the parameters required or something?.</p> The latest comments added to the Post, Rossler system, initial investigation 59702 Fri, 29 Jan 2010 21:01:07 Z PatrickT PatrickT http://www.mapleprimes.com/posts/35891-Rossler-System-Initial-Investigation?ref=Feed:MaplePrimes:Rossler system, initial investigation:Comments#comment59703 <p>Hi PatrickT,</p> <p>I have jsut tried the worksheet on Maple 13.02 (standart on WinXP) and the animation does come up with no changes to Giogios's worksheet.&nbsp; Could you try updating Maple 13 and check to see if the problem goes away?</p> <p>Scott<br /> Application Developer<br /> Maplesoft</p> The latest comments added to the Post, Rossler system, initial investigation 59703 Fri, 29 Jan 2010 21:14:22 Z Scott03 Scott03 http://www.mapleprimes.com/posts/35891-Rossler-System-Initial-Investigation?ref=Feed:MaplePrimes:Rossler system, initial investigation:Comments#comment59704 <p>Thanks Scott, okay I was assuming that the animation would play automatically, but instead I had to trigger it by selecting &quot;play&quot; in the context menu (I don't usually do mouse clicks so it didn't occur to me to try it).</p> <p>Even better, I found that by selecting the following:</p> <pre> Tools -&gt; Options -&gt; Display -&gt; Plot Display -&gt; Window </pre> <p>I get a very intuitive &quot;play&quot; button at the bottom of the pop-up window. Then it doesn't take a genius to figure out that pressing play will trigger the animation. Even I was able to work it out. And this one time I overcame a certain reluctance and touched a mouse.</p> <p>Cheers Scott,</p> <p>Patrick.</p> The latest comments added to the Post, Rossler system, initial investigation 59704 Fri, 29 Jan 2010 21:43:33 Z PatrickT PatrickT