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| View Original: | Simple jump in slow-fast systems.svg (8x8) | |||
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| Keywords: Simple jump in slow-fast systems.svg en Phase portrait of the jump in en slow-fast systems This is a phase portrait of the following system <math> \begin cases \dot x 2-x 2-y \\ \dot y \varepsilon \end cases </math> where <math>\varepsilon 0 1</math> See the code below быст о-медленных системах 2009-04-07 Own Ilya Voyager Other fields O + version 4 3 of W GNU libplot a free library for exporting 2-D vector graphics CPP import graph; import math; import metapost; size 8 inches ; defaultpen 0 45mm ; path phasecurve pair v pair z pair z0 real T real step 0 01 real MAX 3 real direction T>0 1 -1 ; real t; T abs T ; path ret z0; pair cur_z z0; for t 0;t<T;t+ step cur_z cur_z+v cur_z step direction; if abs cur_z x >MAX abs cur_z y >MAX return ret; ret ret cur_z; return ret; pair slowfast pair z real eps 0 1; return eps - z y z y+z x-2 ; path boundary -3 -3 -- 3 -3 -- 3 3 -- -3 3 --cycle; draw boundary ; pair inits -2 3 -1 3 0 3 1 3 2 3 2 5 3 -2 -1 -1 -1 0 -1 1 -1 1 -0 8 -2 -2 1 -1 -2 0 -1 7 1 5 -0 5 1 7 -0 6 ; for pair init inits draw phasecurve slowfast init 15 Arrow 4mm Relative 0 3 ; draw firstcut graph new pair real t return 2-t t t ; -3 0 boundary after p rgb 1 0 0 0 0 ; draw lastcut graph new pair real t return 2-t t t ; 0 3 boundary before p rgb 0 2 0 8 0 2 ; xaxis y BottomTop p fontsize 30 EndArrow ; yaxis x LeftRight p fontsize 30 EndArrow ; Dynamical systems Images with C++ source code | ||||
