Phase plane analysis for nonlinear and linear systems near (6,2)

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SUMMARY

This discussion focuses on performing phase plane analysis for nonlinear and linear systems using Maple software, specifically targeting the points near (6, 2). The user initially struggled with setting the correct initial conditions and plotting trajectories within a specified range. Key commands include the use of DEplot for visualizing the phase plane and the differentiation of functions to derive the system equations. The user successfully resolved their issue with the help of community input.

PREREQUISITES
  • Familiarity with Maple software for mathematical modeling
  • Understanding of differential equations and their graphical representation
  • Knowledge of phase plane analysis techniques
  • Basic skills in manipulating mathematical expressions and functions
NEXT STEPS
  • Explore advanced features of Maple for dynamic system simulations
  • Learn how to implement nonlinear system analysis using Maple
  • Research techniques for linearization of nonlinear systems
  • Investigate the implications of initial conditions on phase plane trajectories
USEFUL FOR

Mathematicians, engineers, and students involved in dynamical systems analysis, particularly those using Maple for phase plane visualization and nonlinear system modeling.

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i need help on this part, does anyone have any idead about maple lab? I should get the cure and trajectories in the red rectangular. But i try to fix the points and range, i still didn't get it

http://img193.imageshack.us/img193/387/deqp.jpg

Code:
trange1 := -3..3: window1 := x=1..3,y=-3..-1: 
inits1:=[[x(0)=2.5,y(0)=-1.5],[x(0)=1.5,y(0)=-1.5],[x(0)=1.5,y(0)=-2.5],
   [x(0)=2.5,y(0)=-2.5],[x(0)=2+2.0/3.0,y(0)=-2+(3.0-sqrt(17.0))/3.0]]:
DEplot([dex,dey],[x(t),y(t)],t=trange1,inits1, window1,color=GREEN,
   linecolor=[RED,BLUE,CYAN,PLUM,BLACK],thickness=2,stepsize=0.002,
   title="Phase plane near (2,-2): nonlinear system");

F1:=4*u+0*v; 
G1:=6*u+6*v;
dex1:=diff(x(t),t)=eval(F1,{u=x(t),v=y(t)});
dey1:=diff(y(t),t)=eval(G1,{u=x(t),v=y(t)});
DEplot([dex1,dey1],[x(t),y(t)],t=trange2,inits2, window1,color=GREEN,linecolor=[RED,BLUE,CYAN,PLUM,YELLOW],thickness=2,stepsize=0.002,
title="Phase plane near (0,0): linearized system");

Modify the above commands to produce plots of the phase plane for the nonlinear and linear systems near (6, 2). There are no straight line trajectories to consider in this case..

 
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ohh i figured this out... thank you for visiting
 

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