MATH528 Lesson11
Qualitative analysis of nonlinear ODE systems

Dampened pendulum

Manipulate[
StreamPlot[{omega,-k Sin[theta]-c theta},{theta,-8Pi,8Pi},{omega,-4Pi,4Pi},StreamColorFunction->Hue,FrameLabel->{"θ","ω"},PlotLegends->Automatic,AspectRatio->Automatic],{k,0.1,10},{c,0.1,10}]

Loktka-Volterra population model

Manipulate[
StreamPlot[{a y1-b y1 y2,k y1 y2-l y2},{y1,0,25},{y2,0,25},StreamColorFunction->Hue,FrameLabel->{"y1","y2"},PlotLegends->Automatic,AspectRatio->Automatic],{a,0.1,10},{b,0.1,10},{k,0.1,10.},{l,0.1,10.}]

Van Der Pol oscillator

Manipulate[
StreamPlot[{y2,μ (1-y1^2) y2-y1},{y1,-10,10},{y2,-10,10},StreamColorFunction->Hue,FrameLabel->{"y1","y2"},PlotLegends->Automatic,AspectRatio->Automatic],{μ,0.1,10}]