Lorenz2
Lorenz2
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(*Parametersforthesystem*)parameters={a0.9,b5,c9.9,d1};(*Systemofdifferentialequations*)equations={x'[t]==-ax[t]-y[t]^2-z[t]^2+ac,y'[t]==x[t]y[t]-bx[t]z[t]+d,z'[t]==-z[t]+bx[t]y[t]+x[t]z[t]}/.parameters;(*Initialconditions*)initialConditions={x[0]==1,y[0]==1,z[0]==1.05};(*Numericalsolution*)solution=NDSolve[{equations,initialConditions},{x,y,z},{t,0,1000},Method"StiffnessSwitching"];(*3Dplotoftheattractorwithcolorgradient*)trajectoryPlot=ParametricPlot3D[Evaluate[{x[t],y[t],z[t]}/.solution],{t,0,1000},PlotRangeAll,AxesLabel{"x","y","z"},PlotStyle{Dashed},ColorFunction"DarkRainbow",ColorFunctionScalingTrue,BoxedTrue,PlotPoints1000];trajectoryPlot
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Plot[{x[t]}/.solution,{t,900,1000},PlotStyle{Thickness[0.001],Blue},PlotRangeAll,PlotPoints200,PlotHighlightingNone]
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Double Wing Chaotic Attractor
Double Wing Chaotic Attractor
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(*Parametersforthesystem*)parameters={a0.2,c1,d-0.4,e-1,g-1};(*Systemofdifferentialequations*)equations={x'[t]==ax[t]+cy[t]z[t],y'[t]==dy[t]-x[t]z[t],z'[t]==ez[t]+gx[t]y[t]}/.parameters;(*Initialconditions*)initialConditions={x[0]==1,y[0]==1,z[0]==1};(*Numericalsolution*)solution=NDSolve[{equations,initialConditions},{x,y,z},{t,0,600}];(*3Dplotoftheattractorwithcolorgradient*)trajectoryPlot=ParametricPlot3D[Evaluate[{x[t],y[t],z[t]}/.solution],{t,0,600},PlotRangeAll,AxesLabel{"x","y","z"},BoxedTrue,PlotStyleThick,ColorFunction"Rainbow",ColorFunctionScalingTrue,PlotPoints1000];trajectoryPlot
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Wang Sun attractor
Wang Sun attractor
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(*Parametersforthesystem*)parameters={a0.2,b-0.01,c1,d-0.4,e-1,g-1};(*Systemofdifferentialequations*)equations={x'[t]==ax[t]+cy[t]z[t],y'[t]==bx[t]+dy[t]-x[t]z[t],z'[t]==ez[t]+gx[t]y[t]}/.parameters;(*Initialconditions*)initialConditions={x[0]==1,y[0]==1,z[0]==1.03};(*Numericalsolution*)solution=NDSolve[{equations,initialConditions},{x,y,z},{t,0,1000}];(*3Dplotoftheattractorwithcolorgradient*)trajectoryPlot=ParametricPlot3D[Evaluate[{x[t],y[t],z[t]}/.solution],{t,0,1000},PlotRangeAll,AxesLabel{"x","y","z"},BoxedTrue,PlotStyleThick,ColorFunction"Rainbow",ColorFunctionScalingTrue,PlotPoints1000];trajectoryPlot
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[TSUCS2] Three-Scroll Unified Chaotic System
[TSUCS2] Three-Scroll Unified Chaotic System
References
References