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# BrianWeinstein/Pursuit-Evasion

Last active August 16, 2019 06:53
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 nc = 15; nr = 3; cx = Table[ToExpression[StringJoin["cx", ToString[i]]], {i, 1, nc}]; cy = Table[ToExpression[StringJoin["cy", ToString[i]]], {i, 1, nc}]; rx = Table[ToExpression[StringJoin["rx", ToString[i]]], {i, 1, nr}]; ry = Table[ToExpression[StringJoin["ry", ToString[i]]], {i, 1, nr}]; coordList = Flatten[{Transpose[{cx, cy}], Transpose[{rx, ry}]}]; cspeed = 1; rspeed = 1.1; eqns = Flatten[ {Table[ {{Derivative[1][cx[[i]]][t], Derivative[1][cy[[i]]][t]} == cspeed*Normalize[Sum[{rx[[j]][t] - cx[[i]][t], ry[[j]][t] - cy[[i]][t]}/((cx[[i]][t] - rx[[j]][t])^2 + (cy[[i]][t] - ry[[j]][t])^2), {j, 1, nr}]], cx[[i]][0] == RandomReal[{-30, 30}], cy[[i]][0] == RandomReal[{-30, 30}] }, {i, 1, nc} ], Table[ {{Derivative[1][rx[[i]]][t], Derivative[1][ry[[i]]][t]} == rspeed*Normalize[Sum[{rx[[i]][t] - cx[[j]][t], ry[[i]][t] - cy[[j]][t]}/((cx[[j]][t] - rx[[i]][t])^2 + (cy[[j]][t] - ry[[i]][t])^2), {j, 1, nc}]], rx[[i]][0] == RandomReal[{-5, 5}], ry[[i]][0] == RandomReal[{-5, 5}] }, {i, 1, nr} ] } ]; soln = NDSolve[eqns, coordList, {t, 0, 200}, MaxSteps -> 200000, PrecisionGoal -> 2][[1]]; coordListFn[t_] := Flatten[Table[{coordList[[i]][t], coordList[[i + 1]][t]}, {i, 1, 2*(nc + nr), 2}]] cops[t_] := Evaluate[coordListFn[t][[1 ;; 2*nc]] /. soln[[1 ;; 2*nc]]] robbers[t_] := Evaluate[coordListFn[t][[2*nc + 1 ;; 2*(nc + nr)]] /. soln[[2*nc + 1 ;; 2*(nc + nr)]]] Manipulate[ Show[ ParametricPlot[ {cops[t], robbers[t]}, {t, 0, tmax}, PlotRange -> All, PlotStyle -> {Darker[Red], {Darker[Green]}} ], ListPlot[ {Partition[cops[0], 2], Partition[robbers[0], 2], Partition[cops[tmax], 2], Partition[robbers[tmax], 2]}, PlotStyle -> {Directive[PointSize[Medium], Black], Directive[PointSize[Medium], Black], Darker[Red], Darker[Green]} ], Axes -> False ], {tmax, 0.001, 200, 1.5} ]
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