Pursuit and evation in one dimensional space

Uniform solution

deq  =  {u'[t] == 
          r (1 - u[t]/K) u[t]  -  
            a u[t] v[t], 
v'[t] == 
          b u[t] v[t] - d v[t], u[0] == u0, 
        v[0] == v0}

para  =  {r -> 1,  K -> 2,  a -> 1,  b -> 1,  
        d -> 1}

deqN  =  deq /. para /. {u0 -> 2,  
          v0 -> 0.01}

endT  =  100;

sol  =  NDSolve[deqN, {u[t], v[t]}, {t, 0, endT}]

Plot[ {Evaluate[u[t]] /. sol, Evaluate[v[t]] /. sol}, {t, 0, endT}, 
      PlotRange -> All, 
      AxesLabel -> {"t", "u[t],v[t]"}]

ParametricPlot[Evaluate[{u[t], v[t]}] /. sol, {t, 0, endT}, 
      PlotRange -> All, 
      AxesLabel -> {"u[t]", "v[t]"}]

2

Reation diffusion

drawFigure[x1_List,  x2_List,  opt___] := 
      Block[{g1, g2}, 
g1  =  
          ListPlot[x1, PlotJoined -> True, 
            PlotStyle -> RGBColor[0, 0, 1], opt, 
            DisplayFunction -> Identity]; 
g2  =  
          ListPlot[x2, PlotJoined -> True, 
            PlotStyle -> RGBColor[1, 0, 0], opt, 
            DisplayFunction -> Identity]; 
Return[
          Show[g1, g2, 
            DisplayFunction -> $DisplayFunction]];
]

size  =  101;
data1  =  
        ReadList["RD-1dim-test-u", {Real, 
            Real}];
data1  =  Partition[data1, size];
Length[data1]

data2  =  
        ReadList["RD-1dim-test-v", {Real, 
            Real}];
data2  =  Partition[data2, size];
Length[data2]

drawFigure[data1[[1]],  data2[[1]], PlotRange -> All, 
      AxesLabel -> {"x", "u, v"}]

drawFigure[Last[data1],  Last[data2], PlotRange -> All, 
      AxesLabel -> {"x", "u, v"}]

Do[
drawFigure[data1[[i]],  data2[[i]], 
        PlotRange -> {0, 2}, 
        AxesLabel -> {"x", "u, v"}], {i, 1, Length[data1], 
        10}
]

gUList  =  {};
\(Do[
g\  = \ 
        ListPlot[data1[\([i]\)], PlotJoined -> True, 
          PlotStyle -> RGBColor[0, 0, 1], PlotRange -> {0, 2}, 
          AxesLabel -> {"x", "u, v"}]; 
AppendTo[gUList, g], {i, 1, Length[data1], 
        10}
]\)

gVList  =  {};
\(Do[
g\  = \ 
        ListPlot[data2[\([i]\)], PlotJoined -> True, 
          PlotStyle -> RGBColor[1, 0, 0], PlotRange -> {0, 2}, 
          AxesLabel -> {"x", "u, v"}]; 
AppendTo[gVList, g], {i, 1, Length[data1], 
        10}
]\)

Show[gUList, gVList]

2