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  • We can build a manipulate interactive tool that allows you to adjust certain parameter values like the carrying capacity, growth rate, and initial conditions.
    • In[]:=
    Manipulate[​​p[n_]:=p[n-1]+R*(1-(p[n-1]/Cap))*p[n-1];p[0]=p0;Column[{Show[ListPlot[Table[{n,p[n]},{n,0,12}],PlotStylecolor,​​PlotLabel"NonLinear Discrete Dynamical System Carrying Capacity",​​LabelStyleDirective[Black,Bold]],ImageSizeLarge],Framed[Labeled[R,"Rate of Growth",Top]],Framed[Labeled[Cap,"Carrying Capacity Cap",Top]],Framed[Labeled[p0,"Inititial Condition p0",Top]],TableForm[Table[{n,p[n]},{n,0,12}],TableHeadings{None,{"n iterations","p[n] output"}}]}],{{R,.6},-1,3,​​.2},{{Cap,1000},1,1000,50},{{p0,30},0,1000,100},{{color,Red},{Red,Blue,Green,Brown,Orange,Yellow}}]
    Out[]=
    ​
    R
    Cap
    p0
    color
    Rate of Growth
    0.6
    Carrying Capacity Cap
    1000
    Inititial Condition p0
    30
    n iterations
    p[n] output
    0
    30
    1
    47.46
    2
    74.5845
    3
    115.998
    4
    177.523
    5
    265.128
    6
    382.029
    7
    523.679
    8
    673.342
    9
    805.314
    10
    899.384
    11
    953.679
    12
    980.184