> #hw25, Tim Nasralla, 12/2/21

                          First Written: Nov. 2021 


This is DMB.txt, A Maple package to explore Dynamical models in Biology (both 

   discrete and continuous)


   accompanying the class Dynamical Models in Biology, Rutgers University. 

      Taught by Dr. Z. (Doron Zeilbeger) 



               The most current version is available on WWW at:

          http://sites.math.rutgers.edu/~zeilberg/tokhniot/DMB.txt .

           Please report all bugs to: DoronZeil at gmail dot com .


             For general help, and a list of the MAIN functions,

        type "Help();". For specific help type "Help(procedure_name);" 


                        ------------------------------

            For a list of the supporting functions type: Help1();

             For help with any of them type: Help(ProcedureName);


                        ------------------------------

  For a list of the functions that give examples of Discrete-time dynamical 

     systems (some famous), type: HelpDDM();


             For help with any of them type: Help(ProcedureName);


                        ------------------------------

 For a list of the functions continuous-time dynamical systems (some famous) 

    type: HelpCDM();


             For help with any of them type: Help(ProcedureName);


                        ------------------------------

> #P8 iii
> Orb([1/(1+x)],[x],[0.5],999,1000)[2];
                                [0.6180339887]

> #P9 iii
> Orb([x/(1+y+z),y/(1+x+z),z/(1+x+y)],[x,y,z],[1.,1.,1.],999,1000)[-1];
             [0.0004992511142, 0.0004992511142, 0.0004992511142]

> #P11'
> Orb([x^2-2*x+2],[x],[1.],1000,1010)
   [[1.], [1.], [1.], [1.], [1.], [1.], [1.], [1.], [1.], [1.], [1.], [1.]]

> Orb([x^2-2*x+2],[x],[1.05],1000,1010)
[[1.000000000], [1.000000000], [1.000000000], [1.000000000], [1.000000000], 

  [1.000000000], [1.000000000], [1.000000000], [1.000000000], [1.000000000], 

  [1.000000000], [1.000000000]]


> Orb([x^2-2*x+2],[x],[0.95],1000,1010)
[[1.000000000], [1.000000000], [1.000000000], [1.000000000], [1.000000000], 

  [1.000000000], [1.000000000], [1.000000000], [1.000000000], [1.000000000], 

  [1.000000000], [1.000000000]]


> #1 is seemingly stable.
> Orb([x^2-2*x+2],[x],[2.05],1000,1010)
        [[Float(undefined)], [Float(undefined)], [Float(undefined)], 

          [Float(undefined)], [Float(undefined)], [Float(undefined)], 

          [Float(undefined)], [Float(undefined)], [Float(undefined)], 

          [Float(undefined)], [Float(undefined)], [Float(undefined)]]


> Orb([x^2-2*x+2],[x],[1.95],1000,1010)
[[1.000000000], [1.000000000], [1.000000000], [1.000000000], [1.000000000], 

  [1.000000000], [1.000000000], [1.000000000], [1.000000000], [1.000000000], 

  [1.000000000], [1.000000000]]


> #2 is obviously not stable.

> #P12'
> Orb([2.5*x*(1-x)],[x],[0.01],1000,1010)
      [[0.6000000000], [0.6000000000], [0.6000000000], [0.6000000000], 

        [0.6000000000], [0.6000000000], [0.6000000000], [0.6000000000], 

        [0.6000000000], [0.6000000000], [0.6000000000], [0.6000000000]]


> Orb([2.5*x*(1-x)],[x],[0.7],1000,1010)
      [[0.6000000000], [0.6000000000], [0.6000000000], [0.6000000000], 

        [0.6000000000], [0.6000000000], [0.6000000000], [0.6000000000], 

        [0.6000000000], [0.6000000000], [0.6000000000], [0.6000000000]]


> #While 0 is not stable, 3/5 is.