http://sites.math.rutgers.edu/~zeilberg/Bio21/projects.html

Last Update: Nov. 11, 2021

ALL PRJECTS ARE DUE DEC. 5, 2021, 9:00pm

Note: After checking the proejcts, I will decide which ones are worth posting in this web-page.

Of course, you are welcome to continue the research during the winter break (and even later), and send me new versions for posting!

Already Committed Projects

• Topic: a full Maple implementation of "Dynamic complexity in predator-prey models framed in difference equations" by J.R. Beddington et. al. , Nature v. 255 (1975), pp 58-60. Hopefully also study related papers.

  Team Leader: HRUDAI BATTINI

  Other members: Julian Jimmenez and John Hermitt

  [Suggested by the team members]

• Investigate numerically (and who knows, even solve some of the conjectures in this intriguing paper "SI and SIR Epidemic models by Linda J.S. Allen.

  Team Leader: Nikita John

  Other members: Shreya Ghosh, Anne Somalwar

  [Suggested by Dr. Z.]

• Investigate numerically (and who knows, even solve, conjecture 4, and related conjectures, in this intriguing paper "Convergence to Periodic Solution" by A.M. Amleh and G. Ladas

  Team Leader: Charles Griebell

  Other member: Julian Herman, Maxim Mekhanikov

  [Suggested by Dr. Z.]

• Investigate numerically (and who knows, even solve, conjecture 1, and related conjectures, in this intriguing paper "Convergence to Periodic Solution" by A.M. Amleh and G. Ladas

  Team Leader: Jeton Hida

  Other members: Alan Ho, Andrew Hussey

  [Suggested by Dr. Z.]

• Investigate numerically (and who knows, even solve, conjecture 2 in this intriguing paper "Convergence to Periodic Solution" by A.M. Amleh and G. Ladas

  Team Leader: Anusha Nagar

  Other members: Nicholas Dimarzio

  [Suggested by Dr. Z.]

• Investigate at depth, both numerically and analytically, generalizations of the Hardy-Weinberg rule with with more realistic assumptions.

  Team Leader: Deven Singh

  Other member: Tim Nasralla

Suggested (Not yet taken) Projects

• Investigate numerically (and who knows, even solve some of the conjectures in this intriguing paper "Convergence to Periodic Solution" by A.M. Amleh and G. Ladas

• Study numerically (by discretization), in detail, the original paper by Kermack and McKendrick (1927) and its follow up papers cited at the end of Chapter 6 of Edeslstein-Keshet's book. Also look up more recent papers of this kind of models and study them.

• Investigate at depth, both numerically and analytically, generalizations of the Hardy-Weinberg rule with with more realistic assumptions.

• Study numerically the ultimate perodic orbits for various parameters of the generalized discrete Logistic Equation

  x(n)=k x(n-1)(1-x(n-1)).

  These generalizations should have more parameters. For exampla:

  x(n)=k x(n-1)^a (1-x(n-1))^b ,

  that has three parameters (k, a, and b). Also study second- (and higher-) order difference equations, e.g.

  x(n)=k x(n-1)(1-x(n-1))(1-x(n-2)) ,

  and more generally

  x(n)=k x(n-1)^a(1-x(n-1))^b(1-x(n-2))^c ,

  etc.