http://sites.math.rutgers.edu/~zeilberg/Bio25/projects.html

Last Update: Dec. 12, 2025

All projects are due (.pdf and .txt and optionally .mw) Wed. Dec. 10, 8:00pm. The project leader should email

ShaloshBEkhad@gmail.com

Subject: Projects X

with attachments: projectX.pdf, projectX.txt, (optionally projectX.mw)

Friday, Dec. 12, 2025, 12:10-1:30 pm via WebEx

Projects and Teams and Schdeule

Project 1

Dynamic complexity in predator-prey models framed in difference equations by

by J.R. Beddington et. al. , Nature v. 255 (1975), pp 58-60. Hopefully also study related papers.

Team Leader: Sydney Yao

Other members: Rachel Adelman, Sophie Droppa, Anna Janik

12:15-12:23 pm

Maple code  write-up    presentation  

Project 2

Team Leader: Brian Koo

Other members: Brian Jin , Praneeth Vedantham

12:25-12:33 pm

Maple code  write-up  

Project 3

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.

Also: Definining in Maple

F:=proc(A,k,x) local i: x-mul(x-A[i],i=1..nops(A))/k:end:

where A is a given increasing list of positive numbers (for the sake of simplicity make them integers), find the smallest k where it starts having non-empty steady-states, let's call it CutOff(A). for k above the cutoffs, find the "basin of attraction" of each of the stable steady-states. For k smaller than the Cutoffs find whether f(f(x)) (use Compk in DMB.txt) has stable steady-states.

Team Leader: Aurelia Altzman

Other member: Adriana Ferreira, Palash Keswani

12:35-12:43 pm

Maple code  write-up  

Project 4

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

Team Leader: Daniyal Chaudhry

Other team members: Katryn Keating, Ezra Chechik, Zach Ali

12:45-12:53 pm

Maple code  write-up  

Project 5

Using procedures

GeneNet(a0,a,b,n,m1,m2,m3,p1,p2,p3) and TimeSeries(F,x,pt,h,A,i)

in the Maple package DMB.txt

Investigate, at depth, the gene network model described in Chapter 4 of the Ellner-Guckenheimer book

Draw may diagrams like those in figures 4.2,4.3, 4.4 in that book, and try to group the `parameter space' into the `periodic case', giving diagrams like figure 4.2, and the `stable equilibrium' case, giving diagrams like figure 4.3.

Team Leader: Allysa Lee

Other members: Victoria Serafin, Sakhti Venkatesan

12:55-1:03 pm

Maple code  write-up  

Project 6

"A numerical investigation of a generalized simple integrate-and-fire neuronal model" according to this paper

Team Leader (and only member): Caroline Hill

1:05-1:13 pm

Maple code   Python code   write-up   presentation slides