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

WATCH THE TALKS

Projects and Teams

1. 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]

   Presentation time: Dec. 10, 2021, 11:00-11:10

   paper    code and data

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2. 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

   Presentation time: Dec. 10, 2021, 11:12-11:22

   paper    code and data    maple worksheet

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

   Team Leader: Charles Griebell

   Other member: Julian Herman

   Presentation time: Dec. 10, 2021, 11:24-11:34

   paper    code and data    maple worksheet

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4. 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.

   Team Leader (and only member): Jeton Hida

   Presentation time: Dec. 10, 2021, 11:36-11:46

   paper    code and data   

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

   Team Leader: Anusha Nagar

   Other member: Tim Nasralla, Nicholas Dimarzio, Deven Singh

   Presentation time: Dec. 10, 2021, 11:48-11:58

   paper    code and data   

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6. 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:Alan Ho

   Other members: Maxim Mekhanikov, Mudassir Lodi

   Presentation time: Dec. 10, 2021, 12:00-12:10

   paper    code and data