"Oscillatory and Excitable Dynamics in an Opinion Model with Group Opinions"

The published version of one of my papers just came out today. Here are some details.

Title: Oscillatory and Excitable Dynamics in an Opinion Model with Group Opinions

Authors: Corbit R. Sampson, Juan G. Restrepo, and Mason A. Porter

Abstract:

RIP Paul Steen (?? – 2020)

I received the sad news early today that Cornell Professor Paul Steen died on Friday.

I took a class on bifurcation theory from Paul, who was very supportive. My class project, in which I needed to use AUTO (an important aspect of the course), led to this publication.

Here is an excerpt from the Acknowledgements section:

Additionally, we express our gratitude toward Alan Champneys for several productive suggestions regarding the numerics, Alejandro Rodríguez-Luis for providing a preprint of his manuscript, and Paul Steen, whose guidance for this work as a project for ChE 753 (on which this paper is based) was particularly valuable.

Tales from the ArXiv: Duck Dodgers and Bifurcation Diagrams

I hope that the authors of this paper make references to Duck Dodgers when they bring up this work in seminars.

What Happens in Columbus Stays in Columbus (Take N)

I am heading over to Columbus, Ohio for the Nth time. (That is the only city in Ohio that I have ever visited, and I have been there several times because of the math department and the Mathematical Biosciences Institute.) I am up way too early because my flight is not a direct one, and I'll be taking one short leg of the triangle and then the hypotenuse. I'll be visiting Marty Golubitsky at The Ohio State University to discuss things like networks and bifurcations. It should be fun!

"Prey Switching with a Linear Preference Trade-Off"

For the third day in a row, one of my papers has appeared in final published form. Here are the details.

Title: Prey Switching with a Linear Preference Trade-Off

Authors: Sofia H. Piltz, Mason A. Porter, and Philip K. Maini


Abstract: In ecology, prey switching refers to a predator’s adaptive change of habitat or diet in response to prey abundance. In this paper, we study piecewise-smooth models of predator-prey interactions with a linear trade-off in a predator’s prey preference. We consider optimally foraging predators and derive a model for a 1 predator-2 prey interaction with a tilted switching manifold between the two sides of discontinuous vector fields. We show that the 1 predator-2 prey system undergoes a novel adding-sliding-like (center to two-part periodic orbit; "C2PO") bifurcation in which the prey ratio transitions from constant to time-dependent. Farther away from the bifurcation point, the period of the oscillating prey ratio doubles, which suggests a possible cascade to chaos. We compare our model predictions with data on freshwater plankton, and we successfully capture the periodicity in the ratio between the predator’s preferred and alternative prey types. Our study suggests that it is useful to investigate prey ratio as a possible indicator of how population dynamics can be influenced by ecosystem diversity.


P.S. Check out the name we introduced for the new bifurcation that we discovered.

"Porter. Mason Porter."

Through a stray Google search during a spare few minutes, I found episode 16 of an audio drama called Action Science Theatre.

This episode contains a spy named "Mason Porter" and has three mathematics-related tags (math, maths, and catastrophe theory). The brief 'explanation' of catastrophe theory in the episode is ok but not quite right. It is amusing, though, that their brief discussion of catastrophe theory is reminiscent of the more science-fictiony aspects of catastrophe theory that were hyped for years. (In Vladimir Arnold's book on catastrophe theory, he has some very snarky things to say about that with respect to the work of René Thom.)

Here are few lines from this episode:



The character with my name, who is a spy who works for British Intelligence: "Let me introduce myself. [...ominous music...] Porter. Mason Porter."

Main character (the mathematician): "What? Really?"

"Me": "I'm sorry."

Mathematician: "Is that really your name?"

"Me": "Well of course it is. Why?"

Mathematician: "It just sounds a bit made up."



Hmpf. That's my real name --- so not exactly made up. Anyway, at least my namesake wasn't killed off in chapter 1 this time. (The link in my old blog entry is now dead. Perhaps that suggests that that book project might not be completed any time soon?)

What Happens in Princeton Stays in Princeton

I am now in The Prince's Town to visit Kevrekidis the Elder.

"Dangerous Intersections"

Steve Strogatz's latest article in the New York Times concerns the fold catastrophe and its manifestation---quantitatively in some cases and in toy models in others---in various phenomena. (By the way, the example in footnote 10 is something that occurs in many of the threshold models of social influence that have become increasingly popular since a paper Duncan Watts published in 2002.)

(Tip of the cap to Mariano Beguerisse Díaz.)