Metapopulation and Coupled Logistic Maps

How a network of city evolves

20 December 2015

A discussion with Prof. Mayank Vahia from TIFR inspired us to study a network of cities using non linear dynamics. The investigation led us towards the study of stability and chaos in coupled logistic maps.

Uncountable games of Microsoft Age of Empires led to an intuitive belief that the game results have a chaotic nature. The army count time series shows in phase oscillations leading to extinction for one party and saturation for the other. We tried modelling the population of a few cities based on parameters of food and area available and migration rate and tendency.

People have modelled metapopulation using logistic maps in the past. Our additional step was to study coupled logistic maps and see if the coupling can remove the chatoic nature for some values of parameters. With a few limitations, the answer, in general, is yes.

The full report can be downloaded here. For the initial part of the project where we explored simple models, the repository is active here.

Thanks to Sandesh Kalantre, Keshav Srinivasan, Basuhi Ravi and Rakshit Jain for working with me on this project, and Prof. Amitabha Nandi and Prof. Raghunath Chelakkot for their guidance.