Heteroclinic dynamics in competitive Lotka-Volterra systems

Ghosh, Souraj (2023) Heteroclinic dynamics in competitive Lotka-Volterra systems. PhD thesis, Indian Institute of Science Education and Research Kolkata.

Text (PhD thesis of Souraj Ghosh (13IP006)) 13IP006.pdf - Submitted Version Restricted to Repository staff only Download (6MB)

Abstract

The dynamics of various ecosystems has been successfully explained using different forms of the Lotka-Volterra model since its inception in 1920. Such a model has application in diverse disciplines ranging from chemistry, economics to biological areas like neuronal dynamics. Specifically the competitive Lotka-Volterra model has been very successful in explaining the winner-less competition of the neuronal systems where single neuronal firing or activity happens sequentially. Rössler like Chaotic attractor was already found in the four-dimensional competitive Lotka-Volterra model believed to be a simplest and realistic instance of chaos occurring in low-dimensional dynamical systems. In this work, we explored ways to get chaotic or unpredictable dynamics in even simpler versions of the competitive Lotka-Volterra model while considering the robustness of the competition among the species populations. Such robustness is already known for the perturbations in the species growth rates. Here we establish that the dynamics is robust even if we change the inter-species connectivity in a random manner. It is shown that a competitive system goes through a rich series of dynamical behavior before becoming unstable as we tune the disorder strength in connectivity. The stability of large ecosystem in regards to local stability analysis has lead to the celebrated May-Wigner stability theorem proposed in 1972. We show that the same stability criterion is applicable even in the presence of non-linearity in the dynamics.

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