[MS10] Model Bifurcations and Ecological Relevance

[MS10-07] Four-species food webs analysis in chemical reaction networks

*Ritwika Mondal¹, Wei Hsiang Lin¹ (1. Institute of Molecular Biology, Academia Sinica (Taiwan))

Keywords:

Chemical reaction network,Food webs,Global Bifurcation,Chaos,Global stability

In this work, we analyze the coexistence of four-species predator-prey food web systems. Considering Chemical Reaction Network Theory (CRNT), we generalize mass action kinetics and Michaelis-Menten kinetics incorporating a large class of parameter-rich kinetics models. For the stability analysis, we embody the idea of stoichiometric matrix analysis. We depict the line of stable equilibrium, several global bifurcations like transcritical bifurcation of limit cycle, chaotic behavior for the two-predator and two-prey systems. Overall, the analytical and numerical results provide an essense of reaction networks theory in ecological food web systems to understand the stability and coexistence of all species. We thoroughly explain the impact of competition within the prey species on coexistence of all organisms. We present a rigorous treatment of different dynamical behaviors like tending to equilibrium from any density, cyclical behavior, irregularity on the food web systems. In adition, we are planning to emphasize on the applicability of CRNT in ecological system to study the different bifurcations like Hopf bifurcation, transcritical bifurcation besides the classical Routh–Hurwitz stability criterion.