Integrability And Linearizability Of A Class Of Lotka-Volterra Systems Of Degree3

In this thesis,we deal with the Lotka-Volterra type system of degree3using the normal form and get integrable and linearizable sufficient and necessary conditions. Specifically, through the theoretical analysis, the main results obtained in this thesis are as follows:1. We give the first three order saddle quantities of the system.2. Using the first three order saddle quantities, we give the necessary and sufficient conditions for integrability of the system.3. Using integrable conditions, we give the necessary and sufficient conditions for linearizablity of the system.