Centre Manifold Analysis of 3-D nonlinear system and Kinetic stability of Protein Assembly

TL;DR

This paper applies centre manifold theory to analyze the stability and oscillatory behavior of a 3-D nonlinear system, with a focus on biochemical protein assembly, providing new theorems and stability criteria.

Contribution

It develops a centre manifold approach for 3-D nonlinear systems with second order nonlinearities and proves a theorem for stability based on nonlinear term parity.

Findings

Identification of fixed points on the centre manifold

Oscillatory dynamics can be generated via the centre manifold

Kinetic stability analysis confirms the theorem's validity for a biochemical example

Abstract

Centre Manifold analysis of a 3-D nonlinear system with general second order nonlinearities have been worked out. The system is shown to possess two fixed points on the reduced 2-D centre manifold. By introducing a 2-D centre manifold one can show how an oscillatory dynamics may be generated in the system. We also state and prove a theorem to find the stability of the resultant centre manifold equation apriori from the parity of the nonlinear terms in the original equations. For a 2-D nonlinear model with the example picked up from biochemistry, the protein molecules in assembly, kinetic stability analysis is provided for the chosen example and establish herewith the validity of the theorem for our chosen example.