Searching bifurcations in high-dimensional parameter space via a feedback loop breaking approach

TL;DR

This paper introduces a feedback loop breaking method to identify bifurcations in high-dimensional parameter spaces of nonlinear systems, demonstrated on a biochemical MAPK cascade model.

Contribution

It presents a novel theoretical and numerical approach for locating bifurcations by analyzing feedback circuit characteristics in complex systems.

Findings

Successfully identified Hopf bifurcation in MAPK cascade model

Developed a numerical algorithm for high-dimensional bifurcation search

Provided a theoretical framework for feedback circuit classification

Abstract

Bifurcations leading to complex dynamical behaviour of non-linear systems are often encountered when the characteristics of feedback circuits in the system are varied. In systems with many unknown or varying parameters, it is an interesting, but difficult problem to find parameter values for which specific bifurcations occur. In this paper, we develop a loop breaking approach to evaluate the influence of parameter values on feedback circuit characteristics. This approach allows a theoretical classification of feedback circuit characteristics related to possible bifurcations in the system. Based on the theoretical results, a numerical algorithm for bifurcation search in a possibly high-dimensional parameter space is developed. The application of the proposed algorithm is illustrated by searching for a Hopf bifurcation in a model of the mitogen activated protein kinase (MAPK) cascade, which is a classical example for biochemical signal transduction.