Equilibrium switching and mathematical properties of nonlinear interaction networks with concurrent antagonism and self-stimulation

Issue Date

4-2015

Abstract

Concurrent decision-making model (CDM) of interaction networks with more than two antagonistic components represents various biological systems, such as gene interaction, species competition and mental cognition. The CDM model assumes sigmoid kinetics where every component stimulates itself but concurrently represses the others. Here we prove generic mathematical properties (e.g., location and stability of steady states) of n-dimensional CDM with either symmetric or asymmetric reciprocal antagonism between components. Significant modifications in parameter values serve as biological regulators for inducing steady state switching by driving a temporal state to escape an undesirable equilibrium. Increasing the maximal growth rate and decreasing the decay rate can expand the basin of attraction of a steady state that contains the desired dominant component. Perpetually adding an external stimulus could shut down multi-stability of the system which increases the robustness of the system against stochastic noise. We further show that asymmetric interaction forming a repressilator-type network generates oscillatory behavior.

Source or Periodical Title

Chaos, Solitons and Fractals

ISSN

0960-0779

Volume

73

Page

166-182

Document Type

Article

Physical Description

illustrations, tables, graphs

Language

English

Identifier

https://doi.org/10.1016/j.chaos.2015.01.018.

Digital Copy

yes

Link to Full Text

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