Equilibrium switching and mathematical properties of nonlinear interaction networks with concurrent antagonism and self-stimulation
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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.
Cite this as
2015. Equilibrium switching and mathematical properties of nonlinear interaction networks with concurrent antagonism and self-stimulation. PeerJ PrePrints 3:e382v3 https://doi.org/10.7287/peerj.preprints.382v3note This preprint is not peer-reviewed. You may wish to reference the subsequent peer-reviewed version of this article.
Author comment
This is an updated version of the preprint. The final version of the manuscript is accepted for publication in Chaos, Solitons and Fractals: the interdisciplinary journal of Nonlinear Science, and Nonequilibrium and Complex Phenomena. DOI of the peer-reviewed manuscript is 10.1016/j.chaos.2015.01.018
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Supplementary Text (includes mathematical proofs of the theorems/properties)
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Competing Interests
The authors declare that there are no conflicts of interest.
Author Contributions
Jomar Rabajante conceived and designed the experiments, analyzed the data, wrote the paper, prepared figures and/or tables, reviewed drafts of the paper.
Cherryl O. Talaue conceived and designed the experiments, wrote the paper, reviewed drafts of the paper.
Funding
This work was financially supported by the Philippine Council for Industry, Energy and Emerging Technology Research and Development (PCIEERD) of the Department of Science and Technology (DOST), and by the University of the Philippines. The funders had no role in study design, data collection and analysis, decision to publish, or preparation of the manuscript.
