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Rabajante J, Talaue CO.2015. Equilibrium switching and mathematical properties of nonlinear interaction networks with concurrent antagonism and self-stimulation. PeerJ PrePrints3:e382v3https://doi.org/10.7287/peerj.preprints.382v3
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.
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
Supplementary Text (includes mathematical proofs of the theorems/properties)
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