Equilibrium switching in nonlinear biological interaction networks with concurrent antagonism

Concurrent decision-making model (CDM) of interaction networks involving more than two antagonistic components can represent various biological systems, such as gene interaction, species competition and mental perception. The model assumes sigmoid kinetics where every component stimulates itself but concurrently represses the others. Here we prove general dynamical properties of the CDM (e.g., location and stability of steady states) for any dimension of the state space even if the reciprocal antagonism between two components is asymmetric. Significant modifications in parameter values serve as biological regulators for inducing steady state switching by leading a temporal state to escape an undesired equilibrium. Increasing the maximal growth rate and decreasing the decay rate expand the basin of attraction of a steady state with the desired dominant component. Perpetually adding an external stimulus can shut down multi-stability of the system that increases the robustness of the system against stochastic noise. We further show that asymmetric interaction that forms a repressilator-type network generates oscillatory behavior.