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

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.

Host-parasite Red Queen dynamics with phase-locked rare genotypes

“…Many cases of evolutionary switching of dominant populations occur because natural ecosystems are inherently noisy (17)(18)(19)(20)(21). Stochastic noise is believed to play a role in regulating the dominant regime in ecological interacting systems (17,21,46). Hence, the consequence of the Red Queen binary oscillations with physical-environmental perturbations might be the temporal biodiversity seen in natural ecosystems (for example, see fig.…”

Red Queen dynamics in multi-host and multi-parasite interaction system

“…The type-II functional response has been used by several empirical and theoretical studies of host-parasites interaction 23 48 49 50 . In Supplementary Figure 7 , we modify the underlying inter-host competition model 51 and the functional response to inspect the possible changes in the behavior of the Red Queen dynamics. In addition, the system of ODEs, equation (1) and (2) , is solved using Runge-Kutta 4 with 0.01 as stepsize.…”