Equilibria in Networks with Steep Sigmoidal Nonlinearities
- Thursday, February 4, 2021 from 3:00pm to 4:00pm
- Webex Meeting number: 120 608 6197, Password: applied
In differential equation models of gene regulatory networks, interactions between genes are often modeled by nonlinear sigmoidal functions. If these sigmoidal functions are replaced by piecewise constant or switching functions, the dynamics of the resulting system are completely determined by a finite number of inequalities between parameters and can be computed efficiently. The expectation is that the equilibria of the switching system correspond to equilibria of steep sigmoidal systems. However, the sigmoidal system will have additional equilibria not present in the switching system. In this talk, I will discuss results which show that all equilibria of steep sigmoidal systems can be determined from the switching system inequalities. In the case of ramp systems, a subclass of sigmoid systems, I discuss bifurcations of these equilibria as the steepness of the functions decrease and give explicit bounds on their slopes that guarantee the equilibria maintain their stability and numbers that are predicted by the switching system.
- Department of Mathematical Sciences