The induced kinetic differential equation of a reaction network endowed with mass action
type kinetics is a system of polynomial differential equations. The problem studied here is …

Abstract Systems of differential equations with polynomial right-hand sides are very common
in applications. In particular, when restricted to the positive orthant, they appear naturally …

There has long been interest in methods to achieve variability of collective modes in systems
of coupled identical oscillators. Extensive multistability and a dynamically rich parameter …

We search for limit cycles in the dynamical model of two-species chemical reactions that
contain seven reaction rate coefficients as parameters and at least one third-order reaction …

In this work, we study the existence of sustained oscillations in the" canonical" repressilator,
a basic synthetic circuit of 3 genes leading to sustained oscillations. Previous works mostly …

Genetic oscillators have been widely used in modeling key processes of biological systems,
especially cell cycles and circadian rhythms. In particular, repressilatory genetic oscillators …

Using dynamical models to reveal dynamical properties of gene regulatory networks can
help us better understand the nature of these biological systems and develop new medical …

As one of the important artificial oscillatory networks, repressilators have attracted many
attentions due to its function of synthesizing oscillations at the cellular level. In this paper, the …

In this article, we study the coupling of a collection of molecular oscillators, called
repressilators, interacting indirectly through enzymatic saturation. We extended a measure …

This thesis deals with several abstractions that create a discrete transition system from an
input continuous-time system with dynamics given by a system of autonomous ODE that are …