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Natural systems are remarkably robust and resilient, maintaining essential functions despite variability, uncertainty, and hostile conditions. Understanding these nonlinear, dynamic behaviours is challenging because such systems involve…
Bistability plays a central role in the gene regulatory networks (GRNs) controlling many essential biological functions, including cellular differentiation and cell cycle control. However, establishing the network topologies that can…
This paper is Part II of a two-part series devoting to the study of systematic measures in a complex bio-network modeled by a system of ordinary differential equations. In this part, we quantify several systematic measures of a biological…
We present conditions which guarantee a parametrization of the set of positive equilibria of a generalized mass-action system. Our main results state that (i) if the underlying generalized chemical reaction network has an effective…
This paper presents a stability test for a class of interconnected nonlinear systems motivated by biochemical reaction networks. One of the main results determines global asymptotic stability of the network from the diagonal stability of a…
The catalytic reaction system (CRS) formalism by Hordijk and Steel is a versatile method to model autocatalytic biochemical reaction networks. It is particularly suited, and has been widely used, to study self-sustainment and…
Chemical reaction networks (CRNs) are foundational models for describing complex biochemical processes. We study noncompetitive CRNs, a class of networks whose static states are rate-independent, and that can implement ReLU neural networks.…
Network translation has recently been used to establish steady state properties of mass action systems by corresponding the given system to a generalized one which is either dynamically or steady state equivalent. In this work we further…
In contrast to electronic computation, chemical computation is noisy and susceptible to a variety of sources of error, which has prevented the construction of robust complex systems. To be effective, chemical algorithms must be designed…
Deterministic reaction networks (RNs) are tools to model diverse biological phenomena characterized by particle systems, when there are abundant number of particles. Examples include but are not limited to biochemistry, molecular biology,…
Motivated by biochemical reaction networks, a generalization of the classical secant condition for the stability analysis of cyclic interconnected commensurate fractional-order systems is provided. The main result presents a sufficient…
Resilience characterizes a system's ability to retain its original function when perturbations happen. In the past years our attention mainly focused on small-scale resilience, yet our understanding of resilience in large-scale network…
The study of dynamical systems on complex networks is of paramount importance in engineering, given that many natural and artificial systems find a natural embedding on discrete topologies. For instance, power grids, chemical reactors and…
A chemical reaction network (CRN) is composed of reactions that can be seen as interactions among entities called species, which exist within the system. Endowed with kinetics, CRN has a corresponding set of ordinary differential equations…
The functioning of many biochemical networks is often robust -- remarkably stable under changes in external conditions and internal reaction parameters. Much recent work on robustness and evolvability has focused on the structure of neutral…
Feedback circuits in biochemical networks which underly cellular signaling pathways are important elements in creating complex behavior. A specific aspect thereof is how stability of equilibrium points depends on model parameters. For…
The nonlinearities found in molecular networks usually prevent mathematical analysis of network behaviour, which has largely been studied by numerical simulation. This can lead to difficult problems of parameter determination. However,…
The connection between network topology and stability remains unclear. General approaches that clarify this relationship and allow for more efficient stability analysis would be desirable. Inspired by chemical reaction networks, I…
Previous studies have inferred robust stability of reaction networks by utilizing linear programs or iterative algorithms. Such algorithms become tedious or computationally infeasible for large networks. In addition, they operate like…
Chemical reaction networks (CRNs) are directed graphs with reactant or product complexes as vertices, and reactions as arcs. A CRN is weakly reversible if each of its connected components is strongly connected. Weakly reversible networks…