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Formal methods have enabled breakthroughs in many fields, such as in hardware verification, machine learning and biological systems. The key object of interest in systems biology, synthetic biology, and molecular programming is chemical…
Autocatalytic chemical networks play a predominant role in a large number of natural systems such as in metabolic pathways and in ecological networks. Despite recent efforts, the precise impact of thermodynamic constraints on these networks…
Autocatalysis is an important feature of metabolic networks, contributing crucially to the self-maintenance of organisms. Autocatalytic subsystems of chemical reaction networks (CRNs) are characterized in terms of algebraic conditions on…
Data replication is used in distributed systems to maintain up-to-date copies of shared data across multiple computers in a network. However, despite decades of research, algorithms for achieving consistency in replicated systems are still…
A crisp survey is given of chemical reaction networks from the perspective of general nonlinear network dynamics, in particular of consensus dynamics. It is shown how by starting from the complex-balanced assumption the reaction dynamics…
In this paper we show that the dynamics of a class of kinetic compartmental models with bounded capacities, monotone reaction rates and a strongly connected interconnection structure is persistent. The result is based on the chemical…
The steady-state degree of a chemical reaction network is the number of complex steady-states, which is a measure of the algebraic complexity of solving the steady-state system. In general, the steady-state degree may be difficult to…
Information geometry is based on classical Legendre duality but allows to incorporate additional structure such as algebraic constraints and Bregman divergence functions. It is naturally suited, and has been successfully used, to describe…
It has been known for nearly a decade that deterministically modeled reaction networks that are weakly reversible and consist of a single linkage class have trajectories that are bounded from both above and below by positive constants (so…
In this work and the supporting Parts II [2] and III [3], we provide a rather detailed analysis of the stability and performance of asynchronous strategies for solving distributed optimization and adaptation problems over networks. We…
A stochastic reaction-diffusion model is studied on a networked support. In each patch of the network two species are assumed to interact following a non-normal reaction scheme. When the interaction unit is replicated on a directed linear…
A suboptimal active disturbance rejection controller (S-ADRC) is proposed for second-order systems with unknown time-varying nonlinear dynamics. The output-feedback controller guarantees a global convergence to the vicinity of an optimal…
Reaction networks are a general framework widely used in modeling diverse phenomena in different science disciplines. The dynamical process of a reaction network endowed with mass-action kinetics is a mass-action system as an ODE defined by…
Network robustness against attacks has been widely studied in fields as diverse as the Internet, power grids and human societies. Typically, in these studies, robustness is assessed only in terms of the connectivity of the nodes unaffected…
This work introduces a novel approach to study properties of positive equilibria of a chemical reaction network $\mathscr{N}$ endowed with Hill-type kinetics $K$, called a Hill-type kinetic (HTK) system $\left(\mathscr{N},K\right)$,…
Reaction networks have become a major modelling framework in the biological sciences from epidemiology and population biology to genetics and cellular biology. In recent years, much progress has been made on stochastic reaction networks…
The quantitative convergence to equilibrium for reaction-diffusion systems arising from complex balanced chemical reaction networks with mass action kinetics is studied by using the so-called entropy method. In the first part of the paper,…
Autocatalytic chemical reaction networks can collectively replicate or maintain their constituents despite degradation reactions only above a certain threshold, which we refer to as the decay threshold. When the chemical network has a…
Perfect adaptation is a phenomenon whereby the output variables of a system can maintain certain values despite external disturbances. Robust perfect adaptation (RPA) refers to an adaptation property that does not require fine-tuning of…
In this paper, the applicability of the entropy method for the trend towards equilibrium for reaction-diffusion systems arising from first order chemical reaction networks is studied. In particular, we present a suitable entropy structure…