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Autocatalysis underlies the ability of chemical and biochemical systems to replicate. Autocatalysis was recently defined stoichiometrically for reaction networks; five types of minimal autocatalytic networks, termed autocatalytic cores were…

The potential for multistationarity, or the existence of steady-state multiplicity, in the Earth System raises concerns that the planet could reach a climatic `tipping point,' rapidly transitioning to a warmer steady-state from which…

Many biochemical processes can successfully be described by dynamical systems allowing some form of switching when, depending on their initial conditions, solutions of the dynamical system end up in different regions of state space…

In a recent paper it was shown that, for chemical reaction networks possessing a subtle structural property called concordance, dynamical behavior of a very circumscribed (and largely stable) kind is enforced, so long as the kinetics lies…

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…

In the first part of this paper we give a short review of the hierarchy of stochastic models, related to physical chemistry. In the basement of this hierarchy there are two models --- stochastic chemical kinetics and the Kac model for…

Finding collective variables to describe some important coarse-grained information on physical systems, in particular metastable states, remains a key issue in molecular dynamics. Recently, machine learning techniques have been intensively…

The present work revisits the reduction of the nonlinear dynamics of an electromechanical system through a quasi-steady state hypothesis, discussing the fundamental aspects of this type of approach and clarifying some confusing points found…

Biochemical reaction systems may be viewed as discrete event processes characterized by a number of states and state transitions. These systems may be modeled as state transition systems with transitions representing individual reaction…

A stable population network is hard to interrupt without any ecological consequences. A communication blockage between patches may destabilize the populations in the ecological network. This work deals with the construction of a safe cut…

The dynamics of many-body systems can often be captured in terms of only a few relevant variables. Mathematical and numerical approaches exist to identify these variables by exploiting a separation of time scales between slow relevant and…

Chemical reaction network theory is a powerful framework to describe and analyze chemical systems. While much about the concentration profile in an equilibrium state can be determined in terms of the graph structure, the overall reaction's…

Remodelling is defined as an evolution of microstructure or variations in the configuration of the underlying manifold. The manner in which a biological tissue and its subsystems remodel their structure is treated in a continuum mechanical…

A faithful description of the state of a complex dynamical network would require, in principle, the measurement of all its $d$ variables, an infeasible task for systems with practical limited access and composed of many nodes with high…

Long-term behaviors of biochemical systems are described by steady states in deterministic models and stationary distributions in stochastic models. Obtaining their analytic solutions can be done for limited cases, such as linear or…

Multi-valued logical models can be used to describe biological networks on a high level of abstraction based on the network structure and logical parameters capturing regulatory effects. Interestingly, the dynamics of two distinct models…

Understanding the emergent behavior of chemical reaction networks (CRNs) is a fundamental aspect of biology and its origin from inanimate matter. A closed CRN monotonically tends to thermal equilibrium, but when it is opened to external…

This paper (parts I and II) provides an expository introduction to monotone and near-monotone dynamical systems associated to biochemical networks, those whose graphs are consistent or near-consistent. Many conclusions can be drawn from…

Food-web perturbations stemming from climate change, overexploitation, invasive species, and habitat degradation often cause an initial loss of species that results in a cascade of secondary extinctions, posing considerable challenges to…

External flows of energy, entropy, and matter can cause sudden transitions in the stability of biological and industrial systems, fundamentally altering their dynamical function. How might we control and design these transitions in chemical…