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Switch-like responses arising from bistability have been linked to cell signaling processes and memory. Revealing the shape and properties of the set of parameters that lead to bistability is necessary to understand the underlying…
Reaction networks taken with mass-action kinetics arise in many settings, from epidemiology to population biology to systems of chemical reactions. Bistable reaction networks are posited to underlie biochemical switches, which motivates the…
Collective organisation of patterns into ring-like configurations has been well-studied when patterns are subject to either weak or semi-strong interactions. However, little is known numerically or analytically about their formation when…
Many biological systems can be modeled as a chemical reaction network with unknown parameters. Data available to identify these parameters are often in the form of a stationary distribution, such as that obtained from measurements of a cell…
Living systems are maintained out-of-equilibrium by external driving forces. At stationarity, they exhibit emergent selection phenomena that break equilibrium symmetries and originate from the expansion of the accessible chemical space due…
Reaction networks (RNs) comprise a set $X$ of species and a set $\mathscr{R}$ of reactions $Y\to Y'$, each converting a multiset of educts $Y\subseteq X$ into a multiset $Y'\subseteq X$ of products. RNs are equivalent to directed…
Steady states are frequently used to investigate the long-term behaviors of (bio)-chemical systems. Recently, there has been a growing interest in network-based approaches due to their efficiency in deriving parametrizations of positive…
Barrier crossing calculations in chemical reaction-rate theory typically assume that the barrier is large compared to the temperature. When the barrier vanishes, however, there is a qualitative change in behavior. Instead of crossing a…
Reactivity boundaries that divide the origin and destination of trajectories are crucial of importance to reveal the mechanism of reactions, which was recently found to exist robustly even at high energies for index-one saddles [Phys. Rev.…
The parameter region of multistationarity of a reaction network contains all the parameters for which the associated dynamical system exhibits multiple steady states. Describing this region is challenging and remains an active area of…
Aspects of cell metabolism are modeled by ordinary differential equations describing the change of intracellular chemical concentrations. There is a correspondence between this dynamical system and a complex network. As in the classic…
A reaction network is a chemical system involving multiple reactions and chemical species. Stochastic models of such networks treat the system as a continuous time Markov chain on the number of molecules of each species with reactions as…
Analyzing qualitative behaviors of biochemical reactions using its associated network structure has proven useful in diverse branches of biology. As an extension of our previous work, we introduce a graph-based framework to calculate steady…
Motivation: A Chemical Reaction Network (CRN) is a set of chemical reactions, which can be very complex and difficult to analyze. Indeed, dynamical properties of CRNs can be described by a set of non-linear differential equations that…
It has recently been shown that structural conditions on the reaction network, rather than a 'fine-tuning' of system parameters, often suffice to impart 'absolute concentration robustness' on a wide class of biologically relevant,…
We study the stationary Keller--Segel chemotaxis models with logistic cellular growth over a one-dimensional region subject to the Neumann boundary condition. We show that nonconstant solutions emerge in the sense of Turing's instability as…
Many real world systems are at risk of undergoing critical transitions, leading to sudden qualitative and sometimes irreversible regime shifts. The development of early warning signals is recognized as a major challenge. Recent progress…
We numerically and analytically investigate the behavior of a non-equilibrium phase transition in the second Schl\"ogl autocatalytic reaction scheme. Our model incorporates both an interaction-induced phase separation and a bifurcation in…
Asymptotic state of an open quantum system can undergo qualitative changes upon small variation of system parameters. We demonstrate it that such 'quantum bifurcations' can be appropriately defined and made visible as changes in the…
Following Part~I, we consider a class of reversible systems and study bifurcations of homoclinic orbits to hyperbolic saddle equilibria. Here we concentrate on the case in which homoclinic orbits are symmetric, so that only one control…