Related papers: Hopf Bifurcations of Reaction Networks with Zero-O…
We address the question of which small, bimolecular, mass action chemical reaction networks (CRNs) are capable of Andronov-Hopf bifurcation (from here on abbreviated to "Hopf bifurcation"). It is easily shown that any such network must have…
Zero-one biochemical reaction networks play key roles in cell signalling such as signalling pathways regulated by protein phosphorylation. Multistability of reaction networks is a crucial dynamics feature enabling decision-making in cells.…
In this paper we study bifurcations in mass-action networks with two chemical species and reactant complexes of molecularity no more than two. We refer to these as planar, quadratic networks as they give rise to (at most) quadratic…
Phosphorylation networks, representing the mechanisms by which proteins are phosphorylated at one or multiple sites, are ubiquitous in cell signalling and display rich dynamics such as unlimited multistability. Dual-site phosphorylation…
Zero-one reaction networks are pivotal to cellular signaling, and establishing the equivalence of such networks represents a foundational computational challenge in the realm of chemical reaction network research. Herein, we propose a…
We study the multistationarity for the reaction networks with one-dimensional stoichiometric subspaces, and we focus on the networks admitting finitely many positive steady states. We prove that if a network admits multistationarity, then…
Autonomous sustained oscillations are ubiquitous in living and nonliving systems. As open systems, far from thermodynamic equilibrium, they defy entropic laws which mandate convergence to stationarity. We present structural conditions on…
Hopf bifurcation in networks of coupled ODEs creates periodic states in which the relative phases of nodes are well defined near bifurcation. When the network is a fully inhomogeneous nearest-neighbour coupled unidirectional ring, and node…
It is known that rank-two bimolecular mass-action systems do not admit limit cycles. With a view to understanding which small mass-action systems admit oscillation, in this paper we study rank-two networks with bimolecular source complexes…
Zero-one biochemical reaction networks are widely recognized for their importance in analyzing signal transduction and cellular decision-making processes. Degenerate networks reveal non-standard behaviors and mark the boundary where…
Gene regulatory networks, i.e. DNA segments in a cell which interact with each other indirectly through their RNA and protein products, lie at the heart of many important intracellular signal transduction processes. In this paper we analyse…
We state two sufficient criteria for periodic oscillations in mass action systems. Neither criterion requires a computation of the Hurwitz determinants. Instead, both criteria exploit the linear algebra concepts of $D$-stability and…
In a previous paper, the authors developed a method for computing normal forms of dynamical systems with a coupled cell network structure. We now apply this theory to one-parameter families of homogeneous feed-forward chains with…
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…
We develop a model-independent reduction method of chemical reaction systems based on the stoichiometry, which determines their network topology. A subnetwork can be eliminated systematically to give a reduced system with fewer degrees of…
We analyze a family of clustered excitatory-inhibitory neural networks and the underlying bifurcation structures that arise because of permutation symmetries in the network as the global coupling strength $g$ is varied. We primarily…
Systems of ODEs coupled with the topology of a closed ring are common models in biology, robotics, electrical engineering, and many other areas of science. When the component systems and couplings are identical, the system has a cyclic…
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…
The localization of bifurcations in large parametric systems is still a challenge where the combination of rigorous criteria and informal intuition is often needed. With this motivation, we address symbolically the Jacobian matrix of…
There is considerable interest in the networking community in explicit congestion control as it may allow the design of a fair, stable, low loss, low delay, and high utilization network. The Rate Control Protocol (RCP) is an example of such…