Related papers: Symbolic hunt of instabilities and bifurcations in…
We consider a problem from biological network analysis of determining regions in a parameter space over which there are multiple steady states for positive real values of variables and parameters. We describe multiple approaches to address…
Multistationarity is the property of a system to exhibit two distinct equilibria (steady-states) under otherwise identical conditions, and it is a phenomenon of recognized importance for biochemical systems. Multistationarity may appear in…
We continue recent attempts to put together concepts and results of Chemical Reaction Networks theory (CRNT) and Mathematical Epidemiology (ME), for solving problems of stability of positive ODEs. We provide first an elegant CRN-flavored…
In this paper mathematical models for the evolutionary conserved Notch-Delta pathway are developed and analyzed in order to better understand how two neighboring biological cells can become different. We pursue a structure-based…
Model-based approaches for (bio)process systems often suffer from incomplete knowledge of the underlying physical, chemical, or biological laws. Universal differential equations, which embed neural networks within differential equations,…
Symbolic dynamics has proven to be an invaluable tool in analyzing the mechanisms that lead to unpredictability and random behavior in nonlinear dynamical systems. Surprisingly, a discrete partition of continuous state space can produce a…
Most differential equations found in chemical reaction networks (CRNs) have the form $dx/dt=f(x)= Sv(x)$, where $x$ lies in the nonnegative orthant, where $S$ is a real matrix (the stoichiometric matrix) and $v$ is a column vector…
We investigate models of the mitogenactivated protein kinases (MAPK) network, with the aim of determining where in parameter space there exist multiple positive steady states. We build on recent progress which combines various symbolic…
We consider stochastic reaction networks modeled by continuous-time Markov chains. Such reaction networks often contain many reactions, potentially occurring at different time scales, and have unknown parameters (kinetic rates, total…
Polynomial dynamical systems are widely used to model and study real phenomena. In biochemistry, they are the preferred choice for modelling the concentration of chemical species in reaction networks with mass-action kinetics. These systems…
We study linear systems of equations with coefficients in a generic partially ordered ring $R$ and a unique solution, and seek conditions for the solution to be nonnegative, that is, every component of the solution is a quotient of two…
Random walks represent an important tool for probing the structural and dynamical properties of networks and modeling transport and diffusion processes on networks. However, when individuals' movement becomes dictated by more complicated…
We discuss a method to describe the qualitative dynamics of chemical reaction networks in terms of symbolic dynamics. The method, that can be applied to mass-action reaction networks with separated timescales, uses solutions of the partial…
We present a mathematical analysis of the effects of Hebbian learning in random recurrent neural networks, with a generic Hebbian learning rule including passive forgetting and different time scales for neuronal activity and learning…
We discuss the symbolic dynamics of biochemical networks with separate timescales. We show that symbolic dynamics of monomolecular reaction networks with separated rate constants can be described by deterministic, acyclic automata with a…
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…
The stable functionality of networked systems is a hallmark of their natural ability to coordinate between their multiple interacting components. Yet, strikingly, real-world networks seem random and highly irregular, apparently lacking any…
Key network motifs searching in complex networks is one of the crucial aspects of network analysis. There has been a series of insightful findings and valuable applications for various scenarios through the analysis of network structures.…
Quantifying interaction strengths between state variables in dynamical systems is essential for understanding ecological networks. Within the empirical dynamic modeling approach, multivariate S-map infers the interaction Jacobian from time…
The Jacobian matrix of a dynamical system describes its response to perturbations. Conversely one can estimate the Jacobian matrix by carefully monitoring how the system responds to environmental noise. Here we present a closed form…