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- Gheorghe Craciun, Fedor Nazarov, Casian Pantea
- SIAM Journal of Applied Mathematics
- 2013

Persistence and permanence are properties of dynamical systems that describe the long-term behavior of the solutions, and in particular specify whether positive solutions approach the boundary of the positive orthant. Mass-action systems (or more generally power-law systems) are very common in chemistry, biology, and engineering, and are often used to… (More)

- Casian Pantea
- SIAM J. Math. Analysis
- 2012

This paper concerns the long-term behavior of population systems, and in particular of chemical reaction systems, modeled by deterministic mass-action kinetics. We approach two important open problems in the field of chemical reaction network theory: the Persistence Conjecture and the Global Attractor Conjecture. We study the persistence of a large class of… (More)

- Casian Pantea, Gheorghe Craciun
- ISCAS
- 2010

—Bistability plays a key role in important biological processes, such as cell division, differentiation, and apoptosis. Examples show that there is a very delicate relationship between the structure of a reaction network and its capacity for bistable behavior. We describe mathematical methods that discriminate between networks that have the capacity for… (More)

- Gheorghe Craciun, Casian Pantea, Grzegorz A. Rempala
- Computational Biology and Chemistry
- 2009

We present a novel method for identifying a biochemical reaction network based on multiple sets of estimated reaction rates in the corresponding reaction rate equations arriving from various (possibly different) experiments. The current method, unlike some of the graphical approaches proposed in the literature, uses the values of the experimental… (More)

Dynamical system models of complex biochemical reaction networks are high-dimensional, nonlinear, and contain many unknown parameters. The capacity for multiple equilibria in such systems plays a key role in important biochemical processes. Examples show that there is a very delicate relationship between the structure of a reaction network and its capacity… (More)

- Murad Banaji, Casian Pantea
- SIAM J. Applied Dynamical Systems
- 2016

Chemical mechanisms for even simple reaction networks involve many highly reactive and short-lived species (intermediates), present in small concentrations , in addition to the main reactants and products, present in larger concentrations. The chemical mechanism also often contains many rate constants whose values are unknown a priori and must be determined… (More)

- Pete Donnell, Murad Banaji, Anca Marginean, Casian Pantea
- Bioinformatics
- 2014

UNLABELLED
We introduce CoNtRol, a web-based framework for analysis of chemical reaction networks (CRNs). It is designed to be both extensible and simple to use, complementing existing CRN-related tools. CoNtRol currently implements a number of necessary and/or sufficient structural tests for multiple equilibria, stable periodic orbits, convergence to… (More)

- Matthew D Johnston, Casian Pantea, Pete Donnell
- Journal of mathematical biology
- 2016

We introduce a mixed-integer linear programming (MILP) framework capable of determining whether a chemical reaction network possesses the property of being endotactic or strongly endotactic. The network property of being strongly endotactic is known to lead to persistence and permanence of chemical species under genetic kinetic assumptions, while the same… (More)