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Extinction in Reaction Network Models
Pranav Agarwal, Gheorghe Craciun, Abhishek Deshpande +1
In this paper, we study extinction in dynamical systems generated by reaction networks. We introduce two notions: weak extinction and strong extinction, and relate them to the stru…
The Computation of the Disguised Toric Locus of Reaction Networks
Gheorghe Craciun, Abhishek Deshpande, Jiaxin Jin
Mathematical models of reaction networks can exhibit very complex dynamics, including multistability, oscillations, and chaotic dynamics. On the other hand, under some additional a…
Realizations through Weakly Reversible Networks and the Globally Attracting Locus
Samay Kothari, Jiaxin Jin, Abhishek Deshpande
We investigate the possibility that for any given reaction rate vector associated with a network , there exists another network with a corresponding reaction rate vecto…
On the Connectivity of the Disguised Toric Locus of a Reaction Network
Gheorghe Craciun, Abhishek Deshpande, Jiaxin Jin
Complex-balanced mass-action systems are some of the most important types of mathematical models of reaction networks, due to their widespread use in applications, as well as their…
A Lower Bound on the Dimension of the -Disguised Toric Locus of a Reaction Network
Gheorghe Craciun, Abhishek Deshpande, Jiaxin Jin
Polynomial dynamical systems (i.e. dynamical systems with polynomial right hand side) are ubiquitous in applications, especially as models of reaction networks and interaction netw…
Weakly reversible deficiency one realizations of polynomial dynamical systems: an algorithmic perspective
Gheorghe Craciun, Abhishek Deshpande, Jiaxin Jin
Given a dynamical system with polynomial right-hand side, can it be generated by a reaction network that possesses certain properties? This question is important because some netwo…
Endotactic and strongly endotactic networks with infinitely many positive steady states
Samay Kothari, Abhishek Deshpande
We show that there exists endotactic and strongly endotactic dynamical systems that are not weakly reversible and possess infinitely many steady states. We provide a few examples i…
Weakly reversible single linkage class realizations of polynomial dynamical systems: an algorithmic perspective
Gheorghe Craciun, Abhishek Deshpande, Jiaxin Jin
Systems of differential equations with polynomial right-hand sides are very common in applications. In particular, when restricted to the positive orthant, they appear naturally (a…
Source-only realizations, weakly reversible deficiency one networks and dynamical equivalence
Abhishek Deshpande
Reaction networks can display a wide array of dynamics. However, it is possible for different reaction networks to display the same dynamics. This phenomenon is called dynamical eq…