# List of main results by topic

From Mathematics of Reaction Networks

This is a **list of main results by topics** for results pertaining to topics within the mathematics of reaction networks. The topics are organized alphabetically with more widely referenced results appearing first within the topics. Results are annotated and may appear in more than one list.

## Contents

- 1 Biochemistry
- 2 Boundedness
- 3 Complex balanced systems
- 4 Computational approaches
- 5 Deficiency theory
- 6 Detailed balanced systems
- 7 Dynamical equivalence
- 8 Enzyme reactions
- 9 Global attractor conjecture
- 10 Identifiability of rate constants
- 11 Injectivity
- 12 Kinetic schemes
- 13 Lumping
- 14 Miscellaneous
- 15 Model Reduction
- 16 Monotonicity
- 17 Multistability
- 18 Persistence
- 19 Reaction-diffusion models
- 20 Stochastic models
- 21 Toric dynamical systems

## Biochemistry

## Boundedness

## Complex balanced systems

- Deficiency zero theorem
- Every weakly reversible mass action system with zero deficiency is complex balanced for all rate constants.

## Computational approaches

## Deficiency theory

- Deficiency zero theorem
- Every weakly reversible mass action system with zero deficiency exhibits locally stable dynamics for all rate constants.
- Every weakly reversible mass action system with zero deficiency is complex balanced for all rate constants.

- Deficiency one theorem
- Presents conditions on the deficiency under which mass action systems with a single terminal strongly linked component in each linkage class has a single equilibrium concentration in each stoichiometric compatibility class.

- Deficiency one algorithm
- Presents necessary and sufficient conditions for certain deficiency one mass action systems to permit multiple positive equilibrium concentrations.

## Detailed balanced systems

## Dynamical equivalence

## Enzyme reactions

## Global attractor conjecture

See persistence.