# The center problem for the Lotka reactions with generalized mass-action kinetics

## TL;DR

This paper characterizes the parameter conditions under which the positive equilibrium of Lotka reactions with generalized mass-action kinetics is a center, contributing to the understanding of power-law dynamical systems in chemical reaction networks.

## Contribution

It provides a complete characterization of parameters leading to a center in the planar ODE of Lotka reactions with generalized mass-action kinetics.

## Key findings

- Identifies parameter conditions for the equilibrium to be a center
- Analyzes power-law dynamical systems in chemical networks
- Contributes to the theory of reaction network dynamics

## Abstract

Chemical reaction networks with generalized mass-action kinetics lead to power-law dynamical systems. As a simple example, we consider the Lotka reactions and the resulting planar ODE. We characterize the parameters (positive coefficients and real exponents) for which the unique positive equilibrium is a center.