Dimensionality reduction is a popular strategy for studying complex dynamical systems, especially high-dimensional networked systems. Its goal to discover more compact version of the system that retains almost important characteristics original and offers insights into inner functioning as well long-term behavior. However, because interaction structures, parameter configurations, initial condit...

We introduce a family of discrete dynamical systems which includes, and generalizes, the mutation dynamics rank two cluster algebras. These exhibit behavior associated with integrability, namely preservation symplectic form, in tropical case, existence conserved quantity. show certain cases that orbits are unbounded. The related to matrix mutation, from theory able special cases, map is periodi...