title: Identification of interactions in fractional-order systems with high dimensions.
abstract: This article proposes an approach to identify fractional-order systems with sparse interaction structures and high dimensions when observation data are supposed to be experimentally available. This approach includes two steps: first, it is to estimate the value of the fractional order by taking into account the solution properties of fractional-order systems; second, it is to identify the interaction coefficients among the system variables by employing the compressed sensing technique. An error analysis is provided analytically for this approach and a further improved approach is also proposed. Moreover, the applicability of the proposed approach is fully illustrated by two examples: one is to estimate the mutual interactions in a complex dynamical network described by fractional-order systems, and the other is to identify a high fractional-order and homogeneous sequential differential equation, which is frequently used to describe viscoelastic phenomena. All the results demonstrate the feasibility of figuring out the system mechanisms behind the data experimentally observed in physical or biological systems with viscoelastic evolution characters.
authors.affiliation: School of Mathematical Sciences and Centre for Computational Systems Biology, Fudan University, Shanghai 200433, China.
authors.forename: Xiaoxi
authors.initials: X
authors.lastname: Ji
authors.affiliation: School of Mathematical Sciences and Centre for Computational Systems Biology, Fudan University, Shanghai 200433, China.
authors.forename: Yu
authors.initials: Y
authors.lastname: Wu
authors.affiliation: School of Mathematical Sciences and Centre for Computational Systems Biology, Fudan University, Shanghai 200433, China.
authors.forename: Wenbo
authors.initials: W
authors.lastname: Sheng
authors.affiliation: School of Mathematical Sciences and Centre for Computational Systems Biology, Fudan University, Shanghai 200433, China.
authors.forename: Wei
authors.initials: W
authors.lastname: Lin
mesh_terms: D000465:Algorithms; D008962:Models, Theoretical