Aggregates of monotonic step response systems: A structural classification

Franco Blanchini, Christian Cuba Samaniego, Elisa Franco, Giulia Giordano

Research output: Contribution to journalArticleScientificpeer-review

5 Citations (Scopus)

Abstract

Complex dynamical networks can often be analyzed as the interconnection of subsystems: This allows us to considerably simplify the model and better understand the global behavior. Some biological networks can be conveniently analyzed as aggregates of monotone subsystems. Yet, monotonicity is a strong requirement; it relies on the knowledge of the state representation and imposes a severe restriction on the Jacobian (which must be a Metzler matrix). Systems with a monotonic step response (MSR), which include input-output monotone systems as a special case, are a broader class and still have interesting features. The property of having a monotonically increasing step response (or, equivalently, in the linear case, a positive impulse response) can be evinced from experimental data, without an explicit model of the system. We consider networks that can be decomposed as aggregates of MSR subsystems and we provide a structural (parameter-free) classification of oscillatory and multistationary behaviors. The classification is based on the exclusive or concurrent presence of negative and positive cycles in the system aggregate graph, whose nodes are the MSR subsystems. The result is analogous to our earlier classification for aggregates of monotone subsystems. Models of biomolecular networks are discussed to demonstrate the applicability of our classification, which helps build synthetic biomolecular circuits that, by design, are well suited to exhibit the desired dynamics.

Original languageEnglish
Pages (from-to)782-792
JournalIEEE Transactions on Control of Network Systems
Volume5
Issue number2
DOIs
Publication statusPublished - 2018

Keywords

  • Bifurcations
  • biological networks
  • graph theory
  • positive impulse response
  • structural analysis

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