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Everything about Marginal stability

Dynamical system which is neither asymptotically stable nor unstable

In the theory of dynamical systems and control theory, a linear time-invariant system is marginally stable if it is neither asymptotically stable nor unstable. Roughly speaking, a system is stable if it always returns to and stays near a particular state, and is unstable if it goes further and further away from any state, without being bounded. A marginal system, sometimes referred to as having neutral stability, is between these two types: when displaced, it does not return to near a common steady state, nor does it go away from where it started without limit. Wikipedia →

🧭 Start here: a 6-step reading path

  1. Read the overview: Marginal stabilityA 5-minute orientation
  2. Skim a recent paper: Marginal stability of soft anharmonic mean field spin glassesInfluential work since 2022
  3. Pick up a classic book: Urban segregation and governance in the AmericasThe most-reprinted book on the subject
  4. Read the landmark paper: Nonlinear Dynamics of a Driven Mode near Marginal StabilityCited 188 times
  5. Go sideways: Exponential stabilityA closely related topic
  6. Go sideways: Stability theoryA closely related topic

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🗂️ The subject at a glance

  1. Continuous time
  2. Discrete time
  3. System response
  4. Stochastic dynamics

🏆 Landmark papers (most cited)

🆕 Influential since 2022

📚 Books worth reading

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