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What drives transient behavior in complex systems?

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We reveal a new stable-transient regime in complex systems, identifying key drivers of transient dynamics and their statistical distributions. This advances understanding of nonlinear system behavior.

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Area of Science:

  • Nonlinear Dynamics
  • Complex Systems Theory
  • Statistical Physics

Background:

  • Transient behavior in complex systems is often destabilizing and difficult to predict.
  • Understanding these dynamics is crucial for fields ranging from ecology to engineering.
  • Existing models often simplify complexity, potentially missing important transient phenomena.

Purpose of the Study:

  • To investigate transient behavior in complex systems governed by nonlinear ordinary differential equations.
  • To connect transient trajectory destabilization with linearization procedures.
  • To introduce and analyze a novel stable-transient regime.

Main Methods:

  • Modeling system complexity using a modified May-Wigner random matrix model.
  • Analyzing the initial system response to identify the stable-transient regime.
  • Calculating abundances of transient trajectories using extreme value statistics (Gaussian and Tracy-Widom distributions).
  • Identifying degrees of freedom via eigenvectors and a nonorthogonality matrix (T0).

Main Results:

  • Identification of a novel stable-transient regime based on initial system response.
  • Exact calculation of typical and extreme transient trajectory abundances, revealing Gaussian and Tracy-Widom distributions.
  • Characterization of transient behavior drivers linked to eigenvectors and the nonorthogonality matrix T0.
  • Extension of the May-Wigner model to include typical transient trajectories.

Conclusions:

  • Transient dynamics in complex systems exhibit a stable-transient regime with predictable statistical properties.
  • Eigenvectors and nonorthogonality play a critical role in driving transient behavior.
  • The extended May-Wigner model provides a more comprehensive framework for analyzing transient dynamics.