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Introduction to Focus Issue: Nonautonomous dynamical systems: Theory, methods, and applications.

Peter Ashwin1, Ulrike Feudel2, Michael Ghil3,4,5

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Nonautonomous dynamical systems (NDS) are crucial in understanding time-dependent models across sciences. This issue explores NDS applications in climate, biodiversity, and machine learning, driving theoretical advancements.

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Area of Science:

  • Mathematics, Physics, and Life Sciences
  • Focus on Nonlinear Dynamics and Time Dependence

Background:

  • Nonlinear dynamics has become a significant field in recent decades.
  • A key area of development involves understanding time-dependent forcing and parameters in models.
  • This is crucial for fields like climate science, biodiversity, and biomedical research.

Purpose of the Study:

  • To present a Focus Issue (NDS-G) on nonautonomous dynamical systems (NDS) in the sciences.
  • To complement a related issue on NDS in climate (NDS-C).
  • To highlight the rapid development and application of NDS theory.

Main Methods:

  • Review and discussion of recent advancements in the mathematical theory of nonautonomous and random dynamical systems.
  • Exploration of applications in various scientific disciplines.
  • Synthesis of current research trends in the field.

Main Results:

  • Nonautonomous dynamical systems are increasingly vital for modeling complex phenomena.
  • Applications span climate change, biodiversity, machine learning, and biomedical problems.
  • The interplay between theory and applications is rapidly advancing.

Conclusions:

  • Nonautonomous dynamical systems are a rapidly developing and crucial area of modern science.
  • The study of time-dependent systems is essential for addressing contemporary scientific challenges.
  • This Focus Issue provides insights into the latest theoretical and applied research in NDS.