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Nonlinear dynamics of delay systems: an overview.

A Otto1, W Just2, G Radons1

  • 1Institute of Physics, Chemnitz University of Technology, 09107 Chemnitz, Germany.

Philosophical Transactions. Series A, Mathematical, Physical, and Engineering Sciences
|July 23, 2019
PubMed
Summary
This summary is machine-generated.

This study explores nonlinear dynamics in systems with time delays, crucial in engineering and biology. New findings cover time-varying, state-dependent, and noisy delays with diverse applications.

Keywords:
chaosdelay differential equationfeedbacknonlineartime delay

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Area of Science:

  • Mathematics
  • Physics
  • Engineering
  • Biology

Background:

  • Time delays are prevalent in engineering, physics, and biology, often leading to memory effects and infinite-dimensional systems.
  • These systems are typically modeled using delay differential equations, frequently incorporating nonlinear dynamics.
  • Understanding nonlinear dynamics of delay systems is crucial for analyzing complex phenomena in various scientific disciplines.

Purpose of the Study:

  • To provide an overview of the theme issue 'Nonlinear dynamics of delay systems'.
  • To highlight new fundamental results and recent developments in the interdisciplinary field of time delay systems.
  • To showcase the broad range of applications for nonlinear delay systems.

Main Methods:

  • The article reviews fundamental theoretical advancements in nonlinear delay systems.
  • It discusses methodologies for analyzing systems with time-varying and state-dependent delays.
  • The impact of noise on delay systems is also considered, reflecting real-world complexities.

Main Results:

  • Significant progress has been made in understanding systems with time-varying and state-dependent delays.
  • New insights into the dynamics of delay systems affected by noise have been achieved.
  • The research encompasses both theoretical advancements and practical applications.

Conclusions:

  • Nonlinear dynamics of delay systems is a rapidly evolving interdisciplinary field.
  • New theoretical results and analytical methods are expanding the understanding of complex delay systems.
  • The findings have broad applicability across diverse fields, from climate modeling to machine tool chatter.