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Related Experiment Video

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Perturbation-response dynamics of coupled nonlinear systems.

Georg Börner1, Malte Schröder1, Moritz Thümler1

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Summary

Inter-unit coupling in nonlinear systems can prevent tipping points and create new response modes. Even weak coupling can stabilize dynamics more effectively than strong coupling.

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Area of Science:

  • Nonlinear dynamics
  • Complex systems theory
  • Network science

Background:

  • Nonlinear systems' functions are determined by their dynamic responses to perturbations.
  • Linear response theory approximates dynamics near stable points for weak perturbations.
  • Stronger perturbations can cause nonlinear responses and tipping transitions.

Purpose of the Study:

  • To analyze how inter-unit coupling affects responses to periodic perturbations in nonlinear systems.
  • To investigate the impact of coupling strength and type on system stability and response modes.

Main Methods:

  • Analysis of minimal systems of two linearly coupled units.
  • Exploration of systems with identical and non-identical units.
  • Consideration of nonlinear coupling and larger networks.

Main Results:

  • Non-zero coupling extends the regime of non-tipping local responses compared to uncoupled systems.
  • Finite coupling can be more effective than infinite coupling in preventing tipping.
  • Weak coupling can induce novel response modes, suggesting multiple tipping points.

Conclusions:

  • Inter-unit coupling significantly alters nonlinear system dynamics under periodic perturbations.
  • Coupling offers a mechanism to control system stability and prevent undesirable tipping transitions.
  • Findings are robust across variations in unit identity, coupling nonlinearity, and network size.