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Experimental Methods to Study Human Postural Control

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Published on: September 11, 2019

Perturbation-response dynamics of coupled nonlinear systems.

Georg Börner¹, Malte Schröder¹, Moritz Thümler¹

¹Chair for Network Dynamics, Institute of Theoretical Physics and Center for Advancing Electronics Dresden (cfaed), TUD Dresden University of Technology, 01062 Dresden, Germany.

Chaos (Woodbury, N.Y.)

|October 29, 2024

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.