Effects of propagation delay in coupled oscillators under direct-indirect coupling: Theory and experiment

Area of Science:

• Nonlinear dynamics
• Coupled oscillator systems
• Signal propagation

Background:

• Propagation delay is a known phenomenon in coupled systems.
• In direct coupling, delay often leads to amplitude death.
• Direct-indirect coupling typically promotes amplitude death.

Purpose of the Study:

• Investigate the effect of propagation delay in indirect coupling paths.
• Determine if propagation delay can influence the dynamics of direct-indirect coupled oscillators.
• Explore the conditions under which delay promotes oscillation.

Main Methods:

• Analysis of direct-indirect coupled oscillators.
• Inclusion of propagation delay in the indirect path.
• Linear stability analysis for identifying oscillation onset.
• Experimental verification using electronic hardware.

Main Results:

• Propagation delay in direct-indirect coupling promotes oscillatory behavior.
• Delay counteracts the amplitude death typically induced by combined direct and indirect coupling.
• Explicit conditions for oscillation revival from the death state were derived.
• Results were robust and experimentally verified.

Conclusions:

• Propagation delay's effect on coupled oscillators is non-trivial and coupling-function dependent.
• Time delay can be a crucial factor in controlling the dynamics of coupled systems.
• This work offers new insights into managing oscillations in complex systems.