Reliability of Coupled Oscillators I: Two-Oscillator Systems

Details Reliability of Coupled Oscillators I: Two-Oscillator Systems Reliability of Coupled Oscillators I: Two-Oscillator Systems

2007-08-22

arxiv.org/abs/0708.3061v2

Nonlinear Sciences

Chaotic Dynamics

Part 1 of 2. Part 2 can be found at 0708.3063

Scientific paper

This paper concerns the reliability of a pair of coupled oscillators in response to fluctuating inputs. Reliability means that an input elicits essentially identical responses upon repeated presentations regardless of the network's initial condition. Our main result is that both reliable and unreliable behaviors occur in this network for broad ranges of coupling strengths, even though individual oscillators are always reliable when uncoupled. A new finding is that at low input amplitudes, the system is highly susceptible to unreliable responses when the feedforward and feedback couplings are roughly comparable. A geometric explanation based on shear-induced chaos at the onset of phase-locking is proposed.

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