In the past, anomalous phase synchronization was observed analytically and experimentally between two nonidentical chaotic oscillators.

In this work, we consider a chain of mutually coupled three oscillators where heterogeneity (in terms of parameter mismatch) is introduced in the middle (relay) oscillator, and the outer two oscillators are identical. We observe an anomalous complete synchronization between the outer oscillators.

A common time-delay between the identical outer oscillators and the mismatched relay oscillator plays an important role for the emergence of anomalous complete synchrony.

We present several example systems to verify our results with and without coupling delay. We also observe generalized synchronization between the relay oscillator and the outer identical oscillators.

The variation of parameter mismatch, coupling strength and coupling delay on the anomalous complete synchronization is studied with diffusive and globally coupled network.

R. Banerjee, S. Acharya, M. Perc, D. Ghosh, Anomalous complete synchronization in relay oscillators, Chaos Solitons & Fractals 193(2025) 116069.