Human social behaviour is complex, and the biological and neural mechanisms underpinning it remain debated. A particularly interesting social phenomenon is our ability and tendency to fall into synchronization with other humans. Our ability to coordinate actions and goals relies on the ability to distinguish between and integrate self and other, which when impaired can lead to devastating consequences. Interpersonal synchronization has been a widely used framework for studying action coordination and self-other integration, showing that even in simple interactions, such as joint finger tapping, complex interpersonal dynamics emerge. Here we propose a computational model of self-other integration via within- and between-person action-perception links, implemented as a simple Kuramoto model with four oscillators. The model abstracts each member of a dyad as a unit consisting of two connected oscillators, representing intrinsic processes of perception and action. By fitting this model to data from two separate experiments we show that interpersonal synchronization strategies rely on the relationship between within- and between-unit coupling. Specifically, mutual adaptation exhibits a higher between-unit coupling than within-unit coupling; leading-following requires that the follower unit has a low within-unit coupling; and leading-leading occurs when two units jointly exhibit a low between-unit coupling. These findings are consistent with the theory of interpersonal synchronization emerging through self-other integration mediated by processes of action-perception coupling. Hence, our results show that chaotic human behaviour occurring on a millisecond scale may be modelled using coupled oscillators.