A model of a pair of coupled limit cycle oscillators is presented in order to investigate the extent of, and the transition between, 1∶1 and 2∶1 phase entrainment, a phenomenon exhibited by numerous diverse biological systems. The mathematical form of the model involves a flow on a phase torus given by two coupled first order nonlinear ordinary differential equations which govern the oscillators' phase angles (i.e. their respective positions around their limit cycles). The regions corresponding to 1∶1 and 2∶1 phase entrainment in an appropriate parameter space are determined analytically and numerically. The bifurcations occurring during the transition from 1∶1 to 2∶1 phase entrainment are discussed.
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Keith, W.L., Rand, R.H. 1∶1 and 2∶1 phase entrainment in a system of two coupled limit cycle oscillators. J. Math. Biology 20, 133–152 (1984). https://doi.org/10.1007/BF00285342
- limit cycles
- phase entrainment