Using network models consisting of gap-junction-coupled Wang-Buszaki neurons, we demonstrate that it is possible to obtain not only synchronous activity between neurons but also a variety of constant phase shifts between 0 and $\pi$. We call these phase shifts intermediate stable phase-locked states. These phase shifts can produce a large variety of wavelike activity patterns in one-dimensional chains and two-dimensional arrays of neurons, which can be studied by reducing the system of equations to a phase model. The $2\pi$ periodic coupling functions of these models are characterized by prominent higher order terms in their Fourier expansion, which can be varied by changing model parameters. We study how the relative contribution of the odd and even terms affects what solutions are possible, the basin of attraction of those solutions, and their stability. These models may be applicable to the spinal central pattern generators of the dogfish and also to the developing neocortex of the neonatal rat.

• Received 13 March 2012

DOI:https://doi.org/10.1103/PhysRevE.86.011907