As a function of the intrinsic control parameters, and the external chemical coupling strength, the conditions for stability of the fixed point of this system are derived.

The stable regions of the master stability function and the strip-like chaotic structure in different parameter-spaces are obtained.

Given some values of control parameter, we propose the interval ranges of the coupling strength in which the two chaotic Rulkov map-based neurons can be synchronized completely.

Compared with the control parameter and the synaptic parameter, the chemical coupling strength plays an opposite role in the process of synchronization transition.

These findings could be useful for further understanding the role of two identical Rulkov chaotic map neurons coupled via the chemical synapses in the field of cooperative behaviors of coupled neurons.