Coupled ionic-electronic effects present intriguing opportunities for device and circuit development. In particular, layered two-dimensional materials such as MoS2 offer highly anisotropic ionic transport properties, facilitating controlled ion migration and efficient ionic coupling among devices. Here, we report reversible modulation of MoS2 films that is consistent with local 2H-1T' phase transitions by controlling the migration of Li+ ions with an electric field, where an increase/decrease in the local Li+ ion concentration leads to the transition between the 2H (semiconductor) and 1T' (metal) phases. The resulting devices show excellent memristive behaviour and can be directly coupled with each other through local ionic exchange, naturally leading to synaptic competition and synaptic cooperation effects observed in biology. These results demonstrate the potential of direct modulation of two-dimensional materials through field-driven ionic processes, and can lead to future electronic and energy devices based on coupled ionic-electronic effects and biorealistic implementation of artificial neural networks.