Synchronization of map-based neurons with memory and synaptic delay

Article history: Received 25 February 2014 Received in revised form 29 April 2014 Accepted 2 May 2014 Available online 10 June 2014 Communicated by C.R. Doering Synchronization of two synaptically coupled neurons with memory and synaptic delay is studied using the Rulkov map, one of the simplest neuron models which displays specific features inherent to bursting dynamics. We demonstrate a transition from lag to anticipated synchronization as the relationship between the memory duration and the synaptic delay time changes. The neuron maps synchronize either with anticipation, if the memory is longer than the synaptic delay time, or with lag otherwise. The mean anticipation time is equal to the difference between the memory and synaptic delay independently of the coupling strength. Frequency entrainment and phase-locking phenomena as well as a transition from regular spikes to chaos are demonstrated with respect to the coupling strength. © 2014 Elsevier B.V. All rights reserved.