Signs of memory in a plastic frustrated Kuramoto model of neurons

We study the effects brought about by adding frustration to the plastic Kuramoto model of neurons; i.e. we simulate for the first time the plastic Kuramoto–Sakaguchi model, in which the nonlocal coupling matrix for the phases is determined from the spike-timing-dependent plasticity rule. We find that frustration leads to the birhythmicity of the synchronous states. The multistability in the dynamics, with frustration as its crucial element, results in hysteresis, even when the learning rule is symmetric. Fine structure in the hysteresis loop reflects the complexity of the underlying energy landscape. A pacemaker is used to probe this landscape. As the neurons spontaneously self-organise, memory is formed by the configuration of synaptic strengths embodied in such synchronous states. We thus have a simple model of synaptic memory.