Generalized synchronization induced by noise and parameter mismatching in Hindmarsh-Rose neurons

Synchronization of two simple neuron models has been investigated in many studies. Thresholds for complete synchronization (CS) and phase synchronization (PS) have been obtained for coupling by diffusion or noise. In addition, it has been shown that it is possible for directional diffusion to induce generalized synchronization (GS) in a pair of neuron models even if the neurons are not identical (and differ in a single parameter). We study a system of two uncoupled, nonidentical Hindmarsh-Rose (HR) neurons and show that GS can be achieved by a combination of noise and changing the value of a second parameter in one of the neurons (the second parameter mismatch cancels the first). The significance of this approach will be the greatest in situations where the parameter that is originally mismatched cannot be controlled, but a suitable controllable parameter can be identified.