Complete Synchronization and Phase
Synchronization of Two Uncoupled Neurons Through Parametrical Drive
Wu Ying, Xu Jianxue, Jin Wuyin
(School of Architectural Engineering and Mechanics, Xi'an Jiaotong University, Xi'an
710049, China)
Abstract: It is investigated to synchronize two uncoupled Hindmarsh-Rose (HR) neurons
under different initial conditions by adopting the external chaotic signal or the membrane
potential of a chaotic neuron as stimulation signal. By modulating the corresponding
parameters of two uncoupled identical HR neurons, complete synchronization is realized
when the largest condition Lyapunov exponent (LCLE) becomes negative at the threshold of
stimulation strength. And by modulating input currents of two uncoupled HR neurons with
parameters mismatch, phase synchronization is obtained when the two LCLEs of both systems
change to negative. This investigation proposes reasonable experimental methods for
synchronizing two uncoupled neuron systems, and provides a theoretical foundation for
studying complex neuron systems.
Keywords: chaos; synchronization; phase synchronization; neuron; largest condition
Lyapunov exponent