2018/09/12 by Sang-Yoon Kim, Kim, Sang-Yoon, Woochang Lim +1
Biochemistry, Genetics and Molecular Biology · Computer Science · Neuroscience · Physics and Astronomy · #Biological Physics (physics.bio-ph) #FOS: Biological sciences #FOS: Physical sciences #Neural dynamics and brain function #Neurons and Cognition (q-bio.NC) #Nonlinear Dynamics and Pattern Formation #physics.bio-ph #q-bio.NC #stochastic dynamics and bifurcation
paper · pdf · doi:10.48550/arxiv.1809.04953
arXiv admin note: text overlap with arXiv:1803.07256, arXiv:1708.04543
openalex publication_date 2018/09/12 · openalex created_date 2018/09/27 · arxiv created 2019/04/01 · arxiv updated 2019/04/02 · openalex updated_date 2026/07/28
We consider a scale-free network of inhibitory Hindmarsh-Rose (HR) bursting neurons, and investigate coupling-induced cluster burst synchronization by varying the average coupling strength J0. For sufficiently small J0, non-cluster desynchronized states exist. However, when passing a critical point J^*c~(≃ 0.16), the whole population is segregated into 3 clusters via a constructive role of synaptic inhibition to stimulate dynamical clustering between individual burstings, and thus 3-cluster desynchronized states appear. As J0 is further increased and passes a lower threshold J^*l~(≃ 0.78), a transition to 3-cluster burst synchronization occurs due to another constructive role of synaptic inhibition to favor population synchronization. In this case, HR neurons in each cluster exhibit burst synchronization. However, as J0 passes an intermediate threshold J^*m~(≃ 5.2), HR neurons begin to make intermittent hoppings between the 3 clusters. Due to the intermittent intercluster hoppings, the 3 clusters are integrated into a single one. In spite of break-up of the 3 clusters, (non-cluster) burst synchronization persists in the whole population, which is well visualized in the raster plot of burst onset times where bursting stripes (composed of burst onset times and indicating burst synchronization) appear successively. With further increase in J0, intercluster hoppings are intensified, and bursting stripes also become smeared more and more due to a destructive role of synaptic inhibition to spoil the burst synchronization. Eventually, when passing a higher threshold J^*h~(≃ 17.8) a transition to desynchronization occurs via complete overlap between the bursting stripes. Finally, we also investigate the effects of stochastic noise on both 3-cluster burst synchronization and intercluster hoppings.