Chaotic burst synchronization in heterogeneous small-world neuronal network with noise

Synchronization analysis of coupled calcium oscillators based on two regular coupling schemes

“…In case of one cell, let x = Ca cyt , y = Ca er , z = IP 3 , r = 0.99, the Jacobian matrix D(F(s(t))) of system (2) at the synchronization manifold s(t) can be rewritten in the following form: 11 , a 212 , a 13 ; a 21 , a 22 , a 23 ; a 31 , a 32 , a 33 ] …”

“…Recently, synchronization in coupled electrical systems has been extensively investigated in the context of biological systems. Much work has been done on synchronization behavior of calcium oscillations such as complete synchronization [5,6], phase synchronization [7][8][9], lag synchronization [10], generalized synchronization [11][12][13][14] etc. But in most of the work, the threshold of synchronization is given by the numerical simulations.…”

Robust synchronization of bursting Hodgkin–Huxley neuronal systems coupled by delayed chemical synapses

“…Various models including the neuronal model, the synapse model, and further the network model need to be constructed when computational approaches are followed. There are a great number of researches on the synchronization of neuronal network coupled by electrical synapses [8][9][10][11][12]. These studies found that neuronal firing in such neuronal networks can be synchronized in different extent depending on the parameter values and network structure.…”

Local and global synchronization transitions induced by time delays in small-world neuronal networks with chemical synapses

“…Modeling studies show that, compared with regular networks, neuronal systems with small-world connectivity are easier to get synchronization. Increasing the number of shortcut links between long-range units can largely enhance the synchronization degree of small-world networks (Han et al 2008). Moreover, the significant role of small-world topology on the resonance dynamics of excitable neural media has been explored (Perc 2007;Ozer et al 2009;Gao et al 2001).…”