Complete and phase synchronization in a heterogeneous small-world neuronal network

Synchronous firing of neurons is thought to be important for information communication in neuronal networks. This paper investigates the complete and phase synchronization in a heterogeneous small-world chaotic Hindmarsh--Rose neuronal network. The effects of various network parameters on synchronization behaviour are discussed with some biological explanations. Complete synchronization of small-world neuronal networks is studied theoretically by the master stability function method. It is shown that the coupling strength necessary for complete or phase synchronization decreases with the neuron number, the node degree and the connection density are increased. The effect of heterogeneity of neuronal networks is also considered and it is found that the network heterogeneity has an adverse effect on synchrony.     

Bursting Ca2+ Oscillations and Synchronization in Coupled Cells

A mathematical model proposed by Grubelnk et al. [Biophys. Chem. 94 （2001） 59] is employed to study the physiological role of mitochondria and the cytosolic proteins in generating complex Ca^2＋ oscillations, lntracellulax bursting calcium oscillations of point-point, point-cycle and two-folded limit cycle types are observed and explanations are given based on the fast/slow dynamical analysis, especially for point-cycle and two-folded limit cycle types, which have not been reported before. Furthermore, synchronization of coupled bursters of Ca^2＋ oscillations via gap junctions and the effect of bursting types on synchronization of coupled cells are studied. It is argued that bursting oscillations of point-point type may be superior to achieve synchronization than that of point cycle type.