Responsiveness of a neural pacemaker near the bifurcation point

Dynamics of firing patterns, synchronization and resonances in neuronal electrical activities: experiments and analysis

“…These experimental results showed that periodic firing and chaotic firing, bifurcation to chaos could be generated in biological system and in nerve system [7]. After these pioneering studies, many experiments performed on different assembles of animals, such as neural pacemaker in rats [8][9][10][11][12][13] , neurons including isolated neuron of pyloric central pattern generating (CPG) in the lobster stomatogastric ganglion [14][15][16][17][18], dopamine neurons [19][20][21][22], extracellular and intracellular measurements from small assembles in hippocampal slices [23], sensory receptors including cold receptors, caudal photoreceptor of crayfish and electroreceptors of the catfish [24][25][26][27], living β-cells in the mouse pancreatic islet [28], dorsal root ganglion (DRG) of rats [29], teleost Mauthner cells' synaptic noise [30], epileptic activity [31,32] and so on, were done to identify the deterministic dynamics underlying complex and irregular firing patterns. The bifurcation routes to chaos and the nonlinear time series analysis method played important roles in identifying chaotic firings.…”

“…Using nonlinear time series analysis methods, such as nonlinear prediction [11], nonlinear forecast [8], correlation dimension, Lyapunov exponent [11] and detection of periodic orbits by the So method [9,11], the dynamics of the chaotic firing patterns, including predictability, sensitivity to initial values, internal skeletons within deterministic structures, were identified [8][9][10][11][12][13]. The ISI series of chaotic firings could be predicated or forecasted in a short term, as shown in Fig.…”

“…The response of chaotic firing patterns of neural pacemaker to external electrical field stimulus was also studied [13]. If the firing pattern was far from the bifurcation point, like periodic firing, with increasing the stimulus intensity, the firing rate increased in an approximately linear manner and no firing pattern transition was observed.…”

Electrophysiological Features of Neurons in the Mesencephalic Trigeminal Nuclei

“…In an interesting study on the chronic compression of rat sciatic nerves, it was shown that at a bifurcation point of critical sensitivity, patterns of bursting in an experimental pacemaker can be altered when the extracellular calcium concentration is changed [12,73,74]. For Mes V neurons, a theoretical study using mathematical models has demonstrated that small changes in the parameters related to ionic currents could lead to transitions between different classes of membrane excitability [72].…”

“…It was Hodgkin who was the first to study crustacean nerve axons to distinguish neuronal excitability into three classes according to responses of the cell to applied stimuli [7]. Correspondingly, alterations in certain parameters, such as the dynamic characteristics of a current, can be crucial, since these change the neuron's firing behavior from one type to another [8,9,10,11,12]. …”