A four-dimensional neuronal model to describe the complex nonlinear dynamics observed in the firing patterns of a sciatic nerve chronic constriction injury model

Mixed Stimulus-Induced Mode Selection in Neural Activity Driven by High and Low Frequency Current under Electromagnetic Radiation

“…As it can be known, the relevant experiments of the neuron electrical activity play a vital role in achieving biological functions of the nervous system [38][39][40][41][42][43]. The latest researches described the complex bifurcations related to real experiments and HR neuron model; the experimental results [38,39] demonstrate the dynamics of a neuronal transition from chaotic bursting to chaotic spiking in the nervous system, which agree with published findings in theoretical neuronal models [40,41].…”

“…In addition, it is found that the firing, spike frequency, and instantaneous spike frequency observed in the experiment were simulated and explained using HH models. References [42,43] illustrate the dynamics of different firing patterns and the frequency and temporal coding mechanisms of aortic baroreceptor.…”

A basic bifurcation structure from bursting to spiking of injured nerve fibers in a two-dimensional parameter space

“…Neural firing patterns play important roles in the neural coding mechanism and the integrated behavior of a nervous system such as synchronization behaviors (Thomas et al 1994;Braun et al 1994;Ivancevic et al 2009). Identification of nonlinear dynamics in a single neuron has attracted much attention in both experimental and theoretical investigations Gu and Pan 2015;Liu et al 2016;Brette 2008;Xu and Wang 2014;Lv and Ma 2016). Biological experiments have been performed on axons, somatosensory cortex neurons, cold sensory neurons, Purkinje cells, hypothalamus neurons, sciatic nerve fibers of CCI models (Mandelblat et al 2001;Braun et al 2011;Yang et al 2009), and chronically compressed dorsal root ganglion (CCD) (Xie et al 2011).…”

“…Different transitions or bifurcation scenarios from period-1 bursting to period-1 spiking were simulated in the HR and Chay models; this was thought to be a universal regularity of biological rhythms (Holden and Fan 1992;Holden 1992, 1993;Fan and Chay 1994;Chay 1985;Chay et al 1995;Duan and Lu 2006; Barrio and Shilnikov 2011). Recently, these bifurcations have been observed in the biological experiments on the sciatic nerve fibers of a CCI model, with adjustment of extracellular potassium or calcium concentration (Li et al 2004;Gu 2013b;Gu and Pan 2015), which provided more information than former investigations, wherein only local parts of the bifurcation scenarios-such as perioddoubling to chaos, period-adding bifurcation with chaos, and period-adding bifurcation without chaos in bursting patterns-were reported . If noise was introduced, the period-adding bifurcation without chaos was changed into period-adding bifurcation with stochastic bursting, which was observed in the experiment (Gu et al 2003Yang et al 2009).…”

“…Compared with experimental observations of different bifurcation scenarios in which one parameter was adjusted (Mandelblat et al 2001;Gu et al 2003Li et al 2004;Yang et al 2009;Braun et al 2011;Gu and Pan 2015), there are far fewer bifurcation scenarios that involve adjusting two parameters (Wu et al 2008;Gu et al 2013;Gu 2013a). Of the two bifurcation scenarios from period-1 bursting to period-1 spiking, one manifested a complex process and the other a simple process; these were observed in an identical CCI model as the extracellular calcium concentration ([Ca 2þ o ) decreased and extracellular cesium concentration was fixed at two different levels (Wu et al 2008).…”