An introduction and guidance for neurodynamics

Abstract

Diseases associated with nervous system have brought much pain and anxiety for patients. As a result, clinical diagnosis such as big data analysis based on functional magnetic resonance imaging (fMRI) [1], computational neurodynamics, and cognitive neurodynamics have been paid much attention. It is believed that potential mechanism for abnormality [2] in nervous system could be discerned by detecting dynamic behavior of central nervous system and discovering general theories of cognitive functions in terms of theoretical biophysics. The brain is a high-dimensional nonlinear system and its collective electrical activities are dependent on signal propagation among one hundred billion neurons and also a variety of gliocytes. Cognitive neurodynamics is considered capable of information processing in the nervous system. Theoretical models have been set up at different levels ranging from microcosmic, mesoscopic, up to macroscopic scale, so that the generation of cognition and potential mechanisms underlying neural information processing could be discerned. Indeed, the deterministic neuronal models could be available for bifurcation analysis, synchronization transition between neurons and networks, networks of networks, and information encoding. Furthermore, some reliable neuronal circuits could be implemented for signal detection as sensors. Some biological experiments and also theoretical neuronal models have shown that single neuron exhibits rich dynamical behaviors such as periodic spiking, periodic bursting, chaotic spiking, and chaotic bursting [3]. In fact, the electrical activities in neuron are very complex, for example, one or more bifurcation parameters are carefully adjusted to produce multiple modes of electrical activities while other suggested the present neuronal model should be improved to include more bifurcation parameters and variables. It is believed that when neuronal systems function abnormally, neurons could fire abnormal spikes. Hence, various control schemes have been presented to recover normal neuronal functions. The delay in the neural system is derived from the finite speed of action potentials propagating along s neuron axons, but it is also associated with finite response period to external forcing or internal signal processing. As a result, the inevitable time delay plays an important role in regulating the electrical activities of neurons and self-organization in networks as well [4, 5]. Neurons are basic structures and functional units of the nervous system, and dynamic changes of neuronal discharge rhythm are critical to understanding functions of the nervous system [6, 7]. For example, experimental results from branching and chaoticity of neural discharge induced by potassium are typical examples and provide additional parameters such as calcium current as well [3]. These findings are important to understand potassium-induced dynamics. Synaptic connections also play an important role in transmitting information among neurons. Synapses are generally divided into electric and chemical synapses to display that they are electrically or chemically activated. It is also base of these Synapses action. It is found that there is a special type of synapse among certain intermediate neurons and it reconnects to cell bodies or axons through certain bypass circuits and forms self-synaptic structures as autapse. In oscillator model based on the electrical activity of neurons [8], the regulation of self-synaptic structures on J. Ma Department of Physics, Lanzhou University of Technology, Lanzhou 730050, China