摘要: Publisher Summary This chapter discusses nonlinear wave phenomena in the brain. Understanding multitude of associated with brain remains one man's greatest scientific and intellectual challenges. Among these are waves, such as nerve impulses, which propagate rapidly down an individual cell axon spreading cortical depression that propagates slowly through a population cells. Nerve impulse propagation has been studied extensively, while only recently modeled mathematically. The various mathematical, numerical, modeling aspects discussed. approach to problems by mathematical modeler is propose representation physical, chemical, or biological system terms some suitable formulation.
sci-hub.se 参考文章(32)
Robert M. Miura, Nonlinear Waves in Neuronal Cortical Structures NATO Advanced Science Institutes (ASI) Series B. ,vol. 75, pp. 369- 400 ,(1981) , 10.1007/978-1-4684-4106-2_10
H.P McKean, Nagumo's equation Advances in Mathematics. ,vol. 4, pp. 209- 223 ,(1970) , 10.1016/0001-8708(70)90023-X
A R Gardner-Medwin, C Nicholson, Changes of extracellular potassium activity induced by electric current through brain tissue in the rat. The Journal of Physiology. ,vol. 335, pp. 375- 392 ,(1983) , 10.1113/JPHYSIOL.1983.SP014540
A. L. Hodgkin, A. F. Huxley, A quantitative description of membrane current and its application to conduction and excitation in nerve The Journal of Physiology. ,vol. 117, pp. 500- 544 ,(1952) , 10.1113/JPHYSIOL.1952.SP004764
R.P. Kraio, C. Nicholson, Extracellular ionic variations during spreading depression Neuroscience. ,vol. 3, pp. 1045- 1059 ,(1978) , 10.1016/0306-4522(78)90122-7
H.C. Tuckwell, R.M. Miura, A mathematical model for spreading cortical depression Biophysical Journal. ,vol. 23, pp. 257- 276 ,(1978) , 10.1016/S0006-3495(78)85447-2
Gail A Carpenter, A geometric approach to singular perturbation problems with applications to nerve impulse equations Journal of Differential Equations. ,vol. 23, pp. 335- 367 ,(1977) , 10.1016/0022-0396(77)90116-4
Richard FitzHugh, Impulses and Physiological States in Theoretical Models of Nerve Membrane Biophysical Journal. ,vol. 1, pp. 445- 466 ,(1961) , 10.1016/S0006-3495(61)86902-6
S. P. HASTINGS, ON THE EXISTENCE OF HOMOCLINIC AND PERIODIC ORBITS FOR THE FITZHUGH-NAGUMO EQUATIONS Quarterly Journal of Mathematics. ,vol. 27, pp. 123- 134 ,(1976) , 10.1093/QMATH/27.1.123
A. N. ZAIKIN, A. M. ZHABOTINSKY, Concentration wave propagation in two-dimensional liquid-phase self-oscillating system. Nature. ,vol. 225, pp. 535- 537 ,(1970) , 10.1038/225535B0