Complex Systems and Theoretical Biology Group (CoSTBiG), Laboratory of Research on Advanced Materials and Nonlinear Science (LaRAMaNS), Department of Physics, Faculty of Science, University of Buea, P.O. Box 63, Buea, Cameroon.
Phys Rev E. 2018 Jan;97(1-1):012211. doi: 10.1103/PhysRevE.97.012211.
Unlike the Hodgkin-Huxley picture in which the nerve impulse results from ion exchanges across the cell membrane through ion-gate channels, in the so-called soliton model the impulse is seen as an electromechanical process related to thermodynamical phenomena accompanying the generation of the action potential. In this work, account is taken of the effects of damping on the nerve impulse propagation, within the framework of the soliton model. Applying the reductive perturbation expansion on the resulting KdV-Burgers equation, a damped nonlinear Schrödinger equation is derived and shown to admit breathing-type solitary wave solutions. Under specific constraints, these breathing pulse solitons become self-trapped structures in which the damping is balanced by nonlinearity such that the pulse amplitude remains unchanged even in the presence of damping.
与 Hodgkin-Huxley 图像不同，在该图像中，神经冲动是通过细胞膜上的离子门通道进行离子交换产生的，而在所谓的孤子模型中，冲动被视为与伴随动作电位产生的热力学现象有关的机电过程。在这项工作中，考虑了阻尼对孤子模型中神经冲动传播的影响。在得到的 KdV-Burgers 方程的基础上应用约化摄动展开，得到了一个阻尼非线性薛定谔方程，并证明它存在呼吸型孤波解。在特定约束下，这些呼吸脉冲孤子成为自陷结构，其中阻尼由非线性平衡，使得即使存在阻尼，脉冲幅度也保持不变。
