Title :
A set of travelling fronts of excitation in the model of homogeneous neuro-like medium with nonlocal coupling
Author :
Pelinovsky, D. ; Yakhno, V.
Author_Institution :
Dept. of Radiophys. Methods in Med., Acad. of Sci., Nizhny Novorod, Russia
Abstract :
The influence of arbitrary nonlocal coupling on the existence and properties of autowave processes in a bistable medium is investigated. Approximation of the individual activity function F(x) by a Heaviside unit function allows one to obtain some analytical results. The calculations clearly testify to the relation between the instability of the plane front of excitation, observed by A.V. Masterov et al. (1988), and nonlocal inhibition of the space-coupling function; they provide mathematical means for determining the characteristic scale of structures emerging in the process of front deterioration. If an ordinary traveling front is unsteady in a two-dimensional medium, the whole set of fronts under study is unsteady. Therefore, a quasi-independent description of wave processes in the longitudinal and transverse directions is possible for a neuro-like medium
Keywords :
neural nets; stability; wave equations; wave propagation; Heaviside unit function; activity function; autowave processes; bistable medium; characteristic scale; front deterioration; homogeneous neuro-like medium; nonlocal coupling; quasi-independent description; space coupling function inhibition; travelling excitation fronts; two-dimensional medium; unsteady fronts; Artificial neural networks; Biological system modeling; Biology; Boundary conditions; Cells (biology); Differential equations; Integral equations; Nonlinear dynamical systems; Partial differential equations; Physics;
Conference_Titel :
Neuroinformatics and Neurocomputers, 1992., RNNS/IEEE Symposium on
Conference_Location :
Rostov-on-Don
Print_ISBN :
0-7803-0809-3
DOI :
10.1109/RNNS.1992.268632
