Local excitation-lateral inhibition interaction yields oscillatory instabilities in nonlocally interacting systems involving finite propagation delay
نویسنده
چکیده
The work studies wave activity in spatial systems, which exhibit nonlocal spatial interactions at the presence of a finite propagation speed. We find analytically propagation delay-induced oscillatory instabilities for various local excitatory and lateral inhibitory spatial interactions. Further, the work shows for general nonlocal interactions analytically that the first kernel Fourier moment defines the stability thresholds. The final numerical simulation confirms the analytical results. © 2007 Elsevier B.V. All rights reserved. PACS: 02.30.Rz; 66.10.Cb; 02.30.Ks
منابع مشابه
Local excitation-lateral inhibition interaction yields wave instabilities in spatial systems involving finite propagation delay
The work studies wave activity in spatial systems, which exhibit nonlocal spatial interactions at the presence of a finite propagation speed. We find analytically propagation delay-induced wave instabilities for various local excitatory and lateral inhibitory spatial interactions. The final numerical simulation confirms the analytical results.
متن کاملOn the crack propagation modeling of hydraulic fracturing by a hybridized displacement discontinuity/boundary collocation method
Numerical methods such as boundary element and finite element methods are widely used for the stress analysis in solid mechanics. This study presents boundary element method based on the displacement discontinuity formulation to solve general problems of interaction between hydraulic fracturing and discontinuities. The crack tip element and a higher order boundary displacement collocation techn...
متن کاملSpontaneous and evoked activity in extended neural populations with gamma-distributed spatial interactions and transmission delay
The spatiotemporal dynamics of neural activity are studied using an integro-differential model of spatially extended neuronal ensembles. The model includes both synaptic and axonal propagation delay while spatial synaptic connectivities are represented by gamma distributions. This family of connectivity kernels has been observed experimentally and covers the cases of divergent, finite, and negl...
متن کاملFramework for nonlocally related PDE systems and nonlocal symmetries: extension, simplification, and examples
Any PDE system can be effectively analyzed through consideration of its tree of nonlocally related systems. If a given PDE system has n local conservation laws, then each conservation law yields potential equations and a corresponding nonlocally related potential system. Moreover, from these n conservation laws, one can directly construct 2 − 1 independent nonlocally related systems by consider...
متن کاملTheory of delayed lateral inhibition in the compound eye of limulus.
Although the magnitude of lateral inhibition in the retina of Limulus polyphemus depends strongly on the distance between ommatidia, the time of delay tau between the response of one ommatidium and the consequent inhibition of another is independent of the distance between them and is approximately 0.1 sec. Moreover, experimental observations indicate that for intact undamaged retinae in intens...
متن کاملذخیره در منابع من
با ذخیره ی این منبع در منابع من، دسترسی به آن را برای استفاده های بعدی آسان تر کنید
عنوان ژورنال:
دوره شماره
صفحات -
تاریخ انتشار 2007