The pioneering work of Hodgkin and Huxley (1952), and subsequent investigations, has established that good mathematical models for the conduction of nerve impulses along an axon can be given. These models take the form of a system of ordinary differential equations, coupled to a diffusion equation. Simpler models, which seem to describe the qualitative behavior, have been proposed by FitzHugh a...

It is known that stimulus-evoked synchronization among neurons occurs in widely separated cortical regions. In this paper we test that how common, random but not deterministic inputs can synchronize groups of neurons with their parameters inside physiologically plausible regions. When a common, random input is presented, we .nd that a group of neurons—of integrate-and-.re or Hodgkin–Huxley mode...

where t is a large real parameter. For enlightening accounts on this topic, the reader is referred to E. Krätzel’s monographs [14] and [15], to a recent survey article by A. Ivić, E. Krätzel, M. Kühleitner, and W.G. Nowak [10], and to M. Huxley’s book [7] where he exposed his breakthrough in the planar case (”Discrete Hardy-Littlewood method”). For the case that ∂B is of bounded nonzero Gaussia...

where the summation runs over primes, a is a fixed non-zero integer and r(n) is the number of representations of n as a sum of two squares. This implies the first unconditional proof that there are infinitely many primes of the form p = m+n+1. Huxley and Iwaniec [1] considered primes of the formm+n+1 with (m,n) = 1 in the short interval (x, x+x]. They proved that for θ = 99/100 this interval co...

The list of success stories of the use of mathematics and mathematical simulation in physics, chemistry and engineering is endless. In the biological sciences the situation is different. The training of students in biology or medicine traditionally puts little emphasis on mathematics and physics, and skepticism towards any benefits of mathematics in describing living systems prevails in the bio...

The field of structural biology lost a giant on July 25, 2013, when Hugh E. Huxley passed away at age 89. At the time of his death, he was professor emeritus of biology at Brandeis University. But for much of his career, he was at the Medical Research Council (MRC) Laboratory of Molecular Biology (LMB) in Cambridge, United Kingdom. Huxley joined the American Society for Cell Biology in 1982. In...

Numerical solution of the generalized Burger?s-Huxley equation is established utilizing two effective meshless methods namely: local differential quadrature method and global line. Both proposed used radial basis functions to discretize space derivatives which convert given model system ODE then we have utilized Euler get required numerical solution. experiments are carried out check efficiency...