Doubly Periodic Traveling Waves in a Cellular Neural Network with Linear Reaction

Doubly Periodic Traveling Waves in a Cellular Neural Network with Linear Reaction

Szekeley observed that the dynamic pattern of the locomotion of salamanders can be explained by periodic vector sequences generated by logical neural networks. Such sequences can mathematically be described by “doubly periodic traveling waves” and therefore it is of interest to propose dynamic models that may produce such waves. One such dynamic network model is built here based on reaction-dif...

Approximate Traveling Waves in Linear Reaction-Hyperbolic Equations

Linear reaction-hyperbolic equations arise in the transport of neurofilaments and membrane-bound organelles in axons. The profile of the solution was shown by simulations to be approximately that of a traveling wave; this was also suggested by formal calculations (Reed et al., 1990). In this paper we prove such a result rigorously1.

Periodic Traveling Water Waves with Isobaric Streamlines

It is shown that in water of finite depth, there are no periodic traveling waves with the property that the pressure in the underlying fluid flow is constant along streamlines. In the case of infinite depth, there is only one such solution, which is due to Gerstner.

Deformation of Traveling Waves in Delayed Cellular Neural Networks

In this paper, we establish the existence and describe the global structure of traveling waves for a class of lattice delay differential equations describing cellular neural networks with distributed delayed signal transmission. We describe the transition of wave profiles from monotonicity, damped oscillation, periodicity, unboundedness and back to monotonicity as the wave speed is varied. We a...

Periodic Traveling Waves in Diatomic Granular Chains