On camel-like traveling wave solutions in cellular neural networks

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This paper is concerned with the existence of camel-like traveling wave solutions of cellular neural networks distributed in the one-dimensional integer lattice Z1. The dynamics of each given cell depends on itself and its nearest m left neighbor cells with instantaneous feedback. The profile equation of the infinite system of ordinary differential equations can be written as a functional differential equation in delayed type. Under appropriate assumptions, we can directly figure out the solution formula with many parameters. When the wave speed is negative and close to zero, we prove the existence of camel-like traveling waves for certain parameters. In addition, we also provide some numerical results for more general output functions and find out oscillating traveling waves numerically.

Original languageEnglish
Pages (from-to)481-514
Number of pages34
JournalJournal of Differential Equations
Issue number2
StatePublished - 20 Jan 2004


  • Camel-like traveling waves
  • Cellular neural networks
  • Lattice dynamical systems
  • Oscillating traveling waves


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