Long-range patterns in Hindmarsh–Rose networks
| Autor: | Alidou Mohamadou, Conrad Bertrand Tabi, Armand Sylvin Etémé |
|---|---|
| Rok vydání: | 2017 |
| Předmět: |
Physics
Numerical Analysis Artificial neural network Applied Mathematics Plane wave Chaotic 01 natural sciences Instability 010305 fluids & plasmas Whole systems Nonlinear system Modulational instability Control theory Modeling and Simulation 0103 physical sciences Statistical physics 010306 general physics |
| Zdroj: | Communications in Nonlinear Science and Numerical Simulation. 43:211-219 |
| ISSN: | 1007-5704 |
| DOI: | 10.1016/j.cnsns.2016.07.005 |
| Popis: | Long-range diffusive effects are included in a discrete Hindmarsh–Rose neural network. Their impact on the emergence of nonlinear patterns is investigated via the modulational instability. The whole system is first shown to fully reduce to a single nonlinear differential-difference equation, which has plane wave solutions. The stability of such solutions is investigated and regions of instability are found to be importantly influenced by long-range parameters. The analytical results are confirmed through direct numerical simulations, where scattered and chaotic patterns illustrate the long-range effect. Synchronized states are described by quasi-periodic patterns for nearest-neighbor coupling. The external stimulus is also shown to efficiently control strong long-range effects via more regular spatiotemporal patterns. |
| Databáze: | OpenAIRE |
| Externí odkaz: |
|
Full Text from ScienceDirect