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.
|Number of pages
|Communications in Nonlinear Science and Numerical Simulation
|Published - Feb 1 2017
All Science Journal Classification (ASJC) codes
- Numerical Analysis
- Modelling and Simulation
- Applied Mathematics