Long-time behavior of solutions and chaos in reaction-diffusion equations
Document Type
Article
Publication Date
6-1-2017
Abstract
It is shown that members of a class (of current interest with many applications) of non-dissipative reaction-diffusion partial differential equations with local nonlinearity can have an infinite number of different unstable solutions traveling along an axis of the space variable with varying speeds, traveling impulses and also an infinite number of different states of spatio-temporal (diffusion) chaos. These solutions are generated by cascades of bifurcations governed by the corresponding steady states. The behavior of these solutions is analyzed in detail and, as an example, it is explained how space-time chaos can arise. Results of the same type are also obtained in the case of a nonlocal nonlinearity.
Identifier
85016795266 (Scopus)
Publication Title
Chaos Solitons and Fractals
External Full Text Location
https://doi.org/10.1016/j.chaos.2017.03.057
ISSN
09600779
First Page
91
Last Page
100
Volume
99
Recommended Citation
Soltanov, Kamal N.; Prykarpatski, Anatolij K.; and Blackmore, Denis, "Long-time behavior of solutions and chaos in reaction-diffusion equations" (2017). Faculty Publications. 9545.
https://digitalcommons.njit.edu/fac_pubs/9545
