Chaotic dynamics of fractional Vallis system for El-Nino
Abstract
Vallis proposed a simple model for El-Nino weather phenomenon (referred as Vallis system) by adding an additional parameter p to the Lorenz system. He showed that the chaotic behavior of the Vallis system is related to the El-Nino effect. In the present article we study fractional version of Vallis system in depth. We investigate bifurcations and chaos present in the fractional Vallis system along with the effect of variation of system parameter p. It is observed that the range of values of parameter p for which the Vallis system is chaotic, reduces with the reduction of the fractional order. Further we analyze the incommensurate fractional Vallis system and find the critical value below which the system loses chaos. We also synchronize Vallis system with Bhalekar-Gejji system.
Keywords
Cite
@article{arxiv.1808.08075,
title = {Chaotic dynamics of fractional Vallis system for El-Nino},
author = {Amey S. Deshpande and Varsha Daftardar-Gejji},
journal= {arXiv preprint arXiv:1808.08075},
year = {2018}
}