Chaotic dynamics of fractional Vallis system for El-Nino

TL;DR

This paper explores the chaotic behavior of a fractional version of the Vallis system modeling El-Nino, analyzing bifurcations, chaos, and synchronization, and how fractional order affects system dynamics.

Contribution

It provides a detailed analysis of the fractional Vallis system, including bifurcation, chaos, and synchronization, highlighting the impact of fractional order on system behavior.

Findings

Chaos range decreases with lower fractional order.

Critical fractional value below which chaos is lost.

Synchronization with Bhalekar-Gejji system achieved.

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.