Abstract
We propose a fractional-order WINDMI system, as a generalization of an integer-order system developed by Sprott (2003). The considered synchronization scheme consists of identical master and slave fractional-order WINDMI systems coupled by linear state error variables. Based on the stability theory of nonlinear fractional-order systems, linear state error feedback control technique is applied to achieve chaos synchronization, and a linear control law is derived analytically to achieve synchronization of the chaotic fractional-order WINDMI system. Numerical simulations validate the main results of this work.
Highlights
The solar-wind-driven magnetosphere-ionosphere is a complex driven-damped dynamical system which exhibits a variety of dynamical states that include low-level steady plasma convection, episodic releases of geotail stored plasma energy into the ionosphere known broadly as substorms, and states of continuous strong unloading 1
In 1998, Horton and Doxas 2 firstly proposed the WINDMI system, a six-dimensional nonlinear dynamics model, which was derived for the basic energy components of the night-side magnetotail coupled to the ionosphere by the region-1 currents
Smith et al 3 explored the dynamical range of the WINDMI model
Summary
The solar-wind-driven magnetosphere-ionosphere is a complex driven-damped dynamical system which exhibits a variety of dynamical states that include low-level steady plasma convection, episodic releases of geotail stored plasma energy into the ionosphere known broadly as substorms, and states of continuous strong unloading 1. In 1998, Horton and Doxas 2 firstly proposed the WINDMI system, a six-dimensional nonlinear dynamics model, which was derived for the basic energy components of the night-side magnetotail coupled to the ionosphere by the region-1 currents. Horton et al 1 introduced reductions to derive a new minimal three-dimensional WINDMI model. Fractional calculus, a generalization of differentiation and integration to an arbitrary order, is an old mathematical topic with over 300-year-old history 5. Synchronization of fractional-order chaotic systems was first presented by Deng and Li 17. As an active research area, chaos synchronization with fractional calculus has received increasing attention in recent years due to its potentials in both theory and applications 18–25.
Sign-in/Register to view highlights & summary Sign-in/Register to access full text options 
Free) 
Talk to us
Join us for a 30 min session where you can share your feedback and ask us any queries you have
Schedule a call
