Fractional-order Oscillator Research Articles

Master–slave synchronization of coupled fractional-order chaotic oscillators

The dynamics of fractional-order systems have attracted increasing attentions in recent years. In this paper, we study the synchronization technique based on the master?slave synchronization scheme and apply it to the synchronization of two coupled nonlinear fractional-order electronic chaotic oscillators. Simulations show that two coupled fractional-order chaotic oscillators can be brought to an exact synchronization with appropriate coupling strength. It is interesting that the synchronization rate of the fractional-order chaotic oscillators is slower than its integer-order counterpart; however, with the increase of system order, the curves of synchronization error can be smoothened, which indicates that the master?slave synchronization of two coupled fractional order oscillators can be smoothened and stabilized.

Chaos and chaotic control in a fractional-order electronic oscillator

In this paper, we study the chaotic behaviours in a fractional-order chaotic electronic oscillator. We find that chaos exists in the fractional-order electronic oscillator with an order being less than 3. In addition, we numerically simulate the continuance of the chaotic behaviours in the electronic oscillator with orders ranging from 2.8 to 3.2. Finally, we further investigate the method of controlling a fractional-order electronic oscillator based on adaptive backstepping. Numerical simulations show the effectiveness and feasibility of this approach.