Chaos and hyperchaos in the fractional-order Rössler equations

The dynamics of fractional-order systems have attracted increasing attentions in recent years. In this paper, we numerically study the chaotic behaviors in the fractional-order Rössler equations. We found that chaotic behaviors exist in the fractional-order Rössler equation with orders less than 3, and hyperchaos exists in the fractional-order Rössler hyperchaotic equation with order less than 4. The lowest orders we found for chaos and hyperchaos to exist in such systems are 2.4 and 3.8, respectively. Period doubling routes to chaos in the fractional-order Rössler equation are also found.