Stability and chaos in the fractional Chen system.

• The fractional Chen system is analyzed. • Stability properties with respect to free entry parameters are described. • A fractional Hopf bifurcation is investigated rigorously. • Other bifurcation phenomena are observed numerically. • The occurrence of a chaotic attractor for low derivative orders is discussed. The paper provides a theoretical analysis of some local bifurcations in the fractional Chen system. Contrary to the integer-order case, basic bifurcation properties of the fractional Chen system are shown to be qualitatively different from those described previously for the fractional Lorenz system. Further, the fractional Hopf bifurcation in the Chen system is expressed rigorously with respect to general entry parameters. Based on these observations, some particularities of the fractional dynamics of the Chen system are documented and its chaotic behavior for low derivative orders is discussed. [ABSTRACT FROM AUTHOR]