Birth of Strange Non-chaotic Attractors in Fractional-Order Systems

In this study, we present the construction of a quasiperiodically driven fractional-order Chua system and investigate its dynamical behavior by varying the fractional order parameters $$q_1$$ and $$q_2$$ using various characterization techniques. Our observations suggest that selecting appropriate combinations of fractional orders allows us to observe bifurcation phenomena for different values of the forcing amplitude. Through the use of Poincaré sections, we visualize the formation of tori and their doubling bifurcation route to strange nonchaotic attractor. Additionally, we employ numerical and statistical tools, such as singular continuous spectra, separation of nearby trajectories, and fast Fourier transform, to verify the occurrence and understand the mechanism behind the birth of strange nonchaotic attractor. We differentiate torus, strange nonchaos, and chaos with the help of 0–1 test and recurrence analysis. Our results provide valuable insights into the dynamical behavior of quasiperiodically driven fractional-order systems, with potential implications for various fields of science and engineering.