Periodic bifurcation of Duffing-van der Pol oscillators having fractional derivatives and time delay.

Highlights: [•] The residue harmonic balance is again introduced in bifurcation analysis. [•] The periodic bifurcations are examined using the fractional order, feedback gain and time delay as continuation parameters. [•] All possible steady state solutions are derived analytically without numerical integration. [•] The fractional order, feedback gain and time delay change the bifurcating curves qualitatively. [•] Control strategies are proposed to avoid jumps and hysteresis phenomena using trials and errors. [ABSTRACT FROM AUTHOR]