title: Resonant behavior of a fractional oscillator with fluctuating frequency.
abstract: The long-time behavior of the first moment for the output signal of a fractional oscillator with fluctuating frequency subjected to an external periodic force is considered. Colored fluctuations of the oscillator eigenfrequency are modeled as a dichotomous noise. The viscoelastic type friction kernel with memory is assumed as a power-law function of time. Using the Shapiro-Loginov formula, exact expressions for the response to an external periodic field and for the complex susceptibility are presented. On the basis of the exact formulas it is demonstrated that interplay of colored noise and memory can generate a variety of cooperation effects, such as multiresonances versus the driving frequency and the friction coefficient as well as stochastic resonance versus noise parameters. The necessary and sufficient conditions for the cooperation effects are also discussed. Particularly, two different critical memory exponents have been found, which mark dynamical transitions in the behavior of the system.
authors.affiliation: Institute of Mathematics and Natural Sciences, Tallinn University, 10120 Tallinn, Estonia. erkki.soika@tlu.ee
authors.forename: Erkki
authors.initials: E
authors.lastname: Soika
authors.forename: Romi
authors.initials: R
authors.lastname: Mankin
authors.forename: Ain
authors.initials: A
authors.lastname: Ainsaar