We study dynamics of two coupled periodically driven oscillators. The internal motion is separated off exactly to yield a nonlinear fourth-order equation describing inner dynamics. Periodic steady-state solutions of the fourth-order equation are determined within the Krylov-BogoliubovMitropolsky approach -we compute the amplitude profiles, which from mathematical point of view are algebraic curves.In the present paper we investigate metamorphoses of amplitude profiles induced by changes of control parameters near singular points of these curves. It follows that dynamics changes qualitatively in the neighbourhood of a singular point.
Dynamics of two coupled periodically driven oscillators is analyzed via approximate effective equation of motion. The internal motion is separated off exactly and then approximate equation of motion is derived. Perturbation analysis of the effective equation is used to study the dynamics of the initial dynamical system.
We reemphasize that the ratio R sµ ≡B(B s → µμ)/∆M s is a measure of the tension of the Standard Model (SM) with the latest measurements ofB(B s → µμ) that does not suffer from the persistent puzzle on the |V cb | determinations from inclusive versus exclusive b → c ν decays and which affects the value of the CKM element |V ts | that is crucial for the SM predictions of bothB(B s → µμ) and ∆M s , but cancels out in the ratio R sµ . In our analysis, we include higher-order electroweak and QED corrections and adapt the latest hadronic input to find a tension of about 2σ for R sµ measurements with the SM independently of |V ts |. We also discuss the ratio R dµ which could turn out, in particular in correlation with R sµ , to be useful for the search for new physics, when data on both ratios improve. R dµ is also independent of |V cb | or more precisely |V td |.
In this paper we investigate the dependence structure for Ornstein-Uhlenbeck process with tempered stable distribution that is natural extension of the classical Ornstein-Uhlenbeck process with Gaussian and α-stable behavior. However, for the α-stable models the correlation is not defined, therefore in order to compare the structure of dependence for Ornstein-Uhlenbeck process with tempered stable and α-stable distribution, we need another measures of dependence defined for infinitely divisible processes such as Lévy correlation cascade or codifference. We show that for analyzed tempered stable process the rate of decay of the Lévy correlation cascade is different than in the stable case, while the codifference of the α-stable Ornstein-Uhlenbeck process has the same asymptotic behavior as in tempered stable case. As motivation of our study we calibrate the Ornstein-Uhlenbeck process with tempered stable distribution to real financial data.
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