Gaussian processes (GPs) are used widely in the analysis of astronomical time series. GPs with rational spectral densities have state-space representations which allow O(n) evaluation likelihood. We calculate analytic state space for damped simple harmonic oscillator and Mat\'ern 1/2, 3/2 5/2 processes.

We study a problem of energy exchange in a system of two coupled oscillators subject to 1 : 1 resonance. Our results exploit the concept of limiting phase trajectories LPTs . The LPT, associated with full energy transfer, is, in certain sense, an alternative to nonlinear normal modes characterized by conservation of energy. We consider two benchmark examples. As a first example, we construct an...

We consider decay of metastable states of forced vibrations of a quantum oscillator close to the bifurcation points where the states disappear. Decay occurs via quantum activation over a quasienergy barrier, a mechanism that differs from both tunneling and thermal activation. The decay probability W scales with the distance eta to the bifurcation point as /ln W/ proportional to eta(xi). The exp...

Conformal symplecticity is generalized to forced-damped multi-symplectic PDEs in 1+1 dimensions. Since a conformal multi-symplectic property has a concise form for these equations, numerical algorithms that preserve this property, from a modified equations point of view, are available. In effect, the modified equations for standard multi-symplectic methods and for space-time splitting methods s...

Harmonic Balance is one of the most popular methods for computing periodic solutions nonlinear dynamical systems. In this work, we address two its major shortcomings: First, investigate to what extent computational burden stability analysis can be reduced by consistent use Chebyshev polynomials. Second, problem a rigorous error bound, which, authors' knowledge, has been ignored in all engineeri...

[1] Laboratory measurements reveal the flow structure within and above a model seagrass meadow (dynamically similar to Zostera marina) forced by progressive waves. Despite being driven by purely oscillatory flow, a mean current in the direction of wave propagation is generated within the meadow. This mean current is forced by a nonzero wave stress, similar to the streaming observed in wave boun...

An oscillatory network of columnar architecture located in 3D spatial lattice was recently designed by the authors as oscillatory model of the brain visual cortex. Single network oscillator is a relaxational neural oscillator with internal dynamics tunable by visual image characteristics - local brightness and elementary bar orientation. It is able to demonstrate either activity state (stable u...

A novel synchronization behavior, nonlocal chaotic phase synchronization, is investigated. For two coupled Rossler oscillators with only one forced by an injected periodic signal, the phase of the unforced oscillator can be locked to the phase of the periodic signal while the forced one is well unlocked by the signal; in a chain of coupled chaotic oscillators with nearest coupling, the phase of...

We study the canonical quantization of the damped harmonic oscillator by resorting to the realization of the q-deformation of the Wheyl-Heisenberg algebra (q-WH) in terms of finite difference operators. We relate the damped oscillator hamiltonian to the q-WH algebra and to the squeezing generator of coherent states theory. We also show that the q-WH algebra is the natural candidate to study the...