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The predictor-corrector methods P(EC)k with equidistant discretization are applied to the nu- merical integration of a linear stochastic oscillator. Their ability in preserving the symplecticity, the...
Abstract: The Binet-Fibonacci formula for Fibonacci numbers is treated as a q-number (and q-operator) with Golden ratio bases $q=\phi$ and $Q=-1/\phi$. Quantum harmonic oscillator for this Golden calc...
Abstract: The classical model of q-damped oscillator is introduced and solved in terms of Jackson q-exponential function for three different cases, under-damped, over-damped and the critical one. It i...
We compare the Gram-Schmidt and covariant phase-space-basis-vector descriptions for three time-reversible harmonic oscillator problems, in two, three, and four phase-space dimensions re- spectively....
We study two-parameter oscillator variations of the classical theorem on har-monic polynomials, associated with noncanonical oscillator representations of sl(n, F) and o(n, F).
In memory of Marcos Moshinsky, who promoted the algebraic study of the har-monic oscillator, some results recently obtained on an infinite family of deformations of such a system are reviewed.
We generalize our recent explicit construction of the full hierarchy of Baxter Q-operators of compact spin chains with su(n) symmetry to the supersymmetric case su(n|m). The method is based on novel...
We study chaotic behavior of order parameters in two coupled ensembles of selfsustained oscillators. Coupling within each of these ensembles is switched on and off alternately, while the mutual intera...
We give the solution of certain parabolic evolution problems (time-depending perturbations of the heat equation for the harmonic oscillator ) as explicit integrals on a space of continuous functions, ...
Starting with an initial random network of oscillators with a heterogeneous frequency distribution, its autonomous synchronization ability can be largely improved by appropriately rewiring the links b...
We study a network of three populations of coupled phase oscillators with identical frequencies. The populations interact nonlocally, in the sense that all oscillators are coupled to one another, but ...
We discuss the exact discretization of the classical harmonic oscillator equation (including the inhomogeneous case and multidimensional generalizations) with a special stress on the energy integral. ...
Starting from a solution of the problem of a mechanical oscillator coupled to a scalar field inside a reflecting sphere of radius $R$, we study the behaviour of the system in free space as the limit ...

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