AB S TRACT We comment on the recent results of a temporal analysis of R Scuti, a star of RV Tauri type, presented by Buchler et al. As an alternative approach, we apply the technique of linear state space analysis to describe the irregular temporal behaviour with a linear stochastic process.We find evidence that the variability of R Scuti can be explained by the superposition of two stochastica...

We establish the results on existence and exponent stability of solutions for a semilinear nonautonomous neutral stochastic evolution equation with finite delay; the linear part of this equation is dependent on time and generates a linear evolution system. The obtained results are applied to some neutral stochastic partial differential equations. These kinds of equations arise in systems relate...

State models of dynamical systems can be used as prototypes in practical realization of electronic chaotic oscillators. Experimental verification shows namely eigenvalue sensitivities of these prototypes are very important for such a purpose. In the paper the optimization design procedure for the second-order linear and piecewise-linear (PWL) autonomous dynamical systems is suggested. This give...

The BN -type Calogero-Sutherland-Moser system in one-dimension is shown to be equivalent to a set of decoupled oscillators by a similarity transformation. This result is used to show the connection of the AN and BN type models and explain the degeneracy structure of the later. We identify the commuting constants of motion and the generators of a linear W∞ algebra associated with the BN system. ...

We investigate the existence and multiplicity of nontrivial periodic bouncing solutions for linear and asymptotically linear impact oscillators by applying a generalized version of the Poincaré–Birkhoff theorem to an adequate Poincaré section called the successor map. The main theorem includes a generalization of a related result by Bonheure and Fabry and provides a sufficient condition for the...

This paper presents a review of phase locked loop (PLL) techniques. The different types of phase detector, loop filter and oscillators are discussed. It alleviates the problems associated with the classical analog PLL. Linear PLL, Digital PLL and All digital PLL models are implemented in Simulink Simulation results in Simulink gives the performance overview of the three types of PLL. Keywords— ...

In linear system theory, it is a well-known fact that regulator given by the cascade of an oscillatory dynamics, driven some regulated variables, and stabiliser stabilising plant oscillators has ability blocking on steady state variables any harmonics matched with ones oscillators. This well-celebrated internal model principle. this paper, we are interested to follow same design route for contr...

We study the existence and stability of phase-locked patterns and amplitude death states in a closed chain of delay coupled identical limit cycle oscillators that are near a supercritical Hopf bifurcation. The coupling is limited to nearest neighbors and is linear. We analyze a model set of discrete dynamical equations using the method of plane waves. The resultant dispersion relation, which is...

Some neurons in the entorhinal cortex (EC) fire bursts when the animal occupies locations organized in a hexagonal grid pattern in their spatial environment. Place cells have also been observed, firing bursts only when the animal occupies a particular region of the environment. Both of these types of cells exhibit theta-cycle modulation, firing bursts in the 4-12 Hz range. Grid cells fire burst...