Synchronisation arises in dynamical systems that are composed of a number of interconnected subsystems. In the paper synchronization in a particular application a supermarket refrigeration system is studied. The temperature control in supermarket display cases is typically maintained by a number of distributed hysteresis controllers. Synchronization is then manifested by the opening and closing...

In this paper, the Poincaré map function as a one-dimensional first-return map is obtained by approximating the scatter plots of inter-peak interval (IPI) during preictal and postictal periods from invasive EEG recordings of nine patients suffering from medically intractable focal epilepsy. Evolutionary Algorithm (EA) is utilized for parameter estimation of the Poincaré map. Bifurcation analyse...

Geometric study of a second-order Fuchsian differential equation u′′ − q(x)u = 0, where q is rational in x, has been made via the Schwarz map as well as via the hyperbolic and the derived Schwarz maps ([SYY]). When the equation admits an irregular singularity, such a study was first made in [SY] treating the confluent hypergeometric equation and the Airy equation. In this paper, we study the hy...

This chapter deals with the control of chaos exhibited in the behavior of a one-degree-of-freedom impact mechanical oscillator with a single rigid constraint. The mathematical model of such impact oscillator is represented by an impulsive hybrid linear non-autonomous dynamics. The proposed control approach is based chiefly on the OGY method. First, an analytical expression of a constrained cont...

A Fourier transform technique is introduced for counting the number of solutions of holomorphic moment map equations over a finite field. This technique in turn gives information on Betti numbers of holomorphic symplectic quotients. As a consequence, simple unified proofs are obtained for formulas of Poincaré polynomials of toric hyperkähler varieties (recovering results of Bielawski-Dancer and...

We propose approximating a Poincaré map of biped walking dynamics using Gaussian processes. We locally optimize parameters of a given biped walking controller based on the approximated Poincaré map. By using Gaussian processes, we can estimate a probability distribution of a target nonlinear function with a given covariance. Thus, an optimization method can take the uncertainty of approximated ...

A mathematical model for the perturbation of a biological oscillator by single and periodic impulses is analyzed. In response to a single stimulus the phase of the oscillator is changed. If the new phase following a stimulus is plotted against the old phase the resulting curve is called the phase transition curve or PTC (Pavlidis, 1973). There are two qualitatively different types of phase rese...

In [7], a notion of noncommutative tangent space is associated with a conical pseudomanifold and the Poincaré duality in K-theory is proved between this space and the pseudomanifold. The present paper continues this work. We show that an appropriate presentation of the notion of symbols on a manifold generalizes right away to conical pseudomanifolds and that it enables us to interpret the Poinc...

A novel time-domain method for finding the periodic steady-state of a free-running electrical oscillator is introduced. The method is based on the extrapolation technique MPE. The new method is applied to a family of artificial benchmark problems and to a real circuit (Colpitt's Oscillator). It turns out to have super-linearly convergence properties in both cases. Full implementation details ar...