BCAM Workshop on Dynamical Systems

The goal of this meeting is to facilitate discussion and collaboration on Dynamical Systems in the Basque Country.

Supported by Basque Government 

Date: June 26, 2013 during 10:00-17:00 


Speaker(s): invited: : Mikhail KAMENSKIY, Sergio SANCHO, Gerard VIDAL, Jesús Palación

Center(s): TVoronezh State University, Russia, Universidad de Cantabria, Santander, Spain, Enigmedia, Donostia-San Sebastián, Spain, Universidad Pública de Navarra, Pamplona, Spain 

Program for June 26:

9:30-10:00 Waking up coffee

10:00-10:40 Mikhail KAMENSKIY 
10:40-11:20 Sergio SANCHO

11:20-11:50 Coffee break

11:50-12:30 Gerard VIDAL
12:30-13:10 Jesús Palación
Mikhail Kamenskiy, Voronezh State University, Russia

"Condensing operators and bifurcation problems"

Abstract: Various problems of bifurcation of periodic solutions in differential equations can be analyzed via the theory of condensing maps. The proposed method permits us to consider the cases where there is only integral continuity in the bifurcation parameter and the strong continuity doesn't hold. In this talk I consider a differential equation of neutral type with a delay viewed as a bifurcation parameter. Some results about bifurcations in abstract parabolic equations in Banach spaces will be discussed. A non-smooth situation will be treated as well.

Sergio Sancho, Universidad de Cantabria, Santander, Spain

"Nonlinear analysis of phase-locked loops (PLL): bifurcation and phase noise analysis. Frequency-domain simulation techniques"

Abstract: The phase-locked loops (PLL) at microwave frequencies are used in a number of applications in communication systems, such as the generation of high frequency signals with low phase noise. These are nonlinear systems whose dynamics can be studied in terms of bifurcation loci. Due to the presence of frequency components of different order, the simulation of these systems require the combination of time and frequency domain techniques. Future research lines like the use of delta-sigma modulators for fractional PLL and the nonlinear stochastic analysis of these systems will be introduced.

Gerard VIDAL, Enigmedia, Donostia-San Sebastián, Basque Country, Spain

"Control and Synchronization of a Codimension-2 Dynamical System"

Abstract: We present a co-dimension 2 system which appears in a convective pattern formation experiment. This pattern appears under square symmetry conditions when the control parameter (the temperature) increases. Keep increasing the temperature, the pattern behavoir can be modelleng as an hyperchaotic ODE system.
Studying how to control and synchronize a system like this we have seen several interesting dynamics. 

Finally we propose and application on secure communications using some features of the equation set.

Jesús Palación, Universidad Pública de Navarra, Pamplona, Spain

"Invariant tori in the three body problem"

Abstract: We will deal with the Newtonian three-body problem in the three-dimensionalspace. The goal is to obtain five-dimensional invariant tori around some relativeequilibria of the system. To achieve it we will reduce the initially 18-dimensional
problem using the symmetries and we will also use techniques of perturbation 
theory such as averaging and KAM theory. We will end up with a description
of all possible quasiperiodic motions of the three bodies. 


Organiser: Oleg MAKARENKOV (omakarenkov@bcamath.org) - registration and other enquiries

Venue: BCAM, Mazarredo, 14, 48009 Bilbao, Basque Country - Spain

IMAGES

• Pictures_WS On Dynamical Systems