Biomedical subjects

Raúl Rechtman

Publications and source records attributed to Raúl Rechtman.

4 recordsLinked to original sources

PubMed2006

Synchronization universality classes and stability of smooth coupled map lattices.

We study two problems related to spatially extended systems: the dynamical stability and the universality classes of the replica synchronization transition. We use a simple model of one-dimensional coupled map lattices and show that chaotic behavior implies that the synchronization transition belongs to the multiplicative noise universality class, while stable chaos implies that the synchronization transition belongs to the directed percolation universality class.

Journal Article↗

PubMed2005

Phase transitions of extended-range probabilistic cellular automata with two absorbing states.

We study phase transitions in a long-range one-dimensional cellular automaton with two symmetric absorbing states. It includes and extends several other models, like the Ising and Domany-Kinzel ones. It is characterized by competing ferromagnetic linear and antiferromagnetic nonlinear couplings. Despite its simplicity, this model exhibits an extremely rich phase diagram. We present numerical results and mean-field approximations.

Journal Article↗

PubMed2004

Complex dynamics in simple systems with periodic parameter oscillations.

We study systems with periodically oscillating parameters that can give way to complex periodic or nonperiodic orbits. Performing the long time limit, we can define ergodic averages such as Lyapunov exponents, where a negative maximal Lyapunov exponent corresponds to a stable periodic orbit. By this, extremely complicated periodic orbits composed of contracting and expanding phases appear in a natural way. Employing the technique of epsilon-uncertain points, we find that values of the control parameters supporting such periodic motion are densely embedded in a set of values for which the motion is chaotic. When a tiny amount of noise is coupled to the system, dynamics with positive and with negative nontrivial Lyapunov exponents are indistinguishable. We discuss two physical systems, an oscillatory flow inside a duct and a dripping faucet with variable water supply, where such a mechanism seems to be responsible for a complicated alternation of laminar and turbulent phases.

Adaptation, Physiological↗

PubMed2003

Noise-induced fluctuations of period lengths of stable periodic orbits.

We discuss a class of one-dimensional maps, which possesses a globally attracting stable periodic orbit. Despite a strongly negative Lyapunov exponent, a small amount of noise can introduce fluctuations of the period length. It is shown that this is a reasonable model for the observed dynamics of a bubble formation experiment in a heated capillary embedded in boiling water.

Journal Article↗