Two models for the dynamics of boiling in a short capillary tube.

We investigate the dynamical origin of the statistical properties of boiling in a short capillary tube. Two different models are proposed (Markov model and rotational model). We show that the behavior of each model may be related to different properties of the physical phenomenon.

Generalized synchronization of chaos in noninvertible maps.

The properties of functional relation between a noninvertible chaotic drive and a response map in the regime of generalized synchronization of chaos are studied. It is shown that despite a very fuzzy image of the relation between the current states of the maps, the functional relation becomes apparent when a sufficient interval of driving trajectory is taken into account. This paper develops a theoretical framework of such functional relation and illustrates the main theoretical conclusions using numerical simulations.

Multivalued mappings in generalized chaos synchronization.

The onset of generalized synchronization of chaos in directionally coupled systems corresponds to the formation of a continuous mapping that enables one to persistently define the state of the response system from the trajectory of the drive system. A recently developed theory of generalized synchronization of chaos deals only with the case where this synchronization mapping is a single-valued function. In this paper, we explore generalized synchronization in a regime where the synchronization mapping can become a multivalued function.