Cellular Automata are simple computational models which can be leveraged to model a wide variety of dynamical systems. Composed of a lattice of discrete cells that take finite number of states based on previous iterations these models differ greatly from dynamic systems that vary continuously in space or time. However given their ability to model many of continuous systems, it could be postulat...

Abstract We generalize the greedy and lazy $\beta $ -transformations for a real base to setting of alternate bases ${\boldsymbol {\beta }}=(\beta _0,\ldots ,\beta _{p-1})$ , which were recently introduced by first second authors as particular case Cantor bases. As in case, these new transformations, denoted $T_{{\boldsymbol }}}$ $L_{{\boldsymbol respectively, can be iterated order generate digi...

We identify a new scenario for dynamical phase transitions associated with time-integrated observables occurring in diffusive systems described by the macroscopic fluctuation theory. It is characterized pairwise meeting of first- and second-order bias-induced transition curves at two tricritical points. formulate simple, general criterion its appearance derive an exact Landau theory behavior. T...

This topical issue collects contributions of recent achievements and scientific progress related to the collective behavior nonlinear dynamical oscillators. The individual papers focus on different questions present-day interest in this topic.

‎In this paper‎, ‎we have investigated the chaotic behavior of thermal convection in couple stress liquid saturated porous layer subject to gravity‎, ‎heated from below and cooled from above‎, ‎based on theory of dynamical system‎. ‎A low dimensional Lorenz‎- ‎like model is obtained by using Galerkin-truncation approximation‎. ‎We found that there is proportional relation between scaled couple ...

In the present article we report the dynamical behavior of entanglement between π-electrons and photons in Graphene. It is shown that the degree of such entanglements depend on the orientation of π-electron momenta relative to the photonic polarization. Moreover, we show that as the detuning between the π-electron transition frequencies and that of the photons is increased, the degree of entang...