A method is known by which any integer n ≥ 2 in a metric Cantor space of right-infinite words ÃN n gives a construction of a non-injective cellular automaton (ÃN n , F̃n), which is chaotic in Devaney sense, has a radius r = 1, continuum of fixed points and topological entropy log(n). As a generalization of this method we present for any integer n ≥ 2, a construction of a cellular automaton (AN n...

In this third of a series of four articles, we continue the study of the representations of the dynamical transformations of systems of correlated quantized oscillators. By including generalized wave function solutions to Schrödinger’s equation (belonging to a rigged Hilbert space), and by considering the algebra of observables as a whole, the presence of Devaney chaos, hyperbolic quasi-invaria...

We study two dynamical properties of linear D-dimensional cellular automata over Zm namely, denseness of periodic points and topological mixing. For what concerns denseness of periodic points, we complete the work initiated in (Theoret. Comput. Sci. 174 (1997) 157, Theoret. Comput. Sci. 233 (1–2) (2000) 147, 14th Annual Symp. on Theoretical Aspects of Computer Science (STACS ’97), LNCS n. 1200,...

A recently developed inverse scattering algorithm [A. J. Devaney and M. Dennison, Inverse Probl., 19, 855 (2003) and M. Dennison and A. J. Devaney, Inverse Probl., 20, 1307 (2004)] is described and applied in a computer simulation study of optical diffraction tomography (ODT). The new algorithm is superior to standard ODT reconstruction algorithms, such as the filtered backpropagation algorithm...

We present in this note an alternative yet simple approach to obtain the Devaney-Nitecki horseshoe region for the Hénon maps. Our approach is based on the anti-integrable limit and the implicit function theorem. We also highlight an application to the logistic maps.

In this paper, we explain why the chaotic model (CM) of Bahi and Michel (2008) accurately simulates gene mutations over time. First, we demonstrate that the CM model is a truly chaotic one, as defined by Devaney. Then, we show that mutations occurring in gene mutations have the same chaotic dynamic, thus making the use of chaotic models relevant for genome evolution.

Citation Merabet, Lotfi B., Kathryn J. Devaney, Corinna M. Bauer, Aparna Panja, Gena Heidary, and David C. Somers. 2016. “Characterizing Visual Field Deficits in Cerebral/Cortical Visual Impairment (CVI) Using Combined Diffusion Based Imaging and Functional Retinotopic Mapping: A Case Study.” Frontiers in Systems Neuroscience 10 (1): 13. doi:10.3389/fnsys.2016.00013. http://dx.doi.org/10.3389/f...

In this paper, we give a family of dynamical systems on the Cantor dust (C C) by using elements 4th Dihedral group with shift map and then express them via code representations points C x C. Moreover, prove that these are chaotic in sense Devaney also investigate topological equivalence systems.

Chaotic neural networks have received a great deal of attention these last years. In this paper we establish a precise correspondence between the so-called chaotic iterations and a particular class of artificial neural networks: global recurrent multi-layer perceptrons. We show formally that it is possible to make these iterations behave chaotically, as defined by Devaney, and thus we obtain th...

We use a combinatorial idea of Peter Lax to construct, on any compact manifold, a self homeomorphism which is chaotic in the sense of Devaney. Moreover we show that such transformations are dense, with respect to the uniform topology, in the space of volume preserving homeomorphisms of the closed unit cube I n ; n 2: This work extends that of John Oxtoby, who in 1937 proved similar results for ...