Search results for " Dynamical systems"
showing 10 items of 165 documents
Normal forms of hyperbolic logarithmic transseries
2021
We find the normal forms of hyperbolic logarithmic transseries with respect to parabolic logarithmic normalizing changes of variables. We provide a necessary and sufficient condition on such transseries for the normal form to be linear. The normalizing transformations are obtained via fixed point theorems, and are given algorithmically, as limits of Picard sequences in appropriate topologies.
A Hardware and Secure Pseudorandom Generator for Constrained Devices
2018
Hardware security for an Internet of Things or cyber physical system drives the need for ubiquitous cryptography to different sensing infrastructures in these fields. In particular, generating strong cryptographic keys on such resource-constrained device depends on a lightweight and cryptographically secure random number generator. In this research work, we have introduced a new hardware chaos-based pseudorandom number generator, which is mainly based on the deletion of an Hamilton cycle within the $N$ -cube (or on the vectorial negation), plus one single permutation. We have rigorously proven the chaotic behavior and cryptographically secure property of the whole proposal: the mid-term eff…
Attractors/Basin of Attraction
2020
It is a controversial issue to decide who first coined the term “attractor”. According to Peter Tsatsanis, the editor of the English version of Prédire n’est pas expliquer, it was René Thom who first introduced such a term. It is necessary, however, to remember that Thom thought that it was first introduced by the American mathe- matician Steven Smale, “although Smale says it was Thom that coined the neolo- gism “attractor”“(Tsatsanis 2010: 63–64 n. 20). From this point of view, Bob Williams expressed a more cautious opinion by saying that “the word “attractor” was invented by these guys, Thom and Smale” (Cucker and Wong 2000: 183). But other mathematicians are of the opinion that the term …
Host–virus evolutionary dynamics with specialist and generalist infection strategies: Bifurcations, bistability, and chaos
2019
In this work, we have investigated the evolutionary dynamics of a generalist pathogen, e.g., a virus population, that evolves toward specialization in an environment with multiple host types. We have particularly explored under which conditions generalist viral strains may rise in frequency and coexist with specialist strains or even dominate the population. By means of a nonlinear mathematical model and bifurcation analysis, we have determined the theoretical conditions for stability of nine identified equilibria and provided biological interpretation in terms of the infection rates for the viral specialist and generalist strains. By means of a stability diagram, we identified stable fixed…
Overlapping self-affine sets of Kakeya type
2009
We compute the Minkowski dimension for a family of self-affine sets on the plane. Our result holds for every (rather than generic) set in the class. Moreover, we exhibit explicit open subsets of this class where we allow overlapping, and do not impose any conditions on the norms of the linear maps. The family under consideration was inspired by the theory of Kakeya sets.
Separation conditions on controlled Moran constructions
2017
It is well known that the open set condition and the positivity of the $t$-dimensional Hausdorff measure are equivalent on self-similar sets, where $t$ is the zero of the topological pressure. We prove an analogous result for a class of Moran constructions and we study different kinds of Moran constructions with this respect.
On James Hyde's example of non-orderable subgroup of $\mathrm{Homeo}(D,\partial D)$
2020
In [Ann. Math. 190 (2019), 657-661], James Hyde presented the first example of non-left-orderable, finitely generated subgroup of $\mathrm{Homeo}(D,\partial D)$, the group of homeomorphisms of the disk fixing the boundary. This implies that the group $\mathrm{Homeo}(D,\partial D)$ itself is not left-orderable. We revisit the construction, and present a slightly different proof of purely dynamical flavor, avoiding direct references to properties of left-orders. Our approach allows to solve the analogue problem for actions on the circle.
Language in Complexity. The Emerging Meaning
2017
This contributed volume explores the achievements gained and the remaining puzzling questions by applying dynamical systems theory to the linguistic inquiry. In particular the book is divided into three parts, each one addressing of the following topics: a) Facing complexity in the right way: mathematics and complexity; b) Complexity and theory of language; c) From empirical observation to formal models: investigations of specifici linguistic phenomena, like enunciation, deixis, or the meaning of the metaphorical phrases.
Statistical geometric affinity in human brain electric activity
2007
10 pages, 9 figures.-- PACS nrs.: 87.19.La; 05.45.Tp.-- ISI Article Identifier: 000246890100105
A short survey on nonlinear models of the classic Costas loop: rigorous derivation and limitations of the classic analysis
2015
Rigorous nonlinear analysis of the physical model of Costas loop --- a classic phase-locked loop (PLL) based circuit for carrier recovery, is a challenging task. Thus for its analysis, simplified mathematical models and numerical simulation are widely used. In this work a short survey on nonlinear models of the BPSK Costas loop, used for pre-design and post-design analysis, is presented. Their rigorous derivation and limitations of classic analysis are discussed. It is shown that the use of simplified mathematical models, and the application of non rigorous methods of analysis (e.g., simulation and linearization) may lead to wrong conclusions concerning the performance of the Costas loop ph…