Consistency and predictability of brain functionalities depend on reproducible activity of a single neuron. We identify a reproducible non-chaotic neuronal phase where deviations between concave response latency profiles of a single neuron do not increase with the number of stimulations. A chaotic neuronal phase emerges at a transition to convex latency profiles which diverge exponentially, ind...

In this paper, a novel formulation of discrete chaotic iterations in the field of dynamical systems is given. Their topological properties are studied: it is mathematically proved that, under some conditions, these iterations have a chaotic behavior in the meaning of Devaney. This chaotic behavior allows us to propose a way to generate new hash functions. An illustration example is detailed in ...

At the Crypto 2005 rump session, a new hash function based upon a chaotic map was presented. We display several messages that collide to the same output for this hash function.

We consider the possibility that chaotic inflation is driven by a Minimal Supersymmetric Standard Model (MSSM) flat direction or a sneutrino. The discrepancy between our present study and past studies is in the mechanism for generating the curvature perturbations. We consider curvature perturbations generated by instant preheating at the end of inflation, instead of a conventional curvature per...

We propose a theory of chaos for discrete systems, based on their representation in a space of " binary histories " , B ∞. We show that B ∞ is a metrizable Cantor set which embeds the attractor Λ, itself also a Cantor set.ciation Générale pour la Coopération et le Développement (Belgium).

‎In the following text for arbitrary $X$ with at least two elements‎, ‎nonempty countable set $Gamma$‎ ‎we make a comparative study on the collection of generalized shift dynamical systems like $(X^Gamma,sigma_varphi)$ where $varphi:GammatoGamma$ is an arbitrary self-map‎. ‎We pay attention to sub-systems and combinations of generalized shifts with counterexamples regarding Devaney‎, ‎exact Dev...

How thoughts arise – 'RunBot' goes mountaineering – The emergence of a sense of orientation – Psychological models – The role of single neurons – The brain on the edge of chaos

—The simplest diploid model of frequency-dependent selection can generate periodic and chaotic trajectories for the allele frequency. The model is of a randomly mating, infinite diploid population with non-overlapping generations, segregating for two alleles under frequency-dependent viability selection. The fitnesses of each of the three genotypes is a linear function of the frequencies of the...

In this paper we critically review that (vast) part of the literature on chaos theory and economic dynamics, in which the final dynamic equation of the model reduces to an equation of the logistic type. To this end, we first characterise and classify existing models in terms of the elements which, in each of them, account for the existence of a fixed (one-period) time-lag and of a unimodal nonl...

We study theoretically quantum states of a pair photons interacting with finite periodic array two-level atoms in waveguide. Our calculation reveals two-polariton eigenstates that have highly irregular wave-function real space. This indicates the Bethe ansatz breakdown and onset chaos, stark contrast to conventional integrable problem two bosons box. identify long-range waveguide-mediated coupl...