Related papers: Computational information for the logistic map at …
We summarize various cases where chaotic orbits can be described analytically. First we consider the case of a magnetic bottle where we have non-resonant and resonant ordered and chaotic orbits. In the sequence we consider the hyperbolic…
We study the computational problem of rigorously describing the asymptotic behaviour of topological dynamical systems up to a finite but arbitrarily small pre-specified error. More precisely, we consider the limit set of a typical orbit,…
We consider an infinite-range interacting quantum spin-1/2 model, undergoing periodic kicking and dissipatively coupled with an environment. In the thermodynamic limit, it is described by classical mean-field equations that can show regular…
We uncover and characterize different chaotic transport scenarios on perfect periodic surfaces by controlling the chaotic dynamics of particles subjected to periodic external forces in the absence of a ratchet effect. After identifying…
Automatic differentiation provides an efficient means of computing derivatives of complex functions with machine precision, thereby enabling differentiable simulation. In this work, we propose the use of the norm of the tangent map,…
This paper investigates the use of dynamical chaotic systems to encrypt and exchange images between different devices. Two devices were used to simulate the Cubic Map, having the same set of initial conditions, to generate an encryption…
We study a random logistic map $x_{t+1} = a_{t} x_{t}[1-x_{t}]$ where $a_t$ are bounded ($q_1 \leq a_t \leq q_2$), random variables independently drawn from a distribution. $x_t$ does not show any regular behaviour in time. We find that…
Motivated by the famous ink-drop experiment, where ink droplets are used to determine the chaoticity of a fluid, we propose an experimentally implementable method for measuring the scrambling capacity of quantum processes. Here, a system of…
Chaos is popularly associated with its property of sensitivity to initial conditions. In this paper we will show that there can be a flip side to this property which is quite fascinating and highly useful in many applications. As a result,…
The hallmark of deterministic chaos is that it creates information---the rate being given by the Kolmogorov-Sinai metric entropy. Since its introduction half a century ago, the metric entropy has been used as a unitary quantity to measure a…
Out-of-time-ordered correlators (OTOCs) have been extensively used over the last few years to study information scrambling and quantum chaos in many-body systems. In this paper, we extend the formalism of the averaged bipartite OTOC of…
The striking fractal geometry of strange attractors underscores the generative nature of chaos: like probability distributions, chaotic systems can be repeatedly measured to produce arbitrarily-detailed information about the underlying…
Many quantitative approaches to the dynamical scrambling of information in quantum systems involve the study of out-of-time-ordered correlators (OTOCs). In this paper, we introduce an algebraic OTOC ($\mathcal{A}$-OTOC) that allows us to…
The dynamics of one dimensional iterative maps in the regime of fully developed chaos is studied in detail. Motivated by the observation of dynamical structures around the unstable fixed point we introduce the geometrical concept of a…
The logistic map is a nonlinear difference equation well studied in the literature, used to model self-limiting growth in certain populations. It is known that, under certain regularity conditions, the stochastic logistic map, where the…
We discuss the characterization of chaotic behaviours in random maps both in terms of the Lyapunov exponent and of the spectral properties of the Perron-Frobenius operator. In particular, we study a logistic map where the control parameter…
The concept of information has emerged as a language in its own right, bridging several disciplines that analyze natural phenomena and man-made systems. Integrated information has been introduced as a metric to quantify the amount of…
In this paper we give a short theoretical description of the general predictive adaptive arithmetic coding technique. The links between this technique and the works of J. Rissanen in the 80's, in particular the BIC information criterion…
We consider a family of singular maps as an example of a simple model of dynamical systems exhibiting the property of robust chaos on a well defined range of parameters. Critical boundaries separating the region of robust chaos from the…
What does the informational complexity of dynamical networked systems tell us about intrinsic mechanisms and functions of these complex systems? Recent complexity measures such as integrated information have sought to operationalize this…