Related papers: Computational information for the logistic map at …
An algorithm to characterize collective motion is presented, with the introduction of ``collective Lyapunov exponent'', as the orbital instability at a macroscopic level. By applying the algorithm to a globally coupled map, existence of…
In the sciences in general, the phrase "route to chaos" has come to refer to a metaphor when some physical, biological, economic, or social system transitions from one exhibiting order to one displaying randomness (or chaos). Sometimes the…
The knowledge of transitions between regular, laminar or chaotic behavior is essential to understand the underlying mechanisms behind complex systems. While several linear approaches are often insufficient to describe such processes, there…
Multivariate information theory provides a general and principled framework for understanding how the components of a complex system are connected. Existing analyses are coarse in nature -- built up from characterizations of discrete…
In a 2D conservative Hamiltonian system there is a formal integral $\Phi$ besides the energy H. This is not convergent near a stable periodic orbit, but it is convergent near an unstable periodic orbit. We explain this difference and we…
In this paper, we introduce a hybrid chaos map for image encryption method with high sensitivity. This new map is sensitive to small changes in the starting point and also in control parameters which result in having more computational…
We give diagrammatic tools to reason about information flow within encrypted communication. In particular, we are interested in deducing where information flow (communication or otherwise) has taken place, and fully accounting for all…
In this paper, I propose a theoretical information-geometric framework suitable to characterize chaotic dynamical behavior of arbitrary complex systems on curved statistical manifolds. Specifically, I present an information-geometric…
Graph compression is a data analysis technique that consists in the replacement of parts of a graph by more general structural patterns in order to reduce its description length. It notably provides interesting exploration tools for the…
Chaotic behavior of quantum systems can be characterized by the adherence of the expectation values of given probes to moments of the Haar distribution. In this work, we analyze the behavior of several probes of chaos using a technique…
Given an arbitrary \(V \times V\) Hermitian matrix, considered as a finite discrete quantum Hamiltonian, we use methods from graph and ergodic theories to construct a \textit{quantum Poincar\'e map} at energy \(E\) and a corresponding…
Several aspects of classical and quantum mechanics applied to a class of strongly chaotic systems are studied. These consist of single particles moving without external forces on surfaces of constant negative Gaussian curvature whose…
In this paper we initiate a somewhat detailed investigation of the relationships between quantitative recurrence indicators and algorithmic complexity of orbits in weakly chaotic dynamical systems. We mainly focus on examples.
The dynamic region of out-of-time-ordered correlators (OTOCs) serves as a powerful indicator of chaos in classical and semiclassical systems, capturing the characteristic exponential growth. In contrast, this signature fails to appear in…
Using predictive adaptive arithmetic coding and the Minimum Description Length principle, we derive an efficient tool for model selection problems : the RIC information criterion. We then present an extension of these coding techniques to…
In previous work, the $k$-logistic map [Machicao and Bruno, Chaos, vol. 27, 053116 (2017)] was introduced as a transformation operating in the $k$ less significant digits of the Logistic map. It exploited the map's pseudo-randomness…
Information theory is a powerful framework to capture aspects of dynamical systems with multiple degrees of freedom. Mathematically, the dynamics can be represented as a continuous curve $\mathcal{C}$ on a suitable hyperplane in flat space…
This paper studies integrated sensing and communication (ISAC) systems with two rate-limited helpers who observe the channel state sequence and the feedback sequence, respectively. Depending on the timing of compressing and using the state…
Complex systems, from the human brain to the global economy, are made of multiple elements that interact in such ways that the behaviour of the `whole' often seems to be more than what is readily explainable in terms of the `sum of the…
In this paper we propose a multi-map orbit hopping chaotic stream cipher that utilizes the idea of spread spectrum mechanism for secure digital communications and fundamental chaos characteristics of mixing, unpredictable, and extremely…