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18 pages, 3495 KiB

Open AccessArticle

A Broken Duet: Multistable Dynamics in Dyadic Interactions

by Johan Medrano and Noor Sajid

Entropy 2024, 26(9), 731; https://doi.org/10.3390/e26090731 - 28 Aug 2024

Cited by 1 | Viewed by 1051

Misunderstandings in dyadic interactions often persist despite our best efforts, particularly between native and non-native speakers, resembling a broken duet that refuses to harmonise. This paper delves into the computational mechanisms underpinning these misunderstandings through the lens of the broken Lorenz system—a continuous dynamical model. By manipulating a specific parameter regime, we induce bistability within the Lorenz equations, thereby confining trajectories to distinct attractors based on initial conditions. This mirrors the persistence of divergent interpretations that often result in misunderstandings. Our simulations reveal that differing prior beliefs between interlocutors result in misaligned generative models, leading to stable yet divergent states of understanding when exposed to the same percept. Specifically, native speakers equipped with precise (i.e., overconfident) priors expect inputs to align closely with their internal models, thus struggling with unexpected variations. Conversely, non-native speakers with imprecise (i.e., less confident) priors exhibit a greater capacity to adjust and accommodate unforeseen inputs. Our results underscore the important role of generative models in facilitating mutual understanding (i.e., establishing a shared narrative) and highlight the necessity of accounting for multistable dynamics in dyadic interactions. Full article

(This article belongs to the Special Issue From Functional Imaging to Free Energy—Dedicated to Professor Karl Friston on the Occasion of His 65th Birthday)

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21 pages, 2632 KiB

Open AccessArticle

A Novel Method to Identify Initial Values of Chaotic Maps in Cybersecurity

by Amir Anees and Iqtadar Hussain

Symmetry 2019, 11(2), 140; https://doi.org/10.3390/sym11020140 - 27 Jan 2019

Cited by 34 | Viewed by 4635

Abstract

Chaos theory has applications in several disciplines and is focusing on the behavior of dynamical systems that are highly sensitive to initial conditions. Chaotic dynamics are the impromptu behavior displayed by some nonlinear dynamical frameworks and have been used as a source of diffusion in cybersecurity for more than two decades. With the addition of chaos, the overall strength of communication security systems can be increased, as seen in recent proposals. However, there is a major drawback of using chaos in communication security systems. Chaotic communication security systems rely on private keys, which are the initial values and parameters of chaotic systems. This paper shows that these chaotic communication security systems can be broken by identifying those initial values through the statistical analysis of standard deviation and variance. The proposed analyses are done on the chaotic sequences of Lorenz chaotic system and Logistic chaotic map and show that the initial values and parameters, which serve as security keys, can be retrieved and broken in short computer times. Furthermore, the proposed model of identifying the initial values can also be applied on other chaotic maps as well. Full article

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