Exploring a family of Bernoulli-like shift chaotic maps and its amplitude control

García-Grimaldo, Claudio; Campos-Cantón, Eric

doi:10.1016/j.chaos.2023.113951

Cited by 3 publications

(1 citation statement)

References 39 publications

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“…The first family is that of maps composed of functions based on fuzzy numbers [44,45]. The other family of piecewise maps is that of no equilibria maps [46,47]. It would thus be of interest to study the aforementioned families of maps, with respect to the ability to tune their statistical characteristics.…”

Section: Discussionmentioning

confidence: 99%

Chaotic Maps with Tunable Mean Value—Application to a UAV Surveillance Mission

Moysis,

Lawnik,

Volos

et al. 2023

Symmetry

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Chaos-related applications are abundant in the literature, and span the fields of secure communications, encryption, optimization, and surveillance. Such applications take advantage of the unpredictability of chaotic systems as an alternative to using true random processes. The chaotic systems used, though, must showcase the statistical characteristics suitable for each application. This may often be hard to achieve, as the design of maps with tunable statistical properties is not a trivial task. Motivated by this, the present study explores the task of constructing maps, where the statistical measures like the mean value can be appropriately controlled by tuning the map’s parameters. For this, a family of piecewise maps is considered, with three control parameters that affect the endpoint interpolations. Numerous examples are given, and the maps are studied through a collection of numerical simulations. The maps can indeed achieve a range of values for their statistical mean. Such maps may find extensive use in relevant chaos-based applications. To showcase this, the problem of chaotic path surveillance is considered as a potential application of the designed maps. Here, an autonomous agent follows a predefined trajectory but maneuvers around it in order to imbue unpredictability to potential hostile observers. The trajectory inherits the randomness of the chaotic map used as a seed, which results in chaotic motion patterns. Simulations are performed for the designed strategy.

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