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

Author:

Moysis Lazaros12ORCID,Lawnik Marcin3ORCID,Volos Christos1ORCID,Baptista Murilo S.4ORCID,Goudos Sotirios K.5ORCID

Affiliation:

1. Laboratory of Nonlinear Systems-Circuits & Complexity, Physics Department, Aristotle University of Thessaloniki, 54124 Thessaloniki, Greece

2. Department of Mechanical Engineering, University of Western Macedonia, 50100 Kozani, Greece

3. Department of Mathematics Applications and Methods for Artificial Intelligence, Faculty of Applied Mathematics, Silesian University of Technology, Kaszubska 23, 44-100 Gliwice, Poland

4. Department of Physics, Institute for Complex Systems and Mathematical Biology, SUPA, University of Aberdeen, Aberdeen AB24 3UX, UK

5. ELEDIA@AUTH, Physics Department, Aristotle University of Thessaloniki, 54124 Thessaloniki, Greece

Abstract

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.

Publisher

MDPI AG

Subject

Physics and Astronomy (miscellaneous),General Mathematics,Chemistry (miscellaneous),Computer Science (miscellaneous)

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