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Research Papers

# On a Discrete Chaos Induction Via an Aperiodic Kicks Pattern

[+] Author and Article Information
Mehdi Nategh

Department of Mathematics and Statistics,
Missouri University of Science and Technology,
Rolla MO, 65401
e-mail: nateghm@mst.edu

Dumitru Baleanu

Department of Mathematics,
Çankaya University,
Ankara 06790, Turkey
e-mail: dumitru@cankaya.edu.tr

Arsh Electronic Company,
Babol, Iran
e-mail: mrv.ir152@gmail.com

1Corresponding author.

Contributed by the Design Engineering Division of ASME for publication in the JOURNAL OF COMPUTATIONAL AND NONLINEAR DYNAMICS. Manuscript received August 10, 2016; final manuscript received October 7, 2016; published online January 20, 2017. Assoc. Editor: Hiroshi Yabuno.

J. Comput. Nonlinear Dynam 12(4), 041008 (Jan 20, 2017) (6 pages) Paper No: CND-16-1378; doi: 10.1115/1.4035078 History: Received August 10, 2016; Revised October 07, 2016

## Abstract

In this work, a class of kicked systems perturbed with an irregular kicks pattern is studied and formation of a chaos in the senses of Devaney and Li–Yorke in the corresponding discretized system is investigated. Beside a discussion on chaotic stability, an example is presented. Then, the existence of a period three orbit of a 2D map which governs a class of dynamic problems on time scales is studied. As an application, a chaotic encryption scheme for a time-dependent plain text with the help of chaos induction in the sense of Li–Yorke is presented.

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## Figures

Fig. 1

Projected orbits in X–P plane with initial values x0=0.1, p0=0.3, μ0=0.9999 and x0=0.1, p0=0.3, μ0=0.999 represented by scattered points and vertical line x ∼ 0.3 respectively

Fig. 2

A schematic view for mapping a block (xk,μk) to the encrypted block Fm(xk,μk) via introducing a new time scale Tk with its corresponding Pk

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