Dynamic Analysis of Modified Duffing System via Intermittent External Force and Its Application
Over the past century, a tremendous amount of work on the Duffing system has been done with continuous external force, including analytical and numerical solution methods, and the dynamic behavior of physical systems. However, hows does the Duffing oscillator behave if the external force is intermit...
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doaj-54c0ccaa8a3e4320a0efe839c336d8092020-11-25T01:35:57ZengMDPI AGApplied Sciences2076-34172019-11-01921468310.3390/app9214683app9214683Dynamic Analysis of Modified Duffing System via Intermittent External Force and Its ApplicationJianbin He0Jianping Cai1College of Mathematics and Statistics, Minnan Normal University, Zhangzhou 363000, China 2 Institute of Meteorological Big Data-Digital Fujian, Minnan Normal University, Zhangzhou 363000, ChinaCollege of Mathematics and Statistics, Minnan Normal University, Zhangzhou 363000, China 2 Institute of Meteorological Big Data-Digital Fujian, Minnan Normal University, Zhangzhou 363000, ChinaOver the past century, a tremendous amount of work on the Duffing system has been done with continuous external force, including analytical and numerical solution methods, and the dynamic behavior of physical systems. However, hows does the Duffing oscillator behave if the external force is intermittent? This paper investigates the Duffing oscillator with intermittent external force, and a modified Duffing chaotic system is proposed. Different from the continuous-control method, an intermittent external force of cosine function was designed to control the Duffing oscillator, such that the modified Duffing (MD) system could behave chaotically. The dynamic characteristics of MD system, such as the strange attractors, Lyapunov exponent spectra, and bifurcation diagram spectra were outlined with numerical simulations. Numerical results showed that there existed a positive Lyapunov exponent in some parameter intervals. Furthermore, by combining it with chaos scrambling and chaos XOR encryption, a chaos-based encryption algorithm was designed via the pseudorandom sequence generated from the MD. Finally, feasibility and validity were verified by simulation experiments of image encryption.https://www.mdpi.com/2076-3417/9/21/4683duffing oscillatorintermittent external forcelyapunov exponentchaos-based encryption |
collection |
DOAJ |
language |
English |
format |
Article |
sources |
DOAJ |
author |
Jianbin He Jianping Cai |
spellingShingle |
Jianbin He Jianping Cai Dynamic Analysis of Modified Duffing System via Intermittent External Force and Its Application Applied Sciences duffing oscillator intermittent external force lyapunov exponent chaos-based encryption |
author_facet |
Jianbin He Jianping Cai |
author_sort |
Jianbin He |
title |
Dynamic Analysis of Modified Duffing System via Intermittent External Force and Its Application |
title_short |
Dynamic Analysis of Modified Duffing System via Intermittent External Force and Its Application |
title_full |
Dynamic Analysis of Modified Duffing System via Intermittent External Force and Its Application |
title_fullStr |
Dynamic Analysis of Modified Duffing System via Intermittent External Force and Its Application |
title_full_unstemmed |
Dynamic Analysis of Modified Duffing System via Intermittent External Force and Its Application |
title_sort |
dynamic analysis of modified duffing system via intermittent external force and its application |
publisher |
MDPI AG |
series |
Applied Sciences |
issn |
2076-3417 |
publishDate |
2019-11-01 |
description |
Over the past century, a tremendous amount of work on the Duffing system has been done with continuous external force, including analytical and numerical solution methods, and the dynamic behavior of physical systems. However, hows does the Duffing oscillator behave if the external force is intermittent? This paper investigates the Duffing oscillator with intermittent external force, and a modified Duffing chaotic system is proposed. Different from the continuous-control method, an intermittent external force of cosine function was designed to control the Duffing oscillator, such that the modified Duffing (MD) system could behave chaotically. The dynamic characteristics of MD system, such as the strange attractors, Lyapunov exponent spectra, and bifurcation diagram spectra were outlined with numerical simulations. Numerical results showed that there existed a positive Lyapunov exponent in some parameter intervals. Furthermore, by combining it with chaos scrambling and chaos XOR encryption, a chaos-based encryption algorithm was designed via the pseudorandom sequence generated from the MD. Finally, feasibility and validity were verified by simulation experiments of image encryption. |
topic |
duffing oscillator intermittent external force lyapunov exponent chaos-based encryption |
url |
https://www.mdpi.com/2076-3417/9/21/4683 |
work_keys_str_mv |
AT jianbinhe dynamicanalysisofmodifiedduffingsystemviaintermittentexternalforceanditsapplication AT jianpingcai dynamicanalysisofmodifiedduffingsystemviaintermittentexternalforceanditsapplication |
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