Development of a Family of Chaotic Systems with Infinite Equilibria and Its Application for Image Encryption
Fourth-order autonomous nonlinear differential equations can exhibit chaotic properties. In this study, we propose a family of fourth-order chaotic systems with infinite equilibrium points whose equilibria form closed curves of different shapes. First, the phase diagrams and Lyapunov exponents (LEs)...
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| Main Authors: | , , , , |
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| Format: | Article |
| Language: | English |
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Wiley
2022-01-01
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| Series: | Complexity |
| Online Access: | http://dx.doi.org/10.1155/2022/1250489 |
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| _version_ | 1832551574434480128 |
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| author | Xiaofeng Li Yulong Bai Weishuan Pan Di Wang Yong-Jie Ma |
| author_facet | Xiaofeng Li Yulong Bai Weishuan Pan Di Wang Yong-Jie Ma |
| author_sort | Xiaofeng Li |
| collection | DOAJ |
| description | Fourth-order autonomous nonlinear differential equations can exhibit chaotic properties. In this study, we propose a family of fourth-order chaotic systems with infinite equilibrium points whose equilibria form closed curves of different shapes. First, the phase diagrams and Lyapunov exponents (LEs) of the system family are simulated. The results show that the system family has complex phase diagrams and dynamic behaviors. Simulation analysis of the Poincarè mapping and bifurcation diagrams shows that the system has chaotic characteristics. The circuit simulation model is constructed and simulated in Multisim. The circuit simulation results coincide with the numerical simulation results, which verifies the circuit feasibility of the system. Then, based on Lyapunov stability theory and the adaptive control method, the synchronous control of the system with infinite equilibria is designed. Numerical simulation results verify that the system synchronization with the adaptive control method is well. Finally, the synchronous drive system is used for image encryption, the response system is used for decryption, and color image encryption is realized by combining deoxyribonucleic acid (DNA) coding and operating rules. Therefore, this study not only enriched the research on infinite equilibria chaotic systems but also further expanded secure communication technology by combining chaotic synchronization control and DNA coding in image encryption. |
| format | Article |
| id | doaj-art-f9bd2523af6c4c94bb52a4abf32f1e2e |
| institution | Kabale University |
| issn | 1099-0526 |
| language | English |
| publishDate | 2022-01-01 |
| publisher | Wiley |
| record_format | Article |
| series | Complexity |
| spelling | doaj-art-f9bd2523af6c4c94bb52a4abf32f1e2e2025-02-03T06:01:17ZengWileyComplexity1099-05262022-01-01202210.1155/2022/1250489Development of a Family of Chaotic Systems with Infinite Equilibria and Its Application for Image EncryptionXiaofeng Li0Yulong Bai1Weishuan Pan2Di Wang3Yong-Jie Ma4College of Physics and Electrical EngineeringCollege of Physics and Electrical EngineeringCollege of Physics and Electrical EngineeringCollege of Physics and Electrical EngineeringCollege of Physics and Electrical EngineeringFourth-order autonomous nonlinear differential equations can exhibit chaotic properties. In this study, we propose a family of fourth-order chaotic systems with infinite equilibrium points whose equilibria form closed curves of different shapes. First, the phase diagrams and Lyapunov exponents (LEs) of the system family are simulated. The results show that the system family has complex phase diagrams and dynamic behaviors. Simulation analysis of the Poincarè mapping and bifurcation diagrams shows that the system has chaotic characteristics. The circuit simulation model is constructed and simulated in Multisim. The circuit simulation results coincide with the numerical simulation results, which verifies the circuit feasibility of the system. Then, based on Lyapunov stability theory and the adaptive control method, the synchronous control of the system with infinite equilibria is designed. Numerical simulation results verify that the system synchronization with the adaptive control method is well. Finally, the synchronous drive system is used for image encryption, the response system is used for decryption, and color image encryption is realized by combining deoxyribonucleic acid (DNA) coding and operating rules. Therefore, this study not only enriched the research on infinite equilibria chaotic systems but also further expanded secure communication technology by combining chaotic synchronization control and DNA coding in image encryption.http://dx.doi.org/10.1155/2022/1250489 |
| spellingShingle | Xiaofeng Li Yulong Bai Weishuan Pan Di Wang Yong-Jie Ma Development of a Family of Chaotic Systems with Infinite Equilibria and Its Application for Image Encryption Complexity |
| title | Development of a Family of Chaotic Systems with Infinite Equilibria and Its Application for Image Encryption |
| title_full | Development of a Family of Chaotic Systems with Infinite Equilibria and Its Application for Image Encryption |
| title_fullStr | Development of a Family of Chaotic Systems with Infinite Equilibria and Its Application for Image Encryption |
| title_full_unstemmed | Development of a Family of Chaotic Systems with Infinite Equilibria and Its Application for Image Encryption |
| title_short | Development of a Family of Chaotic Systems with Infinite Equilibria and Its Application for Image Encryption |
| title_sort | development of a family of chaotic systems with infinite equilibria and its application for image encryption |
| url | http://dx.doi.org/10.1155/2022/1250489 |
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