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Modified Projective Synchronization between Different Fractional-Order Systems Based on Open-Plus-Closed-Loop Control and Its Application in Image Encryption

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  • Hongjuan Liu
  • Zhiliang Zhu
  • Hai Yu
  • Qian Zhu

Abstract

A new general and systematic coupling scheme is developed to achieve the modified projective synchronization (MPS) of different fractional-order systems under parameter mismatch via the Open-Plus-Closed-Loop (OPCL) control. Based on the stability theorem of linear fractional-order systems, some sufficient conditions for MPS are proposed. Two groups of numerical simulations on the incommensurate fraction-order system and commensurate fraction-order system are presented to justify the theoretical analysis. Due to the unpredictability of the scale factors and the use of fractional-order systems, the chaotic data from the MPS is selected to encrypt a plain image to obtain higher security. Simulation results show that our method is efficient with a large key space, high sensitivity to encryption keys, resistance to attack of differential attacks, and statistical analysis.

Suggested Citation

  • Hongjuan Liu & Zhiliang Zhu & Hai Yu & Qian Zhu, 2014. "Modified Projective Synchronization between Different Fractional-Order Systems Based on Open-Plus-Closed-Loop Control and Its Application in Image Encryption," Mathematical Problems in Engineering, Hindawi, vol. 2014, pages 1-10, March.
    • Handle: RePEc:hin:jnlmpe:567898
    DOI: 10.1155/2014/567898
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