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.
Highlights
Fractional calculus, which is a mathematical topic with more than 300-year history, was not applied to physics and engineering until recent decades
A good encryption should be able to resist all kinds of known attacks and some security analyses have been performed on the proposed image encryption scheme
Of two incommensurate or commensurate fractional-order systems can be achieved. Both numerical simulations and computer graphics show that the developed coupling scheme works well
Summary
Fractional calculus, which is a mathematical topic with more than 300-year history, was not applied to physics and engineering until recent decades. Other than the above studies, the Open-Plus-ClosedLoop (OPCL) control method is a more general and physically realizable coupling scheme that can provide stable synchronization in identical and mismatched oscillators [9, 10]. OPCL coupling provides synchronization in all systems without restrictions on the symmetry class of a dynamical system. In the synchronization regimes, the OPCL coupling can realize stable amplification or attenuation in identical and mismatched systems. Many researchers have achieved their synchronization scenarios for integer-order or fractional-order systems through OPCL control [11,12,13]. As a matter of fact, OPCL control can be utilized to achieve synchronization of fractional-order chaotic systems with different structure
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