An Extremely Simple Multi-Wing Chaotic System: Dynamics Analysis, Encryption Application and Hardware Implementation

Abstract

Polynomial functions have been the main barrierrestricting the circuit realization and engineering applicationof multi-wing chaotic systems (MWCSs). To eliminate thisbottleneck, we construct a simple MWCS without polynomialfunctions by introducing a sinusoidal function in a Sprott Csystem. Theoretical analysis and numerical simulations show thatthe MWCS can not only generate multi-butterfly attractors withan arbitrary number of butterflies, but also adjust the numberof the butterflies by multiple ways including self-oscillatingtime, control parameters, and initial states. To further explorethe advantage of the proposed MWCS, we realize its analogcircuit using commercially available electronic elements. Theresults demonstrate that in comparison to traditional MWCSs,our circuit implementation greatly reduces the consumption ofelectronic components. This makes the MWCS more suitablefor many chaos-based engineering applications. Furthermore,we propose an application of the MWCS to chaotic imageencryption. Histogram, correlation, information entropy, and keysensitivity show that the simple image encryption scheme hashigh security and reliable encryption performance. Finally, wedevelop a field-programmable gate array (FPGA) test platformto implement the MWCS-based image cryptosystem. Both the-oretical analysis and experimental results verify the feasibilityand availability of the proposed MWCS