Dynamic Behavior Analysis Of Fractional Memristive Chaotic Circuits And Its Application In Power System Image Encryption

As the fourth basic circuit component besides resistor,capacitor and inductor,memristor has been gradually applied to various nonlinear circuits because of its superior nonlinear,memory characteristics,non-volatile and nano-size advantages.Fractional memristor is a more accurate description of memristor,which has richer dynamic behavior and can generate chaotic signals with stronger pseudo-randomness,making this kind of chaotic circuits have higher research value in image encryption.In this paper,the dynamic behavior of a fractional-order memristive chaotic circuit is analyzed,and the theoretical analysis is verified by circuit and hardware experiments,and it is applied to the digital image encryption scherne of power system.The specific work is as follows:Firstly,the dynamic behaviors of a cubic nonlinear magnetically controlled equivalent Chua’s circuit and an active generalized memristor bridge oscillator circuit are analyzed.The cubic nonlinear magneto-controlled memristor and active generalized memristor are deduced to fractional order by using predictive correction method,and their volt-ampere characteristics under different fractional order and different voltage excitation are analyzed,which still accord with the basic characteristics of memristor.Secondly,a new fractional-order memristive chaotic circuit model is established.A diode bridge memristor is connected in parallel with a negative resistor to form an active generalized memristor which is easy to realize and has.no grounding restriction.Combined with the fractional order theory,the fractional model of the memristor is constructed by the predictive correction method,and the model is connected in parallel with the capacitor to form a second-order nonlinear filter,and then coupled with the RC bridge oscillator to form a chaotic circuit.Its dynamic behavior is analyzed by combining time sequence diagram,phase diagram,bifurcation diagram and Lyapunov exponent diagram,and the effectiveness of theoretical analysis is verified by numerical simulation,circuit simulation and FPGA hardware circuit experiment.Finally,the fractional order memristive chaotic circuit is applied to the digital image encryption protection scheme of power system.The experiment designs the encryption and decryption of the image based on XOR diffusion algorithm,and analyzes the encrypted image including histogram,correlation analysis,information entropy analysis,key sensitivity analysis,anti-cropping and anti-attack.The results show that this scheme can achieve the ideal encryption effect,and all the indexes are close to the ideal value.The algorithm has good encryption performance and robustness.