Study On Fractional Order Memristor-based Chaotic System And Its Application In File Encryption

The concept of memristors was first proposed by professor Chua in the early 1970 s,but it wasn't until 2008 that a memristor made of TiO₂ was discovered by HP LABS.The results show that memristor has important applications for non-volatile memories,logic circuits,artificial neural networks and chaotic oscillations.The fractional-order model of some memristor is more accurate than integral-order model,and the fractional-order model has the effect of historical state memory,therefore,the fractional-order models of memristor are studied at home and abroad.In this paper,memristor modeling and fractional-order calculus are combined to construct a fractional-order memristor model,based on which a fractional-order memristor chaotic oscillation circuit is designed and applied to embedded file encryption system.The main works of this paper are as follows:?1?An ideal voltage-controlled fractional-order memristor model is designed,and the non-volatile characteristics of memristor under the excitation of square wave signal are analyzed and proved by using the dynamic route map method,that is,the state variable can always remember the memristor state before power off.Response expression of the fractional-order memristor model under the excitation of sinusoidal signal is derived,based on which the v-i hysteretic curve,the memristance curve and the instantaneous power curve are drawn.Compare with the integer-order model of the memristor,under the same signal excitation,the angular frequency is 50 rad s when the hysteretic curve approaches a straight line,the frequency characteristic of the fractional order model is better,and the minimum memristance value is-1.12K?,the maximum memristance value is 0.3371K?,the variation range of the memristor value is larger.?2?Based on the fractional-order memristor model and Chua's circuit,a fractional-order chaotic oscillation circuit is designed.The relationship between fractional order,equilibrium point and stability of the circuit is analyzed.Then the bifurcation diagram,poincaré map and Lyapunov exponent are used to explore the dynamic characteristics of the circuit system and it is found that the circuit has multiple coexisting attractors.Finally,the complexity of the system is analyzed by using spectral entropy analysis algorithm.?3?Based on chaos sequence produced in the fractional-order memristor-based chaotic oscillation circuit,a kind of chaos-DES encryption mixed algorithm is designed.Using the encryption algorithm and Qt Linux GUI program development framework,we design an embedded chaotic file encryption system,and the system can encrypt images and texts,which are stored in USB flash disk,hard drives or SD card.