Research On Meminductor-based Chaotic System And Its Application In Information Encryption

As a new type of circuit component,memristors,memcapacitors and meminductors at the nanometer level have unique properties different from other circuit components,and have important applications irn non-volatile storages,neural networks,digital logic circuits and other fields.Among them,HP laboratory successfully developed the physical device of memristor in 2008,which made the memristor quickly become a hotspot for scholars at home and abroad.So far,the physical device of the meminductor has not been realized,and the research on the meminductor is relatively rare,mainly some modelings and simulations.This paper mainly studies the mathematical model of the meminductor and the construction of its simulation circuit.The chaotic oscillation circuit is designed based on the meminductor model to explore the complex dynamic behavior of the meminductor in the circuit,and the meminductor chaotic sequences is applied to the information encryption.The main research contents of this paper are as follows:(1)According to the definition of the meminductor,mathematical model of current-controlled meminductor and flux-controlled meminductor is designed,and the corresponding equivalent circuit were built to analog the electrical characteristics of the actual meminductor.Using Multisim software is to simulate the equivalent circuit of the meminductor,it is found that their Wei!an characteristics are tight hysteresis curves after given sinusoidal excitation,which proves the correctness of the meminductor model.(2)Based on the basic theory and analysis method of chaos,in order to explore the application of the meminductor,a chaotic system with hidden attractors is designed by using the mathematical model of flux-meminductor.The calculation of equilbrium point and dissipative property prove the possibility of chaos in the system.Then the bifurcation diagram and Lyapunov exponent are used to explore the dynamic characteristics of the system.The most important feature of the system is that it can appear symmetric coexisting hidden attractors and give the specific conditions for this phenomenon.Finally,the DSP experiment is used to discretize the signal generated by the chaotic system,which verifies the correctness of Matlab simulation.(3)Based on the flux-controlled meminductor model,a chaotic oscillation circuit was built.The evolution of the system state was observed by the equilibrium point set,the bifurcation diagram,the Lyapunov exponent,the Lyapunov dimension and the dynamics map.It also found that the meminductor chaotic system can appear coexisting attractors when given the specific conditions.The system is also subjected to reduced dimensionality analysis.Firstly,the reduced dimensionality data is discretized,then a pseudo-random sequence is obtained by D/A conversion,and the pseudo-random sequence is tested by NIST.The test resluts show that the sequence has excellent randomness.It is of great value in the application of information encryption and secure communication.(4)The application of the sequence generated by the meminductor chaotic system is studied.The extracted pseudo-random sequence is combined with the popular DES encryption algorithm.An information encryption application based on Linux operating system is designed.The chaotic sequence is used as the encryption algorithm's key,the algorithm is written in C++.Because the key space of the meminductor chaotic system is relatively large,it is very difficult to decipher the encrypted information,so the information transmission security of the application is guaranteed.