Models Of New Memory Device And Its Application In Chaotic Oscillators And Network Transmission

Chua speculated the existence of memristor based on the relationship between the basic circuit variables in 1971.In 2008,HP laboratory found that the nanoscale device TiO₂ has the same characteristics as the memristor,which confirmed the existence of the memristor.In 2009,Chua and others proposed the concept of memcapacitor and meminductor based on memristor,which enriched the concept of memory elements.Memory devices are nonlinear elements with memory function,which can be used in nonvolatile memory device,neural network,computer science and so on.Memory devices have become a hot research topic at home and abroad.The memory devices have not yet realized marketization.Especially researches of the memcapacitor and meminductor are still in the stage of modeling.So the mathematical model and the circuit model of memory devices are the research focus.In this paper,the mathematical models of the TiO₂flux-controlled memristor,charge-controlled memcapacitor,flux-controlled memcapacitor and flux-controlled meminductor are analyzed.The corresponding equivalent circuits are established based on the mathematical models.Two chaotic oscillators with memory devices are designed based on the mathematical models of the memory devices.One is constructed based on the memristor and the memcapacitor,and another is designed based on the memcapacitor and the meminductor.Some basic dynamical properties,includintg bifurcation and Lyapunov exponent spectrum of the designed chaotic oscillator,are analyzed.Finally,the randomness of the chaotic signal based on the memristor and the memcapacitor is analyzed.A new chaotic encryption algorithm based on joseph ring is proposed,and a network security transmission system with Open SSL is designed.The main research points of this paper are as follows:?1?Mathematical models of the TiO₂ flux-controlled memristor,the charge-controlled memcapacitor and the flux-controlled memcapacitor are proposed,and the mathematical model of the smooth curve flux-controlled meminductor is analyzed.The equivalent circuits of these memory devises are designed according to their mathematical models,and the circuit simulations for the equivalent circuits are carried out by using Multisim software.The circuit simulations are basically consistent with numerical simulation results.The results show that voltage and current of the memristor,voltage and charge of the memcapacitor,and magnetic flux and current of the meminductor are satisfied with the characteristic of pinched hysteresis loop.?2?Two chaotic oscillators with memory devices are designed based on the mathematical models of the memory devices and Chua's circuit.One is constructed based on the memristor and the memcapacitor,and another is designed based on the memcapacitor and the meminductor.Some basic dynamical properties,includintg bifurcation and Lyapunov exponent spectrum of the designed chaotic oscillator,are analyzed.Analysis results show that the chaotic oscillator based on two memory devices has complex dynamic behavior,such as the coexistence of attractors.The digital realization of chaotic oscillator based on two memory devices is realized by using DSP technology.The experimental results of DSP are basically consistent with the numerical simulation results.?3?The chaotic oscillation system based on the memristor and the memcapacitor is studied in the application of network security transmission.The random test of chaotic sequences is carried out by using NIST test software.The test result shows that the performance is better than the Lorenz system.The chaotic sequence generated by chaotic system based on the memristor and the memcapacitor has good randomness,and the space of key is large.A new chaotic encryption algorithm based on joseph ring is proposed,and a network security transmission system with Open SSL is designed.The system ensures the security of data in the network transmission.