Dynamic Analysis Of Fractional Delay SBT And TiO₂ Memristor Chaotic Systems

Since 2008,HP LABS developed TiO₂ today implements material model,the performance of many different materials and have resistance were successively research,domestic scholars have put forward the SBT(Sr_0.95.95 Ba_0.05.05 TiO₃)nano today implements model,principle of SBT nano today is resistance to change by the quantity of carrier,realize the function of today,its working principle and working principle of the TiO₂ have resistance are obviously different.Subsequently,some scholars used SBT memristor to replace the nonlinear components in the traditional chaotic circuit,and realized the typical chaotic characteristics,and found that the chaotic circuit based on SBT memristor had complex dynamic characteristics.Chaotic behavior in fractional-order memristor delay systems has become the focus of research.This thesis mainly studies the dynamic behavior of fractional-order memristor delay chaotic systems based on different physical models.First,a nonlinear chaotic circuit with delay based on fractional-order TiO₂ memristor is proposed.According to the theory of fractional calculus today of fractional order model,analyses the frequency characteristics of the fractional order today and the electrical characteristics,structure of chain circuit realization of fractional order unit circuit,and the chaotic circuit of integer order capacitance and integer order today is alternant respectively order capacitance and fractional order today,such a chaotic circuit based on fractional delay TiO₂ have resistance,finally analyzes its dynamic behavior.Then,we refer to fractional delay chaotic circuit resistance of TiO₂ have,for the first time the SBT nano today used in fractional order system,proposed a new fractional delay SBT today the chaos system,and has put forward the fractional order of TiO₂ time-delay chaotic circuit comparing research,the new fractional delay SBT have resistance analysis of the dynamic behavior of chaotic systems.All the research work provides a theoretical basis for building fractional order delay memristor chaotic circuit system and generating chaotic signals.The main innovations of this thesis are as follows:（1）According to the theory of fractional calculus today of fractional order model,analyses the frequency characteristics of the fractional order today and the electrical characteristics,structure of chain circuit realization of fractional order unit circuit,and the chaotic circuit of integer order capacitance and integer order today is alternant respectively order capacitance and fractional order today,so that form the basis of fractional order today time-delay chaotic circuit.Then,the circuit model of fractional-order TiO₂ memristor time-delay chaotic circuit system was established,and the mathematical model of the system was derived to carry out theoretical analysis and dynamics research on the system.（2）Reference to an integer order TiO₂ today delay circuit,proposed a new fractional order SBT today time-delay chaotic systems,and the third chapter has proposed the fractional order of TiO₂ time-delay chaotic circuit comparing research,the results found that this new fractional order SBT today although there is no balance for chaotic systems with time delay,but also can generate chaotic attractor.The mathematical model of fractional-order SBT delay chaotic system is derived,and the fractional-order SBT delay chaotic circuit system is theoretically analyzed,and the influence of system parameter a on the system dynamics is studied by dynamics method（bifurcation diagram,maximum lyapunov exponential diagram,time domain waveform,phase diagram and power spectrum,etc.）.The theoretical analysis of the improved adams-bashforth-moulton method is verified by numerical simulation.