Research On Complex Dynamic Behavior In Memristive Systems

Memristors are considered as the fourth class of nonlinear basic electronic compo-nents besides resistors,capacitors and inductors.The concept of memristors was first proposed by Professor L.O.Chua of University of California-Berkeley in 1971.Owing to the properties of state memory and the storage-computation integration,the memristor has been widely concerned by the academic community.In 2008,the development of the first real physical memristor?HP memristor?inspired a lot of research work including both theoretical and engineering aspects.However,most of the exsiting work is focused on the memristor itself,and the systems-level research is not enough.It is known that,in specific engineering scenarios,memristors will not be used as individuals,but work as a component of a system and deeply influence the behavior of the system.In order to understand the work mechanism of memristor in the system and to serve future engineering applications,this thesis will carry out a study about the dy-namic behavior of the memristive systems.The main research contents are divided into the following four parts:1.The complex dynamic behavior is studied in a new four dimensional autonomous system which has high complexity.First of all,a new four dimensional hyperchaotic system is proposed and the dynamic properties including the characteristics related to en-gineering applications is analyzed;moreover,based on topological horseshoe theory,the existence of system hyperchaos is proved by computer aided verification,and the topolog-ical entropy is calculated;finally,the existence of new types of co-existence and chaotic transformation in the system are discussed.These researches show that the proposed sys-tem is characterized by a highly complex hyperchaotic behavior?with the largest Kaplan-Yorke dimension and the largest topological entropy at present?.Meanwhile,the system has good engineering application potential:1)large bandwidth,2)strong initial value perception,and 3)high robustness of system parameters.2.The complex dynamic behavior is studied in a new four dimensional autonomous system based on the simplest memristor.First of all,the new system is constructed by introducing the simple linear memristor into the Qi chaotic system.Then,the dynamic analysis is perfomed.Through theoretical analysis,it is proved that the proposed system is symmetric,dissipative and has infinitely many unstable equilibrium points.Moreover,it is found that the simplest linear memristor can lead to complex dynamic behaviors such as coexistence of multiple attractors.Through bifurcation analysis,it is found that the system can enter into hyperchaos state through two different route.Finally,In order to understand the generating mechanism of topological horseshoe,an algorithm is first pro-posed to extract the orbits from the topological horseshoe.3.The complex dynamic behavior is studied in foundational circuit systems consist-ing of one HP memristor and one capacitor.First of all,the parallel and series circuits of HP memristor and capacitor are proposed,and the mathematical equations of two cir-cuits are derived and proved to be equivalent.Then,the nonlinear behavior,such as high periodic limit cycles and the chaotic,is studied under a combined periodic stimulation of two sinusoidal signals.Finally,based on the topological horseshoe theory,the chaotic in the parallel circuit is strictly verified.Further,some new features in circuit system are also found out:when the memristor takes some typical values,such as R_OFF/R_ON=100,no matter what other parameter values,there is usually a periodic excitation making the circuit to be chaotic.Under the combined periodic stimulation,chaos still exists in the system and has nothing to do with all these incentive mode.4.For memristive neural networks with leakage,discrete and distributed delays,the problem of state estimation is investigated.First of all,since the memristive neural net-work is a discontinuous system on the right,it is converted to traditional neural networks by using the differential inclusion and set-valued map.Then,by using a proposed multiple integral,a new Lyapunov-Krasovskii functional is constructed,and sufficient conditions are given to make the estimation error system asymptotically stable.Finally,The results are proved to be effective by numerical analysis.