Circuit Implementation And Synchronization Study Of New Multi-Scroll Chaotic Systems

As a unique motion form in nonlinear dynamical systems,chaos exists widely in nature and human society.Due to its nonlinearity,intrinsic randomness,and extreme sensitivity to initial values,chaos has potential applications in fields such as secure communication and image encryption.It has been proved that chaotic signals can be produced from nonlinear circuits,which makes chaos possesses practical physical application value.Compared with general chaotic signals,chaotic signals generated by multi-scroll chaotic systems exhibit more complex dynamical characteristics in phase space,which makes multi-scroll chaotic systems possess better application potential.Therefore,researches on multi-scroll chaotic sytems and their circuit implementations have attracted the attention of many researchers.The new multi-scroll chaotic systems in this thesis refer to the multi-scroll chaotic systems that capable of generating multi-scroll chaotic attractors with more complex topologies,or possess more other complex dynamical characteristics.And in this thesis,the dynamical analyses,circuit implementations,and synchronization studies(chaotic synchronization is the premise for implementing applications such as secure communication)for the proposed new multi-scroll chaotic systems have been performed.The specific contents and innovations of this dissertation can be summarized as follows:(1)A complementary metal-oxide-semiconductor(CMOS)process-based second generation current-controlled conveyor(CCCII)is proposed and designed,which has the advantages of wide dynamic range and wide adjustable range.In this dissertation,an innovative scheme for implementing CMOS CCCII is proposed by combining three kinds of functional parts for the first time,which are linear voltage-current convertor,tunable current mirror,and low-voltage cascade current mirror.The designed CMOS CCCII based on this scheme has excellent characteristics such as the proportional relationship between the intrinsic resistance and the ratio of two bias currents and the adjustment of the intrinsic resistance does not affect the dynamic input range of the CCCII.We performed pre-and post-simulation analysis for the proposed CMOS CCCII and designed the corresponding layout.Moreover,the comparison with related circuits proves that the proposed CMOS CCCII circuit possesses superior performance.(2)A multi-attractor period multi-scroll chaotic system is proposed and the corresponding circuit of the newly proposed chaotic system is constructed on the basis of the designed CMOS CCCII in this dissertation.The proposed chaotic system can generate single-attractor period,double-attractor period,three-attractor period,and even more attractor period multi-scroll.Since the intrinsic resistance of the designed CCCII can be adjusted by external bias voltages or currents,the multi-attractor period multi-scroll chaotic integrated circuit based on it has adjustable characteristics.It is worth noting that current signals,rather than voltage signals,used as state variables in the multi-attractor period multi-scroll chaotic integrated circuit and there no any passive resistors in the circuit.Numerical simulations of the proposed chaotic system are conducted in this dissertation,and the CMOS CCCII is used as basic device to implement the integrated circuit that corresponds to the chaotic system.The feasibility of the implementation of the complex multi-scroll chaotic integrated circuit is verified by the circuit simulations and hardware experiments.In addition,the comparison between the implementation scheme of the chaotic circuit proposed in this dissertation and several reported chaotic circuits is conducted.(3)A new multi-scroll chaotic system is proposed in this dissertation.The system possesses complex dynamical characteristics,which not only has infinite equilibria,but can also generate multi-scroll hyperchaotic attractors.Through the analysis of the Lyapunov exponent spectrum regarding parameter a,we find that the system can exhibit the behaviors of point attractor,limit cycle,quasi-periodic attractor,chaotic attractor,and hyperchaotic attractor under different parameters.In which,one kind of the chaotic attractors exhibits a special topology and has a Kaplan-Yorke fractal dimensions greater than 3.Besides,the system has some other rich dynamical characteristics such as multi-stability,Hopf bifurcation,boundary crisis,and sustained hyperchaotic state depending on initial value w(0).Hardware experiments show that the proposed hyperchaotic system can generate chaotic attractors with controllable number of scrolls.Through the analysis for their attracting basins,the reason why the chaotic attractors with special topologies are difficult to reproduce by hardware experiments is given.Finally,the proposed system is compared with the multi-scroll chaotic systems in related literatures.(4)Based on the multi-attractor period multi-scroll chaotic system and the multi-scroll hyperchaotic system with infinite equilibria,two corresponding synchronized methods are proposed,respectively,and one of which is applied to chaotic secure communication.Two synchronous controllers corresponding to the two kinds of chaotic synchronization systems are respectively designed for achieving the synchronization of their same system structures.For the multi-attractor period multi-scroll chaotic system,a coupled completely synchronous controller is designed.Theoretical calculations and simulation examples have verified the effectiveness of the designed controller.An adaptive antiphase synchronous controller is designed for the multi-scroll hyperchaotic system with infinite equilibria,and its theory is proved.Finally,the synchronous example verifies that the system can realize antiphase synchronization(belong to generalized synchronization)under the action of the designed controller as well as identify the unkown parameters of the system.