Dynamics Analysis And Control Of Multi-scroll Chaotic Attractors

Chaos exists in every field of engineering technology and science research, such as Chemistry, Nonlinear Optics, Electronics and Fluid Dynamics.Most of the nonlinear systems could be generated by modeling with appropriate parameters which leads to chaotic attractors, and in general the number of the chaotic attractors is finite. Some evidences have confirmed that the chaotic system composed of multi-scroll attractor or wings indicate more abundant and complicated dynamical behaviors and are often used in generating complex secure keys, carrying wave for secure communication and image encryption, therefore, the related researches have attracted a lot of attention. In recent decades, the study of the collective behaviors of the coupled oscillators in the network is a hot topic. Controlling the system's evolution to the target state and network synchronization are always the focus of research. In this thesis, we first study the dynamics of the chaotic system composed of multi-scroll chaotic attractors, and then discuss in details the energy transition during the stabilization of multi-scroll attractor and the stabilization of the different number of scrolls attractors. Furthermore, we discuss the collective behaviors of the coupled network system by studying the stable ordered pattern formation of the coupled network composed of multi-scroll attractor chaotic system. From another perspective, we propose a novel network reconstruction method based on linear dynamics.The first chapter is an overview of the background of our thesis, introduces chaotic dynamics, complex network dynamics and pattern dynamics. The research progresses, basic concepts, control and synchronization of nonlinear system are explained in detail in the three parts respectively. Furthermore, the research progresses and production methods of multi-scroll attractor are introduced in details. Finally, several kinds of stability analysis methods of nonlinear system are introduced from the perspective of global and local.In the second chapter, we at first study dynamics of the improved Chua circuit composed of multi-scroll chaotic attractor, and further discuss the energy transition during different number of scrolls attractors and stabilization of scrolls attractors. In general, controllers designed as piecewise-linear functions are used to induce multi-scroll attractors in nonlinear circuits by generating many groups of equilibrium points. In this thesis, we adopt a feasible but practical scheme which can generate multi-scroll attractor by replacing the nonlinear terms in the improved Chua circuit with a sinusoidal function. We found that the number of multi-scroll attractor increases with the calculating period, although the Hamilton energy of the circuits composed of multi-scroll attractor, defined by the Helmholtz's theorem, is decreased with the number increasing of multi-scroll attractor. Furthermore, we find that the system has weak robustness, the number of scrolls is affected by the initial values and time scale; as a result, we present a scheme is to stabilize the multi-scroll attractor by applying negative type of coupling on the chaotic system.Compared with other researchers' work focusing on the methods for generating the multi-scroll attractor and circuit implementation, our work systematically introduces the special dynamics characteristic of the system from the point of the generation mechanism of the multi-scroll attractor, the relation between energy and number of scrolls, and the stabilization of the number of scrolls and the robustness of the system. However, this work has disadvantage of lacking circuit implementations.In the third chapter, the collective behaviors of coupled oscillators with multi-scroll attractor are investigated in the coupled regular network, in which the local kinetics is described by an improved Chua circuit. The stable ordered pattern could not be induced easily in the network with common methods for the system's strong nonlinearity. A feasible scheme of negative feedback with diversity is imposed on the network to stabilize the spatial patterns, i.e. the negative feedback with different gains (D1, D2) are imposed on the local square center area A2 and outer area A1 of the network, it is found that spiral wave, target wave could be developed in the network under appropriate feedback gains with diversity and size of controlled area. Particularly, homogeneous state could be obtained after synchronizing by selecting appropriate feedback gain and controlled size in the network. These results show that emergence of sustained spiral wave and continuous target wave could be effective for further suppression of spatiotemporal chaos in network by generating stable pacemaker completely. Compared with the work of other researchers, we originally discuss the collective dynamics behaviors of the multi-scroll attractor by studying the stable ordered pattern formation of the coupled network, which provides new challenge for studying the synchronization of complex network and pattern formation.In the previous two chapters, we study the dynamics of the nonlinear system from the point of obverse question, for example, the cooperative dynamics of highly inter-wined elements is determined by the connection topology, node dynamical diversity, and the forms of interaction. In the fourth chapter, the reverse question from dynamics to structure is study, namely, how to infer (or reconstruct) the network topology from dynamical observations is discussed. Based on the phase synchronization, we extend the previous network reconstruction method based on phase synchronization with nonlinearly coupled system to a linearly coupled one. We test these two methods and prove that both of them are feasible for the reconstruction for any unknown network structure. However, the linear reconstruction method is always superb,showing its own unique merits, such as simpler in algorithm realization, faster in computing time, and more efficient in final reconstruction result. The significance of this work is that for some nonlinear systems with weak nonlinearity we can apply approximate processing, which brings convenience to our research. Compared with other researchers'work, this method is in a manner limited that it is not suitable for study the nonlinear system with strong nonlinearity,In the fifth chapter, we summarize the thesis.