Parameters Modeling Of Multi-scroll Chaotic Attractors And Its Chaotic Circuit Implementation

After the theory of relativity and quantum mechanics, the third revolution is generated in physics—the birth of chaotic theory, and it is a bridge between deterministic theory and probability theory, the thought of human is changed in scientific aspect. Chaos is a dynamics behavior which generates in deterministic system, but its characteristic is random and ruleless. It has mutual penetration, mutual promotion and common development with other disciplines, and it can be used in several fields, such as electrical engineering, information engineering, communication engineering, mechanics engineering.Recently, chaotic science has been fast developed. Because of more dynamical complexity of multi-scroll chaotic attractor, one-directional(1-D), two-directional(2-D), three-directional(3-D), and higher-order multi-scroll chaotic attractor can be generated by kinds of functions, and the corresponding circuit is designed using the conventional opamps. But their circuits have narrow bandwidth of frequency, low conversion rate, high operation voltage, and many active elements because of conventional opamps own disadvantages. However, current feedback operational amplifier(CFOA) has adjustable bandwidth, high conversion rate, good port characteristics, and it is nothing that low voltage can be adjusted, because of it cope with current. The circuit was designed by CFOA, and its circuit has higher frequency with lower operation voltage, more simple circuit constructer, and fewer active elements. However, circuit design is not good. Some studies have showed that 1-D multi-scroll circuit needs many active devices and more complex circuit construction, there is a few investigation about 2-D multi-scroll circuit and even none investigation about 3-D multi-scroll circuit. Most works focus on the parameters of multi-scroll chaotic attractors, such as Widths, Period, Equilibrium points and Breakpoints, there are a few studies about the parameters of 1-D and 2-D multi-scroll chaotic attractors and even none study about the parameters of 3-D multi-scroll chaotic attractors.The thesis mainly focus on the investigation of 1-D, 2-D, 3-D multi-scroll circuit based on CFOA, the parameters modeling of multi-scroll attractors(such as Widths, Period, Equilibrium points and Breakpoints), and its chaotic circuit implement. Its main context is:(1) The first chapter introduced method of multi-scroll chaotic attractors generated, classification of multi-scroll chaotic attractors, and introduced multi-scroll chaotic circuit based on conventional opamps, CFOA, current conveyor.(2) The second chapter introduced CFOA on circuit structure and topology structure, analyzed gain characteristics, frequency characteristics, function circuit, and nonlinear characteristics.(3) The third chapter introduced history of chaos, define of chaos, characteristics of chaos, and study method of chaos. Begin with Lorenz system, a new three dimensional autonomous chaotic system is proposed. Dynamic behaviors of this new system, including the stability of equilibria, the system dissipativity, Poincare maps, Lyapunov exponent, bifurcation, wave forms and spectrum are theoretically analyzed. And numeral simulation is performed in Matlab. A chaotic circuit is designed, and the corresponding circuit simulation is conducted. The results show that the chaotic attractor truly exists in the new system. The synchronization problem of this chaotic system proposed is solved with a synchronization method, and its synchronization circuit is designed. Numeral simulation and circuit simulation show that the synchronization problem of this chaotic system proposed is solved.(4) Conventional opamps were designed by mainly exploiting 1-D, 2-D, 3-D, and higher order multi-scroll chaotic circuit, and there are some disadvantages such as low central frequency, required many active devices and complex circuit construction. However, CFOA has better frequency characteristics and port characteristics. Multi-scroll circuit based on CFOA only presents its frequency characteristics. Some studies have showed that 1-D multi-scroll circuit needs many active devices and more complex circuit construction, there is a few investigation about 2-D multi-scroll circuit and even none investigation about 3-D multi-scroll circuit. The fourth chapter firstly study that a nonlinear cell circuit is designed only use a CFOA, nonlinear function serial by connecting several basic cells in parallel. This is an important fundamental, 1-D, 2-D, 3-D multi-scroll chaotic circuit are designed. Their circuit has more simple circuit structure, fewer active element, and higher frequency. It made circuit based on CFOA generated multi-scroll chaotic attractor is developed from 1-D and 2-D to 3-D. So multi-scroll chaotic circuit is easily integrated as a chip because of only one kind of active element(CFOA)(5) A few works focus on the parameters of multi-scroll chaotic attractors, such as Widths, Period, Equilibrium points and Breakpoints, there are a few studies about the parameters of 1-D and 2-D multi-scroll chaotic attractors and even none study about the parameters of 3-D multi-scroll chaotic attractors. Parameters modeling of 1-D multi-scroll chaotic attractor and its circuit implement using the current conveyor is reported, and Parameters modeling of 2-D multi-scroll chaotic attractor and its circuit implement using the conventional opamps is also reported. But their circuit has many active elements and complex structure. Firstly, parameter modeling of 1-D multi-scroll chaotic attractor and the corresponding parameters are given. The values of the corresponding parameters are calculated, and which are verified by numerical simulation. 1-D multi-scroll chaotic circuit is designed only use CFOA, and its characteristics are higher frequency, fewer active elements, and simpler circuit structure. Secondly, parameter modeling of 2-D multi-scroll chaotic attractor and the corresponding parameters are given. The values of the corresponding parameters are calculated, and which are verified by numerical simulation. 2-D multi-scroll chaotic circuit is designed only use CFOA, and its characteristics are higher frequency, fewer active elements, and simpler circuit structure. After studying parameter modeling of 1-D and 2-D multi-scroll chaotic attractors, finally, parameter modeling of 3-D multi-scroll chaotic attractor is proposed. The corresponding formulas are derived. The values of the corresponding parameters are calculated, and numerical simulations are performed. 3-D multi-scroll chaotic circuit is designed only use CFOA, and circuit simulation are performed, and its characteristics are higher frequency, fewer active elements, and simpler circuit structure. So study on parameter modeling of multi-scroll chaotic attractor is developed from 1-D to 2-D and 3-D. Multi-scroll chaotic attractors were more accurately described and precisely analyzed. Multi-scroll chaos can be better applied in practical engineering.