【作者】 刘恒；

【导师】 岳丽娟；

【作者基本信息】 东北师范大学 ， 电路与系统， 2006， 硕士

【摘要】 本文主要围绕蔡氏电路展开研究工作。首先利用Pspice仿真软件对实际电感蔡氏电路进行仿真,给出可调参量在不同取值范围时,蔡氏电路所展示的动力学行为。同时,对蔡氏电路中非线性电阻的伏安特性进行了分析。 然后,引入一个模拟电感电路,分析了该模拟电感电路的等效原理,并将该模拟电感代替蔡氏电路中实际的电感,通过电路实验验证了该方案可行,进一步证实了该模拟电感在振荡电路中性能更加优越。 在蔡氏电路的基础上,对多涡卷混沌吸引子的产生也进行了研究,理论推导了其产生规律,同时对其平衡点也进行了分析,通过数值仿真能产生10个涡卷的混沌吸引子。同样用一个模拟电感代替多涡卷混沌电路中实际的电感,在电路实验中最多产生了8个涡卷的混沌吸引子。 本文还对蔡氏电路的一个变形电路(用三次方模块代替分段线性函数)进行了研究,根据变形蔡氏系统,设计了一个电子电路,并通过Pspice仿真验证了该设计电路可行。在此基础上,通过正比于系统变量的周期脉冲扰动法对其混沌进行控制,根据脉冲强度γ_i>0和γ_i<0分别设计了两个不同的控制器,都得到了较好的控制结果。 最后,利用限幅控制法对蔡氏电路中的混沌进行控制。通过Pspice仿真验证了该方案的可行性。在此基础上,通过电路实验对基于模拟电感的双涡卷、5涡卷和6涡卷混沌吸引子,利用限幅控制法对其混沌进行控制,可控制到各种周期轨道。更多还原

【Abstract】 Chua’s circuit is mainly studied in the paper. Firstly, Chua’s circuit with real inductor is stimulated by Pspice software. When the adjustable Parameter is selected different values, the chaotic behaviors what Chua’s circuit displays are analyzed. At the same time, the piecewise-linear v - i characterstic of the nolinear resistor in the chua’s circuit is analyzed.Secondly, a stimulated inductor circuit is introducted. the equal principle of its is analyzed. And let the stimulated inductor to replace the real inductor of Chua’s circuit. The project is verified to be available by circuit experiment. Further, the characteristic of the stimulated inductor is confirmed to be better in oscillating circuit.Based on Chua’s circuit, the generation of n-scroll chaotic attractors are also studied. Its generation regulation is deduced theoretically, and its equilibrium is also analysised in the paper. A ten-scroll attracror can be obtained by numerical simulation. Similarly, n-scroll chaotic attractors are also studied based on the stimulated inductor. The attractors with a maximum of eight-scroll can be obtained by electric circuit experiment.A transformed circuit(using three power mold to replace piecewise-linear function) of Chua’s circuit is studied. According to the transformed Chua’s system, an electric circuit is designed. The circuit what we designed is verified to be viable by Pspice simulation. Based on the circuit system, its chaos are controlled by using proportional pulses in the system variables. According to the pulse strength γ_i > 0 and γ_i < 0, two different controllers arerespectively designed. Controlling results are all very good.At last, the chaos of Chua’s circuit are controlled by limiting amplitude method. The method is verified to be viable by Pspice simulation. Further, making use of limiting amplitude method, the double-scroll, 5- scroll and 6-scroll chaotic attractors based on the stimulated inductor are controlled to different period orbits by electric circuit experiment.更多还原