Analysis And Design Of The Nonlinear Chaotic Circuits

Chaos is a special movement, which appears in the non-linear system. More than 40 years, people always study chaos and obtain many achievements.We must learn to design chaotic circuits before we use chaos, so it is significant for us to analyze and design the chaotic circuits.The relevant knowledge of the chaos was described and the study status of the chaotic circuits was introduced. Then this paper introduces the Chua's circuit, which is one of the best chaotic circuits because its structure is simple and can show a rich dynamic behavior. Subsequently we design a variant of the Chua's circuit. We deduce its state equation, analyze its balance points and carry on the simulation to study its dynamic behavior. Finally, the phase diagrams and timing waveforms were obtained and they are consistent with Chua's circuit, thereby the chaotic characteristics of the circuit were confirmed.The Lorenz system is the first physical and mathematical model of chaos. A new three-order autonomous chaotic system was designed based on the Lorenz system. The new system also belongs to Lorenz system. The nonlinear dynamic properties of the system such as strange attractor, the largest Lyapunov index, fractal dimension, spectrum, power spectrum and bifurcation are researched via theoretical analysis and digital simulation. EWB software is used to design and simulate the circuit. Finally the chaotic characteristics of the system are confirmed.We can design a simple feedback allows a Lorenz system from non-chaotic state turn into chaotic state, base on this principle the Chen system was discovered. A new Hyperchaos Chen system was designed based on Chen system. It has four parameters, four variables and two nonlinear terms. Firstly, the theoretical analysis to this system was carried on, and then the numerical simulation in Matlab was completed, finally the circuit diagram was drawn based on the equation and the circuit simulation was carried on through selecting the appropriate circuit parameters.The experimental results are consistent with the numerical simulation results, so the feasibility of the design method was confirmed from the perspective of circuit simulation.