Analysis And Simplified Circuit Implementation Of A Class Of Generalized Lorenz Chaotic Systems

Taking a class of generalized Lorenz chaotic systems as the main research object,the generalized Lorenz chaotic systems are analyzed by means of Lyapunov exponent and bifurcation diagram,by using the power series expansion method of the central manifold theorem,the local bifurcation of the hyperchaotic Lorenz system is analyzed and simulated.By using the topological horseshoe lemma,the existence of attractor of the hyperchaotic Lorenz system is proved.By analyzing the Lyapunov exponent and phase diagram,it can be proved that the state of the automatic switching system is not affected by the state of the subsystem,the switching results can be verified by both analog and digital circuit experiments,and the results are consistent with the analysis.The existence of attractors is proved by topological horseshoe lemma A non-equilibrium hyperchaotic system with hidden attractors is constructed on the basis of a generalized Lorenz system,the circuit of hidden attractor hyperchaotic system and multi-wing hyperchaotic system are designed by modularization method,and the experimental results are consistent with the numerical simulation.A manual switching chaotic system composed of the classical Lorenz chaotic system and the deformed Lorenz chaotic system is designed and realized by using the simplified method,the simplified circuit of Qi chaotic system is designed and implemented.The experimental results show that,like the modularization method,the parameters of the system can be realized by changing the resistance of the resistor,the dynamic behaviors of single-period,double-period,four-period,quasi-period,single-wing chaotic attractor and double-wing chaotic attractor are verified,the simplified circuit of Yang-chen chaotic system is designed and realized.The results of the dynamic behavior of the system are in agreement with the experimental results of the simplified method,which proves the effectiveness of the simplified method.This thesis presents a new chaotic system which is not topologically equivalent to the generalized Lorenz system.The system has some new characteristics different from the generalized Lorenz chaotic system,such as simpler algebraic structure,Lyapunov dimension close to 3,divergence is not constant,the topological entropy of the system is not less than log 3 by the topological horseshoe lemma.Taking hyperchaotic Lorenz system as an example,according to Poincar é-Andronov-Hopf bifurcation theorem and using power series expansion method of central manifold theorem,the conditions of Hopf bifurcation are discussed,based on the practical algorithm of 3D chaotic mapping,we find the topological horseshoe of hyperchaotic Lorenz system,the hyperchaotic charactic is verified,the mechanism is revealed,a hyperchaotic Lorenz system is designed and implemented by using a simplified circuit,and the experimental results are in agreement with those obtained by the modularization method.