Gaussian White Noise Phase Suppression Of Several Types Of Chaotic Systems

Nonlinear science is a basic science which studies nonlinear phenomena in common,and chaos theory is an important branch of nonlinear science. Chaos is an extremelycomplex phenomenon which a deterministic nonlinear system produces, and it widespreads in nature and human society. On the one hand, the chaotic system is extremelysensitive to initial conditions, so the output does not meet the people's requirement, evenharmful. Therefore, in many practical systems, we often need to control or keep down thesystem's Chaos. On the other hand, chaos is very useful in some cases; therefore, theresearch on chaos theory has great significant and practical value.In recent years, Chaotic system becomes a hot academic research. And how toeffectively inhibit harmful chaos and guide a useful control has become a hot researcharea and difficulty. This paper studies the extended Duffing-Van der Pol system, MLCcircuit and chaotic behavior of Duffing system, by applying Gauss white noise as arandom phase for these types to inhibit chaotic systems. This control method of randomphase is one of non-feedback control methods, and it is the system of equations adding arandom phase(Gauss white noise) that has weak strength in, based on the changes inaverage maximum Lyapunov exponent sign, anglicizing the effect of random phase ofthe non-linear on dynamic behavior of the system. By the numerical simulation usingMATLAB software, it could find that when the noise level exceeds a critical value, thechaotic system can be effectively inhibited and transformed to non-chaotic systems,where the largest Lyapunov exponent is calculated based on Khasminskii's sphericalcoordinate transformation formula in the random system. Whether the chaotic systems isinhibited is determined by the changes on the sign of average maximum Lyapunovexponent sign. In addition, combination of the phase diagram, the time course ofdiagrams and Poincarésection analysis indicates that this method is effective. This method of random phase with a weak strength to suppress chaos in practice can save a lotof energy, while convenient and simple, with very important practical value.