The research on chaos characteristic in a deformable Lorenz system

Based on Lorenz chaos system, a deformable Lorenz system is constructed by adding cycle motive power signals.The validity of Melnikov’s method in the generalized Hamilton proves that deformable Lorenz system has a deformation transformation in the sense of Smale chaos. The deformable Lorenz system is further proved that it has dynamical behavior, such as power spectrum, Lyapunov exponents pectrum, Poincare mapping.The deformable Lorenz chaotic system has two kinds of states, chaos state and class period state. When the system is in the critical state a small perturbation of the system parameters may lead to the qualitative change of the system state,making the maximum Lyapunov exponent from positive to negative.The simulation experiences show that the deformable Lorenz chaotic system is sensitive to weak periodic signals and this system can effectively restrain the strong noise,at the same time, the properties of which demonstrate their potential application in weak signal detection. The deformable chaotic system can detect weak periodic signals in strong noise effectively and automatically. The deformable Lorenz system has a stable working-detection limit of-29dB.If deformable Lorenz system further optimizes parameters of system,still can continue to reduce signal-to-noise ratio Lower limit.