Study On Chaotic Measuring Of Signals

Chaotic system has initial-conditions-sensitivity and parameters-sensitivity,and can be used to detect or measure weak signals. But it is unstable and it is also sensitive to noise,reducing noise is the key step in measuring procedure. This problem is solved in this paper by coupled several measuring systems. Meanwhile,we use a simple nonlinear circuit for decreasing the complexity of chaotic measuring system and use symbolic dynamics for simplifying analysis on the system.The idea to reduce the noise with coupling the measuring systems was from the chaos synchronization. In suitable coupling intensity,coupled chaotic systems can be synchronized,so we think that synchronizing is the procedure of coupled trajectories attracting and coinciding each other at last. Two initial conditions,measured by coupled two trajectories,may be confined tightly and do not diverge over initial noise distortion,this point is useful for chaotic measuring. We studied the synchronizable property of our chaotic measuring system,established the equations of coupled two subsystems and three subsystems respectively,analyzed the synchronizing process and synchronization stability on the basis of symbolic dynamics. Theoretical analysis and numerical simulations show that the chaotic measuring systems can be synchronized stably.Whether two coupled chaotic measuring systems can reduce noise or not,we carried out the following simulations in four situations:(1) noise only in starting point,no noise elsewhere in trajectories,(2)noise only in somewhere on trajectories,elsewhere no noise,(3) coupling intensity change,noise only in initial point,(4) system parameters fluctuation,noise only in initial point. The noise-reduction effect was observed in all cases.Comparing the results from coupled three circuits with coupled two circuits,it is discovered that the error in the former is smaller than that in the latter. Namely,the former has the stronger noise-reduction function.Extended measuring system to coupled N units,firstly,we investigated the trajectory distance between unit one and unit two in coupled many units with units number increasing,secondly,we tested the statistical properties of the initial conditions recovery from the coupled Logistic map lattices. Gaussian white noise as the initial signals and no noise in mapping,simulations show that the mean of the recovered signals equals that of the given,and the variance of the former is smaller than that of the latter. In the same coupling coefficient,the global coupling model has the smaller variance than local coupling. Following this,we tested the statistical properties of the initial conditions recovery from the coupled chaotic measuring system lattices,some results are the similar to the former case. All tests indicate noise-reduction is effective in coupled TV systems.These achievements are preliminary,but they are heuristic. Use single system to measure many times is to sample the stochastic process in time dimension. Here we use N coupled units to measure is to sample the stochastic process in space dimension or ensemble,and this sampling is not independent,but data processing is independent. This is a new measurement model.A single neuron or a small ensemble of neurons is known to exhibit chaotic behaviors. Biological neural systems are complex coupled chaotic systems. Our model may be model these systems. In some situations,one must solve reverse problem,our model can be taken as reference.