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Register a new userDynamic Separation of Chaotic Signals in the Presence of Noise
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The problem of separation of an observed sum of chaotic signals into the individual components in the presence of noise on the path to the observer is considered. A noise threshold is found above which high-quality separation is impossible. Below the threshold, each signal is recovered with any prescribed accuracy. This effect is shown to be associated with the information content of the chaotic signals and a theoretical estimate is given for the threshold.
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Various phonemes are considered in terms of nonlinear dynamics. Phase portraits of the signals in the embedded space, correlation dimension estimate and the largest Lyapunov exponent are analyzed. It is shown that the speech signals have comparatively small dimension and the positive largest Lyapunov exponent
Chaos is associated with stochasticity, complex, irregular motion, etc. It has some peculiar properties such as ergodicity, highly initial value sensitivity, non-periodicity and long-term unpredictability. These pseudo random features lead chaotic systems to enormous applications such as random number generator, image encryption and secure communication. In general, the concept of chaos is never associated with similarity. However, we found the chaotic systems belonging to one chaos family (OCF) have similar dynamic behavior, which is a novel characteristic of chaos. In this work, three classical chaotic system family are studied, which are Lorenz family, Chua family and hyperbolic sine family. These systems contain different derived chaotic systems (Lorenz system, Chen system and Lu system), different order chaotic systems (Chua family and hyperbolic sine family), and different kinds of chaotic systems (chaos and hyper-chaos). Their PSPs demonstrate that there exist strong correlation in OCF. Moreover, we found that high order/dimensional chaotic systems will inherit all dynamic behavior of lower ones, and the similarity will decrease as the order/dimensional goes higher, which is analogous to genetic process in biology. All of these features are quantitatively evaluated by PPMCC and SSIM.
The noise-enhanced trapping is a surprising phenomenon that has already been studied in chaotic scattering problems where the noise affects the physical variables but not the parameters of the system. Following this research, in this work we provide strong numerical evidence to show that an additional mechanism that enhances the trapping arises when the noise influences the energy of the system. For this purpose, we have included a source of Gaussian white noise in the Henon-Heiles system, which is a paradigmatic example of open Hamiltonian system. For a particular value of the noise intensity, some trajectories decrease their energy due to the stochastic fluctuations. This drop in energy allows the particles to spend very long transients in the scattering region, increasing their average escape times. This result, together with the previously studied mechanisms, points out the generality of the noise-enhanced trapping in chaotic scattering problems.
Giant Random Telegraph Noise (RTN) in the resistance fluctuation of a macroscopic film of perovskite-type manganese oxide La2/3Ca1/3MnO3 has been observed at various temperatures ranging from 4K to 170K, well below the Curie temperature (TC = 210K). The amplitudes of the two-level-fluctuations (TLF) vary from 0.01% to 0.2%. We use a statistical analysis of the life-times of the TLF to gain insight into the microscopic electronic and magnetic state of this manganite. At low temperature (below 30K) The TLF is well described by a thermally activated two-level model. An estimate of the energy difference between the two states is inferred. At higher temperature (between 60K and 170K) we observed critical effects of the temperature on the life-times of the TLF. We discuss this peculiar temperature dependence in terms of a sharp change in the free energy functional of the fluctuators. We attribute the origin of the RTN to be a dynamic mixed-phase percolative conduction process, where manganese clusters switch back and forth between two phases that differ in their conductivity and magnetization.
This paper deals with two types of synchronous behavior of chaotic oscillators -- generalized synchronization and noise--induced synchronization. It has been shown that both these types of synchronization are caused by similar mechanisms and should be considered as the same type of the chaotic oscillator behavior. The mechanisms resulting in the generalized synchronization are mostly similar to ones taking place in the case of the noise-induced synchronization with biased noise.
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