Some Problems In The Research On Chaos Theory And Its Application

Intermittency as a route to chaos is one important research field of chaotic theory. Chaos is a new interdisciplinary subject, and its application research is of far-reaching significance. The application of chaos in communication field is one of its important applications. Besides, the study of chaos in Bioinformatics is still in the primary stage. With regard to these three aspects, much more research work is needed.The paper is mainly concerned with design and analysis of on-off intermittent chaotic system models, application research of chaos in digital fountain coding technology and analysis of chaotic properties of DNA sequences. The main work and conclusions are as follows:1. Propose a new method of designing on-off intermittent system model. Design a class of five-dimensional continuous on-off intermittent systems with simple drive-response structure. By calculating the transverse Lyapunove exponent, the parameter conditions for the onset of on-off intermittency are found. After blowout bifurcations one-state and two-state on-off intermittency are observed in the systems, and on the other side of the bifurcation, intermingled basins are observed. The statistical properties of the intermittency are in accord with those of on-off intermittency. The simulation results verify the feasibility of the proposed design method.By changing coupling coefficient, we observe hyperchaos-chaos-hyperchaos transition in the on-off intermittent systems driven by Generalized Lorenz system. It is found that the transition is caused by blowout bifurcation. This finding provides a possible route to hyperchaos in this class of on-off intermittent systems.2. Apply chaos in the digital fountain codes, which is in the transport and application layer of communication network. An encoding and decoding algorithm of LT codes based on Kent chaotic map is proposed. In the encoding process, we use the randomness and ergodic properties of chaotic sequence to determine degree value and neighbors of each encoding packet. The performance of LT codes based on chaos is compared with that of LT codes implemented with standard pseudorandom number generator in C programming language. It is found that LT codes based on chaos have better performance.In order to improve the performance of LT codes, we propose an improved Robust Soliton distribution of LT codes and compare it with original degree distribution and an optimized degree distribution. Simulation results show that the improved Robust Soliton distribution can perform as well as the original distribution. Mover, it can greatly reduce the operations in the decoding.3. Investigate the existence of low-dimensional deterministic chaos in the AT and GC skew profiles of DNA sequences. We take DNA sequence samples from Archaea, Bacteria, Plants and Animals, each kind with two typical samples. The skew profiles are denoised using continuous wavelet transform method and then are analyzed using phase space reconstruction method. The invariant measures of correlation dimension and the largest Lyapunov exponent of these DNA skew profiles are calculated. It is demonstrated that the AT and GC skew profiles of these DNA sequences all exhibit low dimensional chaotic behavior. We suggest that chaotic properties may be ubiquitous in the DNA sequences of all organisms.