Generic Characteristics Analysis Of Chaotic Neural Networks And Their Application In Pattern Recognition And Cryptosystems

Chaos plays an important role in human brain function. Researchers have confirmed that human brain rhythms can switch between chaos and order. The classical neural networks are not able to simulate such evolution. Recently, Chaotic Neural Networks (CNNs) are utilized to mimic such brain behavior. The theory of CNNs has been extensively studied in the last two decades. Compared to classical Neural Networks (NNs), CNNs have fixed point attractors, periodic attractors and strange attractors. Due to these special properties, CNNs have been widely used in artificial intelligence, information security, massive storage, intelligent search and optimization. The current studies of CNNs mainly focus on the analysis of chaotic neurons'properties, network dynamic behaviors and its applications. However, the fundamental problem associated with current CNNs and other NNs is the fully connected topology, which implies quadratic computational requirement. In this thesis, we give a deep insight of the generic characteristics, topology structure and potential applications of CNNs. The main contributions of this thesis can be summarized as following:(1) The author analyzes the dynamic properties of the Adachi chaotic neurons and the Adachi Neural Network (AdNN). How the control parameters affect the Adachi neurons'bifurcation is also well illustrated. According to Lyapunov Exponent (LE) analysis, we figure out that all the LEs of the AdNN are negative, which implies the dynamic properties of the AdNN are not strictly"chaotic". Besides, by experimental analysis, we demonstrate the Associative Memory (AM) and Pattern Recognition (PR) properties of the AdNN in various conditions. All these results are not found in other relevant articles. To the best of our knowledge, the conclusions given in this thesis are novel. Some of the achievements can be found in my paper [1], which is EI indexed. (Accession number: 20090511877722)(2) The author proposes four novel CNNs with lower connection complexity. Based on the AdNN, by means of maximum spanning tree, random graph, small-world network, scale-free network and gradient search, we construct four CNNs named Linear-Adachi, Random-Adachi, Small-World Adachi and ScaleFree-Adachi respectively. The connection complexity of these new CNNs are much lower than O ( N 2). To be more precise, the Linear-Adachi has only N -1 edges. The distribution of the degrees of a single Random-Adachi neuron and SmallWorld-Adachi neuron satisfies Poisson distribution. Therefore, compared to the orginal AdNN, all these new networks have lower computational burden and more powerful PR properties. Some of the achievements have been published in IEEE trans NN [2] and chaotic system [3].(3) The author puts forward a novel Logistic NN (LNN) based on the discrete Hopfield network and Logistic map. The dynamic property of the LNN is also analyzed by LE calculation. By experimental results, we prove the LNN has powerful Chaotic PR properties. To be more specific, when stimulated by a known pattern, the internal states of the LNN are more"ordered". On the contrary, when stimulated by an unknown pattern, the LNN is more"chaotic". The switch between order and chaos can lead to a new model of PR. Partial of the results can be found in [4], which will be EI indexed.(4) The author points out some severe security issues of current chaotic based cryptosystems. Considering some special requirments of secure multicast applications, we propose two multicast key management schemes based on Chebyshev polynomial and Jacobian Elliptic Rational Map respectively. The security and performance analysis of both the schemes are also discussed deeply. Some of the results can be found in my paper [5, 6, 7, 8], where [5] is EI indexed (Accession number: 20080411054447) and [6] will be EI indexed.(5) The author gives an insight of some CNNs-based cryptosystems, and then figure out the encryption algorithm based on the Chebyshev neural network is not as secure as it is announced since any attacker is able to decrypt the cipher-text by network synchronization. The message authentication algorithm based on CNN is not secure neither since attackers can possibly find some collisions. In addition, the network output is not sensitive to the key or the plain text in some cases. The encryption algorithm based on delayed chaotic neural network is also vulnerable. Attackers can decrypt partial plaintext without knowing any network parameters. Considering the weaknesses of all above algorithms, this thesis gives some remedial measures to enhance the security level. As far as we know, these analysis given here are novel.