1980 Preface * 1999 Preface * 1999 Acknowledgements * Introduction * 1 Circular Logic * 2 Phase Singularities (Screwy Results of Circular Logic) * 3 The Rules of the Ring * 4 Ring Populations * 5 Getting Off the Ring * 6 Attracting Cycles and Isochrons * 7 Measuring the Trajectories of a Circadian Clock * 8 Populations of Attractor Cycle Oscillators * 9 Excitable Kinetics and Excitable Media * 10 The Varieties of Phaseless Experience: In Which the Geometrical Orderliness of Rhythmic Organization Breaks Down in Diverse Ways * 11 The Firefly Machine 12 Energy Metabolism in Cells * 13 The Malonic Acid Reagent ('Sodium Geometrate') * 14 Electrical Rhythmicity and Excitability in Cell Membranes * 15 The Aggregation of Slime Mold Amoebae * 16 Numerical Organizing Centers * 17 Electrical Singular Filaments in the Heart Wall * 18 Pattern Formation in the Fungi * 19 Circadian Rhythms in General * 20 The Circadian Clocks of Insect Eclosion * 21 The Flower of Kalanchoe * 22 The Cell Mitotic Cycle * 23 The Female Cycle * References * Index of Names * Index of Subjects

https://www.cambridge.org/core/services/aop-cambridge-core/content/view/596B270197FE27DE5FABB598B6210622/S0025557200150892a.pdf/div-class-title-span-class-italic-the-geometry-of-biological-time-span-by-a-t-winfree-pp-544-dm68-corrected-second-printing-1990-isbn-3-540-52528-9-springer-div.pdf

The geometry of biological time , by A. T. Winfree. Pp 544. DM68. Corrected Second Printing 1990. ISBN 3-540-52528-9 (Springer)

We explore in this chapter questions of existence and uniqueness for solutions to stochastic differential equations and offer a study of their properties. This endeavor is really a study of diffusion processes. Loosely speaking, the term diffusion is attributed to a Markov process which has continuous sample paths and can be characterized in terms of its infinitesimal generator.

Stochastic Differential Equations

The objective of this paper is to give a comprehensive introduction to applied cryptography with an engineer or computer scientist in mind. The emphasis is on the knowledge needed to create practical systems which supports integrity, confidentiality, or authenticity. Topics covered includes an introduction to the concepts in cryptography, attacks against cryptographic systems, key use and handling, random bit generation, encryption modes, and message authentication codes. Recommendations on algorithms and further reading is given in the end of the paper. This paper should make the reader able to build, understand and evaluate system descriptions and designs based on the cryptographic components described in the paper.

[서평]「Applied Cryptography」

Differential-Difference Equations. By Richard Bellman and Kenneth L. Cooke. Pp. xvi, 465. 1963. (Academic Press)

In recent years, a large amount of work on chaos-based cryptosystems have been published. However, many of the proposed schemes fail to explain or do not possess a number of features that are fundamentally important to all kind of cryptosystems. As a result, many proposed systems are difficult to implement in practice with a reasonable degree of security. Likewise, they are seldom accompanied by a thorough security analysis. Consequently, it is difficult for other researchers and end users to evaluate their security and performance. This work is intended to provide a common framework of basic guidelines that, if followed, could benefit every new cryptosystem. The suggested guidelines address three main issues: implementation, key management and security analysis, aiming at assisting designers of new cryptosystems to present their work in a more systematic and rigorous way to fulfill some basic cryptographic requirements. Meanwhile, several recommendations are made regarding some practical aspects of analog chaos-based secure communications, such as channel noise, limited bandwith and attenuation.

/pdf/some-basic-cryptographic-requirements-for-chaos-based-4qsyrod8nl.pdf

Some basic cryptographic requirements for chaos-based cryptosystems

With the increasing interest and emphasis on customer demands in e-commerce, customer classification is in a crucial position for the development of e-commerce in response to the growing complexity in Internet commerce logistical markets. As such, it is highly desired to have a systematic system for extracting customer features effectively, and subsequently, analyzing customer orientations quantitatively. This paper presents a new approach that employs a modified fuzzy neural network based on adaptive resonance theory to group users dynamically based on their Web access patterns. Such a customer clustering method should be performed prior to Internet bookstores as the basis to provide personalized service. The experimental results of this clustering technique show the promise of our system.

Applying modified fuzzy neural network to customer classification of e-business

Most of existing optical color image encryption schemes have born security risks due to the adoption of linear transform, and data redundancy for the generation of complex image. To settle these problems effectively, a self-adaptive scheme for double color-image encryption is proposed in this paper. In this scheme, each RGB color component of two secret color images is first compressed and encrypted by 2D compressive sensing (CS) in which measurement matrices are generated by compound chaotic systems. Then, the two measured images are regarded as the real part and imaginary part, constituting a complex image to reduce data redundancy caused by following optical encryption. In the end, the complex image is reencrypted by self-adaptive random phase encoding and discrete fractional random transform (DFrRT) to obtain the final encrypted data. In the process of DFrRT and random phase encoding, the correlations between R, G, B components are adequately utilized. The production of key streams not only depends on the initial value but also on plain-text, and the three color components affect each other to enhance the ability against the known plaintext attack. The projection neural network algorithm is adopted to obtain the decryption images. Simulation results also verify the validity and security of the proposed method.

A self-adaptive scheme for double color-image encryption

Publisher's Note: Time-varying linear and nonlinear parametric model for Granger causality analysis [Phys. Rev. E 85, 041906 (2012)]

In this paper, we propose a novel feedback block chaotic cipher algorithm (FBCCA) based on the chaotic time-delay neuron system and feistel network. The inherent features of chaotic system make the cryptosystem more complex and more difficult to be analyzed or predicted. In FBCCA, the output ciphertext block corresponding to the current input plaintext block is fed back into the generation process of the number of round, which will be used for encrypting the next plaintext block. Furthermore, the round numbers (times iterated for each block) and the sequence number of S-box (used in each round) have a closely relationship with the secret key, and both are dynamically generated by chaotic system. The results of computer simulation experiments show that the proposed cipher has excellent cryptographic properties, i.e., the cipher is very sensitive with respect to the slight change of the plaintext and the secret key, and the randomicity of the ciphertext is very ideal. At last, the security of the algorithm is studied, and the results indicate that the algorithm possesses higher capability of resisting the brute-force attack. Some further studies are also suggested in this paper.

A Novel Feedback Block Cipher Based on the Chaotic Time-Delay Neuron System and Feistel Network

In this paper, we propose an observer-based synchronization scheme for piecewise-linear discrete chaotic systems based on piecewise quadratic Lyapunov functions. Firstly, due to the properties of piecewise-linear discrete chaotic systems, we use a switching observer for state synchronization. Then, we derive a sufficient condition represented by linear matrix inequalities (LMIs) for global asymptotic synchronization. Finally, we give some numerical simulations to demonstrate the effectiveness of our theoretical results.

Xiaofeng Liao

Papers

Applying modified fuzzy neural network to customer classification of e-business

A self-adaptive scheme for double color-image encryption

Publisher's Note: Time-varying linear and nonlinear parametric model for Granger causality analysis [Phys. Rev. E 85, 041906 (2012)]

A Novel Feedback Block Cipher Based on the Chaotic Time-Delay Neuron System and Feistel Network

Observer-based synchronization for piecewise-linear discrete chaotic systems based on piecewise quadratic lyapunov functions