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Investigation of the behaviour and development of theory associated with chaotic and complex signals from simple non-linear discrete-time systems. Particular emphasis is upon overflow oscillations in recursive digital filters. The research is directed towards applications in signal processing and communications, especially for pseudorandom sequence generation and coding. Progress:Theoretical investigations and simulations of overflow oscillations have been carried out, and supporting software tools developed. With these tools the oscillations can be simulated and analysed efficiently for all parameter values of a second-order digital filter including specification of the signal wordlength. This supports a deeper investigation, extending previously published work. In parallel investigation of pseudo-random sequence generators has been carried out and we hope the theory will be applicable to the study of finite signal wordlength effects.Collaboration has continued with a group in Dresden, resulting in annual international workshops on non-linear dynamics in electronic systems (NDES), a jointly edited book and several publications. Papers were presented at IEEE ISCAS94 (London, June 1994) and NDES94 (Krak3/4w, Poland, July 1994).Arising from the work at Kings College a paper and a proposal for a one-day tutorial for the IEEE ISCAS95 (Seattle) was submitted. The tutorial proposal (which includes contributions from colleagues in Dresden and Lausanne) was accepted and is currently under development. A paper will be submitted to NDES95 (Dublin, July 1995). An invited paper has been written for a special issue (on Chaos in electronic systems) of the Royal Society Phil. Trans. A. Problems remain to be solved but we believe that the work done so far has made a useful advance in this field of research and that we have laid a good foundation for future progress. Publications so far include the following: Chaotic signals generated by digital-filter overflow ,in Proc. ISCAS94, London, England, pp 6.17-6.20. Nonlinear Dynamics of Electronic Systems , World Scientific, 1994. (book of extended versions of papers presented at NDES93 in Dresden). Digital-filter overflow - explaining the fractal , Proc. NDES94, Krak3/4w, Poland, pp 73-78. Noise-generators with adjustable spectra based on Discrete-time maps ,Proc. NDES94, Krak3/4w, Poland, pp85-90. Generating pseudochaotic number sequences , Proc. NDES94, Krak3/4w, Poland, pp197-202. Two Stream Ciphers ,Springer Verlag, Lecture Notes in Computer Science, 1994, pp. 51-55. On Random Mappings and Random permutations ,1994 Leuven Algorithms Workshop, K. U. Leuven, Belgium.
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