Binary Periodic Signals and Flows


Series: Mathematics Research Developments
BISAC: MAT003000

The signals from digital electrical engineering are modeled by discrete time and real time functions, whose values are binary n-tuples and which are also called signals. The asynchronous circuits, representing the devices that work with such signals, are modeled by Boolean autonomous deterministic regular asynchronous systems, shortly by asynchronous flows. The attribute ‘Boolean’ vaguely refers to the binary Boole algebra; ‘autonomous’ means that there is no input; ‘deterministic’ means the existence of a unique state function; and ‘regular’ indicates the existence of a Boolean function that iterates its coordinates independently on each other (i.e. asynchronously). Strong analogies exist with the real, usual dynamical systems.

The purpose of this research monograph is to study the periodicity of the signals and of their values, as well as the periodicity of the asynchronous flows. The monograph addresses systems theory and computer science that apply to researchers, but it is also interesting to those that study periodicity itself. From this last perspective, the signals may be thought of as functions with finitely many values. At the same time, the asynchronous flows may be considered as special cases of variable structure systems.

The bibliography consists of works of real, dynamical systems that produce analogies. (Imprint: Nova)

Table of Contents

Table of Contents


Chapter 1. Preliminaries

Chapter 2. The Main Definitions on Periodicity

Chapter 3. Eventually Constant Signals

Chapter 4. Constant Signals

Chapter 5. Eventually Periodic Points

Chapter 6. Eventually Periodic Signals

Chapter 7. Periodic Points

Chapter 8. Periodic Signals

Chapter 9. Examples

Chapter 10. Computation Functions

Chapter 11. Flows

Chapter 12. A Wider Point of View: Control and Systems

Chapter 13. Eventually Constant Flows

Chapter 14. Constant Flows

Chapter 15. The Periodicity of the Flows


Appendix A. Notations

Appendix B. Index

Appendix C. Lemmas


[1] Dmitri V. Anosov, Vladimir I. Arnold (Eds.), ”Dynamical systems I”, Springer-Verlag, Berlin, (1988).

[2] David K. Arrowsmith, C. M. Place, ”An introduction to dynamical systems”, Cambridge University Press, New York, (1990).[3] Michael Brin, Garrett Stuck, ”Introduction to dynamical systems”, Cambridge University Press, New York, (2002).[4] Constant¸a-Dana Constantinescu, ”Haos, factali s¸i aplicat¸ii”, editura Flower Power, Pites¸ti, (2003).[5] Robert L. Devaney, ”A first course in chaotic dynamical systems. Theory and experiment”, Perseus Books Publishing, (1992).[6] Robert W. Easton, ”Geometric methods in discrete dynamical systems”, Oxford University Press, (1998).[7] Adelina Georgescu, MihneaMoroianu, Iuliana Oprea, ”Teoria Bifurcat¸iei, Principii s¸i Aplicat¸ii”, editura Universit˘at¸ii din Pites¸ti, Pites¸ti, (1999).[8] Boris Hasselblatt, Anatole Katok, ”Handbook of dynamical systems”, Volume 1, Elsevier, (2005).[9] Richard A. Holmgren, ”A first course in discrete dynamical systems”, Springer-Verlag, New York, (1994).[10] Jurgen Jost, ”Dynamical systems. Examples of complex behaviour”, Springer-Verlag, Berlin, Heidelberg, (2005).[11] Rudolf E. Kalman, Peter L. Falb, Michael A. Arbib, ”Teoria sistemelor dinamice”, Editura tehnic˘a, Bucures¸ti, (1975).[12] Yuri A. Kuznetsov, ”Elements of Applied Bifurcation Theory”, Second Edition, Springer, New York, (1997).[13] Mihaela Sterpu, ”Dinamic˘a s¸i bifurcat¸ie pentru dou˘amodele van der Pol generalizate”, editura Universit˘at¸ii din Pites¸ti, Pites¸ti, (2001).[14] Mariana P. Trifan, ”Dinamic˘a s¸i bifurcat¸ie ˆın studiulmatematic al cancerului”, editura P˘amˆantul, Pites¸ti, (2006).[15] Ivan Tyukin, ”Adaptation in dynamical systems”, Cambridge University Press, Cambridge, New York, (2011).[16] Serban E. Vlad, Boolean dynamical systems, ROMAI Journal, vol. 3, Nr. 2, 277-324, (2007).[17] Serban E. Vlad, Universal Regular Autonomous Asynchronous Systems: Fixed Points, Equivalencies and Dynamical Bifurcations, ROMAI Journal, vol. 5, Nr. 1, 131-154, (2009).[18] Serban E. Vlad, ”Asynchronous systems theory”, second edition, LAP LAMBERT Academic Publishing, Saarbrucken, (2012).[19] Serban E. Vlad, Eventually periodic points of the binary signals: definition, accessibility and limit of periodicity, ROMAI Journal, vol. 10, Nr. 2, 213-224, (2014).[20] Serban E. Vlad, Binary signals: the set of the periods of a periodic point, Buletinul Institutului Politehnic din Ias¸i, Sect¸ia Matematic˘a. Mecanic˘a teoretic˘a. Fizic˘a, Tomul LX (LXIV), Fasc. 4, 23-30, (2014). [21] Serban E. Vlad, The double eventual periodicity of the asynchronous flows, Proceedings of the Third Conference of Mathematical Society of Moldova IMCS-50, August 19-23, Chis¸in˘au, Republic of Moldova, (2014). [22] Serban E. Vlad, Binary signals: necessary and sufficient conditions of periodicity of a point, Analele Universit ˘at¸ii din Oradea, Fascicola Matematic˘a, TOMXXII, Issue No. 1, 23-31, (2015).[23] Stephen Wiggins, ”Introduction to Applied Nonlinear Dynamical Systems and Chaos”, Second Edition, Springer, New York, (2003).

The monograph addresses systems theory and computer science that apply to researchers, but it is also interesting to those that study periodicity itself.

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