Impulsive Mathematical Models of Endocrine Regulation demonstrates recently-developed mathematical models portraying pulse-modulated regulation in endocrine systems, taking a pragmatic engineering stance by starting with the necessary theoretical background on analytical tools, progressing through a number of mathematical models of increasing complexity, and illustrating the feasibility and fidelity of the mathematical constructs on actual biological data. Compared to a commonplace, theory-oriented book on dynamical systems and control which typically presents a group of design or analysis techniques, the book originates from a real-life problem of fundamental value and introduces mathematical tools that have specifically been devised to solve it.
- Presents results on impulsive mathematical models of endocrine regulation in a systematic, comprehensive and accessible manner
- Introduces researchers and engineers specializing in dynamical systems to a rapidly-growing topic
- Provides biomedical engineering and biological researchers with mathematical modeling and analysis tools for continuous systems using episodic feedback exemplified by non-basal endocrine regulation
Researchers in biomedical engineering, biomathematics, biomedical control, and signal processing
Chapter 1: Endocrine Regulation
1.1 Biological Facts
1.2 Mathematical Mdoels
Chapter 2: Mathematical Grounds
2.1 Impulsive Differential Equations
2.2 Hereditary Impulsive Differential Equations
2.3 Bifurcation Analysis of Impulsive Systems
Chapter 3: Bifurcations and Nonlinear Phenomena in Impulsive Models of Endocrine Regulation
3.1 Nonlinear Phenomena in the Impulsive Goodwin’s Oscillator with Small and Without Time Delays
3.2 Quasiperiodicity, Border-Collision and Multistability in the Impulsive Goodwin’s Oscillator with a Large Time Delay
3.3 Hidden Attractors and Quasiperiodic Period-Doubling the Impulsive Goodwin’s Oscillator with an Arbitrary Time Delay
3.4 Bifurcation Phenomena and Mode-locking Dynamics for the Periodically Forced Impulsive Goodwin’s Oscillator
Chapter 4: Applications
4.1 State Estimation
4.2 Parameter Estimation
- No. of pages:
- © Academic Press 2020
- 1st November 2019
- Academic Press
- Paperback ISBN:
Alexander Medvedev is currently a professor in Control Engineering and the program director for Automatic Control at Uppsala University. He received his M. Sc. in Automatic and Remote Control, followed by his Ph. D. in Control Engineering, from Leningrad Electrical Engineering Institute. Dr. Medvedev has been a recipient of numerous awards, including Best Paper Awards from The First International Conference on Smart Portable, Wearable, Implantable, and Disability-Oriented Devices and Systems (June 2015) and the IEEE-sponsored 6th International Congress on Ultra Modern Telecommunications and Control Systems (October 2014). He is an editorial board member for EURASIP Journal on Signal Processing and Bioinformatics, and has contributed to over 240 peer-reviewed journal and conference papers.
Professor, Director of Program in Automatic Control, Uppsala University, Sweden
Alexander N. Churilov is currently a professor of Theoretical Cybernetics at St. Petersburg State University, as well as a professor of Computer Science at St. Petersburg Marine Technical University. He received his M. Sc. in Mathematics and later his Ph. D. in Mathematical Cybernetics from Leningrad State University. He also received his Doctor of Sciences in mathematical cybernetics and mathematical modeling from St. Petersburg State University. Dr. Churilov is a member of the International Physics and Control Society and the St. Petersburg Informatics and Control Society. He has published four books and hundreds of papers on mathematical modeling. His research areas include nonlinear control systems, impulsive control systems, stability, and oscillations.
Professor of Theoretical Cybernetics, St. Petersburg State University, St. Petersburg, Russia
Zhanybai T. Zhusubaliyev is currently a professor of Computer Science and the Head of the Nonlinear Dynamical System Group at Southwest State University. He received his M. Sc. in Computer Science and later his Ph. D. in Electrotechnical Systems from Tomsk State Politechnical University. Dr. Zhusubaliyev is a member of the International Physics and Control Society and the Italian Society for Chaos and Complexity, and also serves as Associate Editor of Dynamical Systems for Frontiers in Applied Mathematics and Sciences. He has written four books including Bifurcations and Chaos in Piecewise-Smooth Dynamical Systems and his research interests include mathematical modeling, bifurcations, and nonlinear dynamics.
Professor, Department of Computer Science, Southwest State University, Kursk, Russia