Biological oscillators: their mathematical analysis.

by Theodosios Pavlidis

Publisher: Academic Press in New York

Written in English
Published: Pages: 207 Downloads: 995
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  • Biological rhythms -- Mathematical models.,
  • Biological control systems -- Mathematical models.,
  • Oscillations.

Edition Notes

Bibliography: p. 187-204.

LC ClassificationsQH527 .P38
The Physical Object
Paginationxiii, 207 p.
Number of Pages207
ID Numbers
Open LibraryOL5293105M
ISBN 100125473508
LC Control Number72013615

Oscillation is the repetitive variation, typically in time, of some measure about a central value (often a point of equilibrium) or between two or more different term vibration is precisely used to describe mechanical oscillation. Familiar examples of oscillation include a swinging pendulum and alternating current.. Oscillations occur not only in mechanical systems . The mathematical analysis of mutual synchronization is a challenging problem. It is difficult enough to analyze the dynamics of a single nonlinear oscillator, let alone a whole population of them. The seminal work in this area is due to Winfree [47]. He simplified the problem by assuming that the oscillators are strongly attracted to their. Mathematical modeling in the biological and medical sciences. Topics will include continuous and discrete dynamical systems describing interacting and structured populations, resource management, biological control, reaction kinetics, biological oscillators and switches, and the dynamics of infectious diseases. Mathematicians who attempt to understand biological oscillators face difficult mathematical questions. "It would be very desirable to start building in a little more reality," Strogatz says. But, as so often happens in mathematics, "one problem may turn out relatively easy to solve, and everything else in every direction around [it] is hard.".

  1. Introduction. The aim of synthetic biology is to design and synthesize biological networks or devices that perform a desired function in a predictable manner (Endy ; Andrianantoandro et al. ; Serrano ; Haseloff & Ajioka ).Achieving this goal requires a combination of in silico and in vivo analysis, and combines approaches from the fields of engineering, mathematics Cited by: Contents are organized into a set of first‐level and a set of advanced‐level topics. The book is rich in examples and includes numerous solved problems. Further topics, such as signal processing and modeling of non-electric physical phenomena (e.g., hysteresis or biological oscillators) will be discussed in volume 2.   This textbook is aimed at newcomers to nonlinear dynamics and chaos, especially students taking a first course in the subject. The presentation stresses analytical methods, concrete examples, and geometric intuition. The theory is developed systematically, starting with first-order differential equations and their bifurcations, followed by phase plane analysis, limit cycles and their 5/5(1). A new technique for calculating signal- to-noise ratio (SNR) for biological rhythms to characterize their precision has yielded support for this hypothesis. SNR of rhythms of the allelic series of mutations at the period (per) locus of Drosophila melanogaster were compared. per 0 was the noisiest, grading through per L, per +, and per s, the Cited by:

Coupled Oscillators and Biological Synchronization SCIENTIFIC AMERICAN December STEVEN H. STROGATZ and IAN STEW ART work in the middle ground between pure and applied mathematics. studying such subjects as chaos and biological os­ cillators. Strogatz is associate professor ofapplied mathematics at the Massachu­ setts Institute File Size: 2MB. With our growing awareness of the complexity underlying biological phenomena, our need for computational models becomes increasingly apparent. Due to their properties, biological clocks have always lent themselves to computational modelling. Their capacity to oscillate without dampening — even when deprived of all rhythmic environmental information — required the Cited by: J. D. Murray, Lectures on Nonlinear Differential-Equation Models in Biology, Oxford U. P., , ix+ pp., index; $ This is a collection of deterministic models of problems which come from the biological sciences, for the most part. The five chapters of the book take up the. thesis begins with a description of observer design, nonlinear control systems analysis, and all mathematical notions used. Each subsequent section discussing the four -neuronal models outlines the biological motivations for each model and the mathematical analysis that follows. 2. MATHEMATICAL NOTIONS MATRIX ANALYSIS 9.

Biological oscillators: their mathematical analysis. by Theodosios Pavlidis Download PDF EPUB FB2

Description. Biological Oscillators: Their Mathematical Analysis introduces the main features of the dynamic properties of biological oscillators and the mathematical techniques necessary for their investigation.

It is not a comprehensive description of all known biological oscillators, since this would require a much bigger volume as well as. Biological Oscillators: Their Mathematical Analysis introduces the main features of the dynamic properties of biological oscillators and the mathematical techniques necessary for their investigation.

It is not a comprehensive description of all known biological oscillators, since this would require a much bigger volume as well as a different type of Book Edition: 1.

Buy Biological Oscillators: Their Mathematical Analysis on FREE SHIPPING on qualified orders Biological Oscillators: Their Mathematical Analysis: Theodosios Pavlidis: : Books. Biological Oscillators: Their Mathematical Analysis introduces the main features of the dynamic properties of biological oscillators and the mathematical techniques necessary for their investigation.

It is not a comprehensive description of all known biological oscillators, since this would require a much bigger volume as well as a different type of expertise. Instead.

Additional Physical Format: Online version: Pavlidis, Theodosios. Biological oscillators: their mathematical analysis. New York, Academic Press, The University of Chicago Press. Books Division.

Chicago Distribution Center. Genre/Form: Electronic books: Additional Physical Format: Print version: Pavlidis, Theodosios. Biological Oscillators: Their Mathematical Analysis. Oxford: Elsevier. This book is a classic. I basically skimmed through this (partly a reflection of a current dificulty with focus and concentration).

This book covers a large number of areas: simple population models, Biological oscillators: their mathematical analysis. book determination in crocodiles, mathematical models of marriage, biological oscillators, diffusion and chemotaxis, wave phenomena in biological systems and finally a Cited by: Biological and Biochemical Oscillators compiles papers on biochemical and biological oscillators from a theoretical and experimental standpoint.

This book discusses the oscillatory behavior, excitability, and propagation phenomena on membranes and membrane-like interfaces; two-dimensional analysis of chemical oscillators; and Biological oscillators: their mathematical analysis.

book in oscillatory oxidation. An introduction to the mathematical, computational, and analytical techniques used for modeling biological rhythms, presenting tools from many disciplines and example applications.

All areas of biology and medicine contain rhythms, and these behaviors are best understood through mathematical tools and techniques. This book offers a survey of mathematical.

Pattern formation Theory. In each topics, we shall derive the biological models, then we do the non- dimensional analysis to reduce the model to a simple model with fewer parameters.

We shall only do the elementary analysis, for example, the linearized stability anal- ysis or heuristic arguement for the models. The book is a textbook (with many exercises) giving an in-depth account of the practical use of mathematical modelling in the biomedical sciences.

The mathematical level required is generally not high and the emphasis is on what is required to solve the real biological /5(9).

Abstract. This paper presents an alternative representation of a system of differential equations qualitatively showing the behavior of the biological rhythm of a crayfish during their transition from juvenile to adult stages. The model focuses on the interaction of four cellular oscillators coupled by diffusion of a hormone, Cited by: 9.

A simple model for synchronous firing of biological oscillators based on Peskin’s model of the cardiac pacemaker [Mathematical aspects of heart physiology, Courant Institute of Mathematical Sciences, New York University, New York,pp. –] is studied. The model consists of a population of identical integrate-and-fire by: Optimal phase control of biological oscillators using augmented phase reduction, by Monga and Moehlis [28], details control algorithms for the optimal control of nonlinear oscillators.

Reconciling mathematical models of biological clocks by averaging on approximate manifolds. SIAM Journal on Applied Mathematics – Forger, D. B., and D. Paydarfar. The milestone here was to consider biological oscillators as phase oscillators, neglecting the amplitude.

Working within the framework of a mean field analysis of synchronization processes has benefited from the advance in the understanding of the topology The mathematical abstraction of a complex network is a graph G comprising a set Cited by: What this book aims to achieve Mathematical modelling is becoming an increasingly valuable tool for molecular cell biology.

Con-sequently, it is important for life scientists to have a background in the relevant mathematical tech-niques, so that they can participate in the construction, analysis, and critique of published Size: 5MB.

Abstract. The circadian rhythmicity of eukaroytic organisms is dictated by an innate program that specifies the time course through the day of many aspects of metabolism and behavior.

The programmed sequence of events in each cycle of the rhythm has been evolved to parallel the sequence of predictable change (physical and biological) Cited by: From cell division to heartbeat, clocklike rhythms pervade the activities of every living organism.

The cycles of life are ultimately biochemical in mechanism but many of the principles that dominate their orchestration are essentially mathematical.

The Geometry of Biological Time describes periodic processes in living systems and their non-living analogues in the abstract. A simple model for synchronous firing of biological oscillators based on Peskin's model of the cardiac pacemaker [Mathematical aspects of heart physiology, Courant Institute of Mathematical.

Abstract. All major organ systems of the body display rhythmic activity. These rhythms interact with one another and with the external environment to provide complex dynamics which underly fundamental life processes.

The point of this presentation is to provide a brief summary of the role of coupled oscillators in normal and pathophysiology Cited by: 7. Biological oscillators can be classified according to the topology of the positive- and negative-feedback loops in the underlying regulatory mechanism. You Cited by: Advances in Mathematical Physics / / Article.

Article Sections. the dynamic properties of biological oscillators, the analysis of single and coupled low-noise microwave oscillators, the Mathieu oscillator, Biological Oscillators: Their Mathematical Analysis, Academic Press, New York, NY, USA and London, Cited by: 1.

Pavlidis has published several books, and numerous articles and papers in leading engineering journals and conference proceedings. He is also a named inventor on 15 U.S. issued patents. Additional aspects of Pavlidis' career may be found in the sidebar of his IAPR mater: UC Berkeley, Athens Polytechnic.

sequence Math A,B,C on Mathematical Models in Biology is an introduction to mathematical modeling and analysis of phenomena in biological sciences accessible to undergraduates.) This dual purpose is made possible for a number of reasons.

A principal aspect of mathematical modeling is to identify the particular issues(s). THIS OFFER IS NOW CLOSED. Mathematical analysis, control design and coupling for models of biological oscillators. Context: Mammalian cells have evolved highly sophisticated intracellular communication pathways to enable their development and growth, under multiple environmental stresses and major cyclic processes are at the basis of cell.

TEXT BOOK ANALYSIS INTRODUCTION This chapter is a comparative analysis of the mathematics textbook used in the different schools surveyed as a part of the research. Textbooks have always been an integral part of is especially true in developing countries where itFile Size: KB. Nonlinear Observer Design and Synchronization Analysis for Classical Models of Neural Oscillators systems perspective by designing nonlinear observers for them and studying their synchronization properties.

The four models are the Hodgkin-Huxley model, the The next section discusses the biological motivation and mathematical analysis of Cited by: 2. Are central pattern generators understandable. Allen I On the nature of the fundamental activity of the nervous centres; together with an analysis of the conditioning of rhythmic activity in progression, and a theory of the evolution of Pavlidis, T.

() Biological Oscillators: Their Mathematical Analysis, pp. New York Cited by:. A dataset of million taxi trips and a new type of mathematical analysis enabled the untapped potential of New York City’s fleet of more t taxis to be quantified.

Synchronization of Pulse-Coupled Biological Oscillators (PDF) – SIAM Journal on and certain chemical reactions. Scroll waves, their three-dimensional cousins.heavily on the strong tools of functional analysis. Numerical approximation of PDEs is a cornerstone of the mathematical modeling since almost all modeled real world problems fail to have analytic solutions or they are not known in the scope of pure mathematics because of their.

The mechanisms which could underlie circadian rhythms fall naturally into groups with qualitatively different responses to disruption. Experiments designed to distinguish between these mechanisms Cited by: