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Biomathematics. Biometry. Biostatistics --- Mathematical statistics --- Biomembranes

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Biological Transport --- Cell Membrane Permeability --- Ions --- metabolism

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This book shows how densities arise in simple deterministic systems. Recently there has been explosive growth in interest in physical, biological, and economic systems that can be profitably studied using densities. Due to the inaccessibility of the mathematical literature there has been little diffusion of the applicable mathematics into the study of these 'chaotic' systems. This book will help to bridge that gap. The authors give a unified treatment of a variety of mathematical systems generating densities, ranging from one-dimensional discrete time transformations through continuous time systems described by integro-partial differential equations. They have drawn examples from many scientific fields to illustrate the utility of the techniques presented. The book assumes a knowledge of advanced calculus and differential equations, but basic concepts from measure theory, ergodic theory, the geometry of manifolds, partial differential equations, probability theory and Markov processes, and stochastic integrals and differential equations are introduced as needed.

System analysis --- Probabilities --- Analyse de systèmes --- Probabilités --- 519.2 --- 517.9 --- 519.7 --- #KVIV --- Network theory --- Systems analysis --- System theory --- Mathematical optimization --- Probability --- Statistical inference --- Combinations --- Mathematics --- Chance --- Least squares --- Mathematical statistics --- Risk --- Probability. Mathematical statistics --- Differential equations. Integral equations. Other functional equations. Finite differences. Calculus of variations. Functional analysis --- Mathematical cybernetics --- Probabilities. --- System analysis. --- 519.7 Mathematical cybernetics --- 517.9 Differential equations. Integral equations. Other functional equations. Finite differences. Calculus of variations. Functional analysis --- 519.2 Probability. Mathematical statistics --- Analyse de systèmes --- Probabilités --- Network analysis --- Network science --- Analyse globale (mathématiques) --- Analyse stochastique --- Systèmes dynamiques

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In an important new contribution to the literature of chaos, two distinguished researchers in the field of physiology probe central theoretical questions about physiological rhythms. Topics discussed include: How are rhythms generated? How do they start and stop? What are the effects of perturbation of the rhythms? How are oscillations organized in space? Leon Glass and Michael Mackey address an audience of biological scientists, physicians, physical scientists, and mathematicians, but the work assumes no knowledge of advanced mathematics. Variation of rhythms outside normal limits, or appearance of new rhythms where none existed previously, are associated with disease. One of the most interesting features of the book is that it makes a start at explaining "dynamical diseases" that are not the result of infection by pathogens but that stem from abnormalities in the timing of essential functions. From Clocks to Chaos provides a firm foundation for understanding dynamic processes in physiology.

Biological rhythms --- Biological rhythms. --- Mathematics. --- AV block. --- Cantor function. --- GABA receptors. --- Hodgkin-Huxley equations. --- Liapunov number. --- Parkinsonian tremor. --- accessory pathways. --- alternans. --- bistability. --- blood vessel rhythms. --- cardiac rhythm. --- circle map. --- depolarization. --- differential equations. --- dynamical diseases. --- electrocardiogram. --- equilibrium points. --- fibrillation. --- fictive locomotion. --- graphical iteration. --- hyperventilation. --- insulin administration. --- lamprey locomotion. --- mechanical ventilation. --- mutual inhibition. --- neuromuscular junction. --- organizing centers. --- quadratic map. --- refractory period. --- sequential disinhibition. --- tachycardia. --- vagus nerve.

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This book shows how densities arise in simple deterministic systems. There has been explosive growth in interest in physical, biological and economic systems that can be profitably studied using densities. Due to the inaccessibility of the mathematical literature there has been little diffusion of the applicable mathematics into the study of these 'chaotic' systems. This book will help to bridge that gap. The authors give a unified treatment of a variety of mathematical systems generating densities, ranging from one-dimensional discrete time transformations through continuous time systems described by integro-partial differential equations. They have drawn examples from many scientific fields to illustrate the utility of the techniques presented. The book assumes a knowledge of advanced calculus and differential equations, but basic concepts from measure theory, ergodic theory, the geometry of manifolds, partial differential equations, probability theory and Markov processes, and stochastic integrals and differential equations are introduced as needed.

System analysis. --- Probabilities.