Devoted to local and global analysis of weakly connected systems with applications to neurosciences, this book uses bifurcation theory and canonical models as the major tools of analysis. It presents a systematic and well motivated development of both weakly connected system theory and mathematical neuroscience, addressing bifurcations in neuron and brain dynamics, synaptic organisations of the brain, and the nature of neural codes. The authors present classical results together with the most recent developments in the field, making this a useful reference for researchers and graduate students in various branches of mathematical neuroscience.

Weakly Connected Neural Networks (Applied Mathematical Sciences, 126)

Computers & Technology

Hoppensteadt, Frank C.

Izhikevich, Eugene M.

Certification

Springer

The result of lectures given by the authors at New York University, the University of Utah, and Michigan State University, the material is written for students who have had only one term of calculus, but it contains material that can be used in modeling courses in applied mathematics at all levels through early graduate courses. Numerous exercises are given as well as solutions to selected exercises, so as to lead readers to discover interesting extensions of that material. Throughout, illustrations depict physiological processes, population biology phenomena, corresponding models, and the results of computer simulations. Topics covered range from population phenomena to demographics, genetics, epidemics and dispersal; in physiological processes, including the circulation, gas exchange in the lungs, control of cell volume, the renal counter-current multiplier mechanism, and muscle mechanics; to mechanisms of neural control. Each chapter is graded in difficulty, so a reading of the first parts of each provides an elementary introduction to the processes and their models.

Modeling and Simulation in Medicine and the Life Sciences (Texts in Applied Mathematics, 10)

Reference

Peskin, Charles S.

Encyclopedias & Subject Guides

This book develops methods for describing random dynamical systems, and it illustrats how the methods can be used in a variety of applications. Appeals to researchers and graduate students who require tools to investigate stochastic systems.

Random Perturbation Methods with Applications in Science and Engineering (Applied Mathematical Sciences, 150)

Science & Math

Skorokhod, Anatoli V.

Salehi, Habib D.

Mathematics

Designed to be used at the graduate level in applied mathematics, studying mathematical analysis and computer simulation of dynamical systems. Computations and computer simulations are used throughout to illustrate the phanomena discussed and to supply readers with probes for use on new problems. 74 illustrations.

Analysis and Simulation of Chaotic Systems (Applied Mathematical Sciences, 94)

Beginning with realistic mathematical or verbal models of physical or biological phenomena, the author derives tractable models for further mathematical analysis or computer simulations. For the most part, derivations are based on perturbation methods, and the majority of the text is devoted to careful derivations of implicit function theorems, the method of averaging, and quasi-static state approximation methods. The duality between stability and perturbation is developed and used, relying heavily on the concept of stability under persistent disturbances. Relevant topics about linear systems, nonlinear oscillations, and stability methods for difference, differential-delay, integro-differential and ordinary and partial differential equations are developed throughout the book. For the second edition, the author has restructured the chapters, placing special emphasis on introductory materials in Chapters 1 and 2 as distinct from presentation materials in Chapters 3 through 8. In addition, more material on bifurcations from the point of view of canonical models, sections on randomly perturbed systems, and several new computer simulations have been added.

This introduction to mathematical methods that are useful for studying population phenomena is intended for advanced undergraduate and graduate students, and will be accessible to scientists who do not have a strong mathematics background. The material is graded in mathematical difficulty. The earlier parts of the book involve elementary diference equations while later chapters present topics that require more mathematical preparation. Models of total population and population age structure are first derived and studied, and then models of random population events are presented in terms of Markov chains. The last two chapters deal with mathematical methods used to uncover qualitative behaviour of more complicated difference equations. Each chapter begins with a simple model, usually of some historical interest, that defines the primary goals of the chapter. Exercises, for which solutions are provided, illustrate material in the text and also deal with models more advanced than those derived and studied in the text.

Mathematical Methods of Population Biology (Cambridge Studies in Mathematical Biology, Series Number 4)

Cambridge University Press

This introduction to mathematical methods that are useful for studying population phenomena is intended for advanced undergraduate and graduate students, and will be accessible to scientists who do not have a strong mathematics background. The material is graded in mathematical difficulty. The earlier parts of the book involve elementary diference equations while later chapters present topics that require more mathematical preparation. Models of total population and population age structure are first derived and studied, and then models of random population events are presented in terms of Markov chains. The last two chapters deal with mathematical methods used to uncover qualitative behaviour of more complicated difference equations. Each chapter begins with a simple model, usually of some historical interest, that defines the primary goals of the chapter. Exercises, for which solutions are provided, illustrate material in the text and also deal with models more advanced than those derived and studied in the text.

Biological Sciences

An Introduction to the Mathematics of Neurons: Modeling in the Frequency Domain (Cambridge Studies in Mathematical Biology, Series Number 6)

This book describes signal processing aspects of neural networks, how we receive and assess information. Beginning with a presentation of the necessary background material in electronic circuits, mathematical modeling and analysis, signal processing, and neurosciences, it proceeds to applications. These applications include small networks of neurons, such as those used in control of warm-up and flight in moths and control of respiration during exercise in humans. Next, Hoppensteadt develops a theory of mnemonic surfaces and presents material on pattern formation and cellular automata. Finally, the text addresses the large networks, such as the thalamus-reticular complex circuit, that may be involved in focusing attention, and the development of connections in the visual cortex. This book will serve as an excellent text for advanced undergraduates and graduates in the physical sciences, mathematics, engineering, medicine and life sciences.

This book describes signal processing aspects of neural networks, how we receive and assess information. Beginning with a presentation of the necessary background material in electronic circuits, mathematical modeling and analysis, signal processing, and neurosciences, it proceeds to applications. These applications include small networks of neurons, such as those used in control of warm-up and flight in moths and control of respiration during exercise in humans. Next, Hoppensteadt develops a theory of mnemonic surfaces and presents material on pattern formation and cellular automata. Finally, the text addresses the large networks, such as the thalamus-reticular complex circuit, that may be involved in focusing attention, and the development of connections in the visual cortex. This book will serve as an excellent text for advanced undergraduates and graduates in the physical sciences, mathematics, engineering, medicine and life sciences.

Politics & Social Sciences

Anthropology

Nonlinear Oscillations in Biology (Lectures in Applied Mathematics (American Mathematical Society), V. 17.)

Summer Seminar on Applied Mathematics 1978 (University of Utah)

Society for Industrial and Applied Mathematics

American Mathematical Society

Amer Mathematical Society

See the best price to sell, buy, or rent books by Hoppensteadt, Frank C.. BookScouter helps to compare book prices from 25+ online bookstores and 30+ buyback vendors with a single search.

Books by Hoppensteadt, Frank C.

See the best price to sell, buy, or rent books by Hoppensteadt, Frank C.. BookScouter helps to compare book prices from 25+ online bookstores and 30+ buyback vendors with a single search.

Weakly Connected Neural Networks (Applied Mathematical Sciences, 126)

Modeling and Simulation in Medicine and the Life Sciences (Texts in Applied Mathematics, 10)

Random Perturbation Methods with Applications in Science and Engineering (Applied Mathematical Sciences, 150)

Analysis and Simulation of Chaotic Systems (Applied Mathematical Sciences, 94)

Analysis and Simulation of Chaotic Systems (Applied Mathematical Sciences, 94)

Mathematical Methods of Population Biology (Cambridge Studies in Mathematical Biology, Series Number 4)

Mathematical Methods of Population Biology (Cambridge Studies in Mathematical Biology, Series Number 4)

An Introduction to the Mathematics of Neurons: Modeling in the Frequency Domain (Cambridge Studies in Mathematical Biology, Series Number 6)

An Introduction to the Mathematics of Neurons: Modeling in the Frequency Domain (Cambridge Studies in Mathematical Biology, Series Number 6)

Nonlinear Oscillations in Biology (Lectures in Applied Mathematics (American Mathematical Society), V. 17.)