Frank C. Hoppensteadt F. C. Hoppensteadt Charles S. Peskin
Mathematics in Medicine and the Life Sciences grew from 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 but 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, and solutions to selected exercises are included. Numerous illustrations depict physiological processes, population biology phenomena, models of them, and the results of computer...
Mathematics in Medicine and the Life Sciences grew from lectures given by the authors at New York University, the University of Utah, and Michigan ...
Beginning with realistic mathematical or verbal models of physical or biological phenomena, the author derives tractable mathematical models that are amenable to further mathematical analysis or to elucidating computer simulations. For the most part, derivations are based on perturbation methods. Because of this, 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...
Beginning with realistic mathematical or verbal models of physical or biological phenomena, the author derives tractable mathematical models that are ...
F. C. Hoppensteadt Frank C. Hoppensteadt C. Cannings
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...
This introduction to mathematical methods that are useful for studying population phenomena is intended for advanced undergraduate and graduate studen...
In studying the dynamics of populations, whether of animals, plants or cells, it is crucial to allow for intrinsic delays, due to such things as gestation, maturation or transport. This book is concerned with one of the fundamental questions in the analysis of the effect of delays, namely determining whether they effect the stability of steady states. The analysis is presented for one or two such delays treated both as discrete, where an event which occurred at a precise time in the past has an effect now, and distributed, where the delay is averaged over the population's history. Both of...
In studying the dynamics of populations, whether of animals, plants or cells, it is crucial to allow for intrinsic delays, due to such things as gesta...
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....
This book describes signal processing aspects of neural networks, how we receive and assess information. Beginning with a presentation of the necessar...
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....
This book describes signal processing aspects of neural networks, how we receive and assess information. Beginning with a presentation of the necessar...
Frank C. Hoppensteadt E. M. (Arizona State University, Usa) Izhikevich
This book is devoted to an analysis of general weakly connected neural networks (WCNNs) that can be written in the form (0.1) m Here, each Xi E IR is a vector that summarizes all physiological attributes of the ith neuron, n is the number of neurons, Ii describes the dynam- ics of the ith neuron, and gi describes the interactions between neurons. The small parameter indicates the strength of connections between the neurons. Weakly connected systems have attracted much attention since the sec- ond half of seventeenth century, when Christian Huygens noticed that a pair of pendulum clocks...
This book is devoted to an analysis of general weakly connected neural networks (WCNNs) that can be written in the form (0.1) m Here, each Xi E IR is ...
Mathematics in Medicine and the Life Sciences grew from 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 but 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, and solutions to selected exercises are included. Numerous illustrations depict physiological processes, population biology phenomena, models of them, and the results of computer...
Mathematics in Medicine and the Life Sciences grew from lectures given by the authors at New York University, the University of Utah, and Michigan ...
Frank C. Hoppensteadt Eugene M. Izhikevich Frank C
This book is devoted to an analysis of general weakly connected neural networks (WCNNs) that can be written in the form (0.1) m Here, each Xi E IR is a vector that summarizes all physiological attributes of the ith neuron, n is the number of neurons, Ii describes the dynam- ics of the ith neuron, and gi describes the interactions between neurons. The small parameter indicates the strength of connections between the neurons. Weakly connected systems have attracted much attention since the sec- ond half of seventeenth century, when Christian Huygens noticed that a pair of pendulum clocks...
This book is devoted to an analysis of general weakly connected neural networks (WCNNs) that can be written in the form (0.1) m Here, each Xi E IR is ...
