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El. knyga: Modeling Natural Phenomena via Cellular Nonlinear Networks

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  • Formatas: 220 pages
  • Išleidimo metai: 23-Jan-2018
  • Leidėjas: Cambridge Scholars Publishing
  • ISBN-13: 9781527507357
Kitos knygos pagal šią temą:
Modeling Natural Phenomena via Cellular Nonlinear NetworksDidesnis paveikslėlis
  • Formatas: 220 pages
  • Išleidimo metai: 23-Jan-2018
  • Leidėjas: Cambridge Scholars Publishing
  • ISBN-13: 9781527507357
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This book presents a study of neuroscience models and natural phenomena, such as tsunami waves and tornados. The first part discusses various mathematical models of tsunamis, including the Kortewegde Vries equation, shallow water equations and the CamassaHolm equation (CH). In order to study the dynamics of these models, the text uses the Cellular Nonlinear Networks (CNN) approach to discretize the governing equation using a suitable mathematical grid. The second part discusses some of the models arising in the field of neuroscience. It examines the Fitzhugh-Nagumo systems, which are very important for understanding the qualitative nature of nerve impulse propagation.The volume will be of interest to a wide-ranging audience, including PhD students, mathematicians, physicists, engineers and specialists in the domain of nonlinear waves and their applications.
Preface vii
Part I Modelling Environmental Problems via the Cellular Nonlinear Networks Approach
Chapter One Study of Shallow Water Waves
2(9)
Chapter Two Tsunami Modelling
11(9)
Chapter Three Travelling Wave Solutions of Shallow Water Models
20(16)
Chapter Four Modelling Tornado Dynamics
36(4)
Chapter Five Cellular Nonlinear Network Architecture
40(15)
Chapter Six Modelling Nonlinear PDEs via CNN
55(9)
Chapter Seven CNN Dynamics and Stability
64(19)
Chapter Eight CNN Tsunami Models Dynamics
83(11)
Chapter Nine Travelling Wave Solutions of CNN Tsunami Models
94(17)
Chapter Ten Simulations and Discussions
111(15)
Part II Studying Neuroscience Models via the CNN Approach
Chapter One FitzHugh Nagumo Reaction-diffusion CNN Systems
126(18)
Chapter Two Travelling Wave Solutions of FitzHugh Nagumo CNN Systems
144(9)
Chapter Three Polynomial Cellular Nonlinear Networks
153(5)
Chapter Four Modelling FitzHugh Nagumo Systems via Polynomial CNNs
158(6)
Chapter Five Complex Behaviour of FitzHugh Nagumo CNN Models
164(17)
Chapter Six Edge of Chaos in FitzHugh Nagumo CNN Models
181(9)
Chapter Seven Simulations and Discussions
190(7)
References 197
Professor Angela Slavova holds a PhD in Mathematics, and is Full Professor at the Institute of Mathematics and Informatics at the Bulgarian Academy of Sciences, where she also serves as Head of the Department of Differential Equations and Mathematical Physics. She has been a Visiting Professor at numerous universities in various countries, and has participated in more than 30 conferences, workshops and seminars as an invited speaker. She has more than 100 publications in journals on applied mathematics to her credit, and she has written and co-written three monographs. Professor Pietro Zecca is Full Professor in the Department of Mathematics and Computer Science at the University of Florence, Italy. He served as a Director of the International Mathematical Summer Center (CIME) from 2001 to 2014. Professor Zecca has been a Visiting Professor at numerous universities in various countries and has participated in more than 40 conferences, workshops and seminars in the field of differential equations and control theory as an invited lecturer. He has published more than 120 journal articles on differential equations and nonlinear analysis, and he has written and co-written three monographs.
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