Analysis of a Model for Epilepsy: Application of a Max-Type Difference Equation to Mesial Temporal Lobe Epilepsy: Chapman & Hall/CRC Monographs and Research Notes in Mathematics
Autor Candace M. Kent, David M. Chanen Limba Engleză Hardback – 8 iun 2022
Recently, the authors of Analysis of a Model for Epilepsy: Application of a Max-Type Difference Equation to Mesial Temporal Lobe Epilepsy and their colleagues investigated the first known application of a "max-type" difference equation. Their equation is a phenomenological model of epileptic seizures. In this book, the authors expand on that research and present a more comprehensive development of mathematical, numerical, and biological results. Additionally, they describe the first documented instance of a novel dynamical behavior that they call rippled almost periodic behavior, which can be described as an unpredictable pseudo-periodic behavior.
Features:
- Suitable for researchers in mathematical neuroscience and potentially as supplementary reading for postgraduate students
- Thoroughly researched and replete with references
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Specificații
ISBN-13: 9781032255385
ISBN-10: 1032255382
Pagini: 172
Ilustrații: 12 Tables, black and white; 12 Line drawings, color; 16 Line drawings, black and white; 12 Illustrations, color; 16 Illustrations, black and white
Dimensiuni: 156 x 234 x 11 mm
Greutate: 0.44 kg
Ediția:1
Editura: CRC Press
Colecția Chapman and Hall/CRC
Seria Chapman & Hall/CRC Monographs and Research Notes in Mathematics
ISBN-10: 1032255382
Pagini: 172
Ilustrații: 12 Tables, black and white; 12 Line drawings, color; 16 Line drawings, black and white; 12 Illustrations, color; 16 Illustrations, black and white
Dimensiuni: 156 x 234 x 11 mm
Greutate: 0.44 kg
Ediția:1
Editura: CRC Press
Colecția Chapman and Hall/CRC
Seria Chapman & Hall/CRC Monographs and Research Notes in Mathematics
Cuprins
1. Introduction: Epilepsy. 1.1. Brief Overview. 1.2. Mesial Temporal Lobe Epilepsy and Other Examples. 2. The Model. 2.1. Model Description. 2.2. Connection to a Simpler Model. 2.3. Connection Between the Model and Epileptic Seizures. 2.4. Open Problem: Seizure Threshold as a Function of Time. 3. Eventual Periodicity of the Model. 3.1. Bounded and Persistent Solutions. 3.2. Eventually Periodic Solutions with Periods Multiples of Six. 3.3. Eventually Periodic Solutions with Period 4. 3.4. Partially and Completely Seizure-Free States. 4. Rippled Almost Periodic Solutions. 4.1. Rippled Behaviour. 4.2. Rippled Almost Periodic Solutions. 4.3. Lyapunov Exponent. 4.4. The State of Status Epilepticus. 4.5. On Termination of Repetition. 5. Numerical Results and Biological Conclusions. 5.1. Bifurcation Diagrams. 5.2. Variability in Seizure Characteristics. 5.3. A Case of Variability in Region 1. 5.4. The Hyperexcitable State. 5.5. Impact of Individual Historical Differences. 6. Epilogue
Notă biografică
Since age seventeen, Candace M. Kent has had an intense interest in mathematical neuroscience, including the mathematical modeling of psychiatric and neurological disorders, adult neurogenesis, and ethology. In pursuit of this interest, she earned a B.A. in mathematics and molecular biology in 1979. She later enrolled in a graduate program in discrete dynamics at the University of Rhode Island, and earned an M.S. in mathematics in 1993 and a Ph.D. in mathematics in 1998. In between, while searching for the appropriate path to take for an eventual career in mathematical neuroscience, she attended the following universities:
David M. Chan earned a B.S. in Aerospace Engineering from Syracuse University in 1991. He then earned a M.A. in Mathematics at the University of Maine in 1994, and a Ph.D. in Applied Mathematics with a minor in Biomathematics from North Carolina State University in 1999. He is currently an associate professor at Virginia Commonwealth University. Using dynamical systems he models and studies problems that arise in medicine, epidemiology, ecology, and social/support networks.
- □Johns Hopkins University Graduate School, Biophysics, 1980-81.
- □ University of Iowa Medical College, M.D. Program, 1981-1984.
- □ Brown University, Applied Mathematics, 1986-88.
David M. Chan earned a B.S. in Aerospace Engineering from Syracuse University in 1991. He then earned a M.A. in Mathematics at the University of Maine in 1994, and a Ph.D. in Applied Mathematics with a minor in Biomathematics from North Carolina State University in 1999. He is currently an associate professor at Virginia Commonwealth University. Using dynamical systems he models and studies problems that arise in medicine, epidemiology, ecology, and social/support networks.
Descriere
The authors of this book and their colleagues investigated the first known application of a "max-type" difference equation. Their equation is a phenomenological model of epileptic seizures. In this book, the authors expand on that research and present a more comprehensive development of mathematical, numerical, and biological results.