Advanced Mathematical Methods in Biosciences and Applications

Description

Featuring contributions from experts in mathematical biology and biomedical research, this edited volume covers a diverse set of topics on mathematical methods and applications in the biosciences. Topics focus on advanced mathematical methods, with chapters on the mathematical analysis of the quasispecies model, Arnold’s weak resonance equation, bifurcation analysis, and the Tonnelier-Gerstner model. Special emphasis is placed on applications such as natural selection, population heterogeneity, polyvariant ontogeny in plants, cancer dynamics, and analytical solutions for traveling pulses and wave trains in neural models. A survey on quasiperiodic topology is also presented in this book. Carefully peer-reviewed, this volume is suitable for students interested in interdisciplinary research. Researchers in applied mathematics and the biosciences will find this book an important resource on the latest developments in the field. In keeping with the STEAM-H series, the editors hope to inspire interdisciplinary understanding and collaboration. Front Matter ....Pages i-xii Arnold’s Weak Resonance Equation as the Model of Greek Ornamental Design (Faina Berezovskaya, Georgiy P. Karev)....Pages 1-25 Rigorous Mathematical Analysis of the Quasispecies Model: From Manfred Eigen to the Recent Developments (Alexander S. Bratus, Artem S. Novozhilov, Yuri S. Semenov)....Pages 27-51 A Survey on Quasiperiodic Topology (Roberto De Leo)....Pages 53-88 Combining Bifurcation Analysis and Population Heterogeneity to Ask Meaningful Questions (Irina Kareva)....Pages 89-110 Polyvariant Ontogeny in Plants: When the Second Eigenvalue Plays a Primary Role (Dmitrii O. Logofet)....Pages 111-130 Recurrence as a Basis for the Assessment of Predictability of the Irregular Population Dynamics (Alexander B. Medvinsky)....Pages 131-145 Total Analysis of Population Time Series: Estimation of Model Parameters and Identification of Population Dynamics Types (Lev V. Nedorezov)....Pages 147-157 Modelling Cancer Dynamics Using Cellular Automata (Álvaro G. López, Jesús M. Seoane, Miguel A. F. Sanjuán)....Pages 159-205 Analytical Solutions for Traveling Pulses and Wave Trains in Neural Models: Excitable and Oscillatory Regimes (Evgeny P. Zemskov, Mikhail A. Tsyganov)....Pages 207-219 Numerical Study of Bifurcations Occurring at Fast Timescale in a Predator–Prey Model with Inertial Prey-Taxis (Yuri V. Tyutyunov, Anna D. Zagrebneva, Vasiliy N. Govorukhin, Lyudmila I. Titova)....Pages 221-239 Within Host Dynamical Immune Response to Co-infection with Malaria and Tuberculosis (Edme Soho, Stephen Wirkus)....Pages 241-261 Back Matter ....Pages 263-264