Mathematical Modelling: Theory and Application

This volume is a collection of chapters that present key ideas and theories, as well as their rigorous applications, required for the development of mathematical models in areas such as travelling waves, epidemiology, the chemotaxis system, atrial fibrillation, and vortex nerve complexes. The techniques, methodologies and approaches adopted in this book have relevance in several other fields including physics, biology, and sociology. Each chapter should also a. Cover Title page Contents Preface Travelling waves in nonlinear lattices 1. Introduction 2. Metamaterial formed by a discrete array of nonlinear resonators 3. Implicit nonlinear lattices with applications in metamaterials 4. Nonlinear magnetic metamaterials with parity-time-symmetric potentials 5. Discrete nonlinear Schrödinger equations with nonlocal interactions 6. Discrete nonlinear Schrödinger equations with local interactions 7. Forced Fermi-Pasta-Ulam-type lattices 8. Fractional differential equations on lattices Acknowledgments References Dynamics of an SEIR Model for Infectious Diseases in Random Environments 1. Introduction 2. The models 3. Preliminaries 4. Long term dynamics 5. Numerical simulations 6. Closing remarks Acknowledgment References On a Parabolic-ODE chemotaxis system with periodic asymptotic behavior 1. Introduction 2. Global existence of solutions 3. Asymptotic behavior 4. Numerical approach References Atrial fibrillation through strange attractor dynamics 1. Introduction 2. Experimental aspects 3. The reconstruction of EKG signals through Scale Relativity Theory Conclusions Appendix A Appendix B References Good covers for vortex nerve cell complexes. free group presentation of intersecting nested cycles in planar CW spaces 1. Introduction 2. Preliminaries 3. Rotman Free Group Presentation 4. Main Results 5. Good covers for Cell Complexes 6. Application 7. Conjectures Acknowledgments Appendix A. Cell Complexes References Back Cover