Mathematics of continuous and discrete dynamical systems : AMS Special Session in Honor of Ronald Mickens's 70th birthday Nonstandard Finite-Difference Discretizations and Nonlinear Oscillations, January 9-10, 2013, San Diego, CA / / Abba B. Gumel, editor

• Record Nr.: UNINA9910788257203321
• Pubbl/distr/stampa: Providence, Rhode Island : , : American Mathematical Society, , 2014; ©2014
• ISBN: 1-4704-1686-7
• Descrizione fisica: 1 online resource (310 p.)
• Collana: Contemporary mathematics, ; 618 , 0271-4132
• Classificazione: 34C1534D0534D2034D2337M2039A2839A3092B05
• Disciplina: 515.392
• Soggetti: Nonlinear oscillations; Differential equations - Asymptotic theory
• Lingua di pubblicazione: Inglese
• Formato: Materiale a stampa
• Livello bibliografico: Monografia
• Note generali: Description based upon print version of record.
• Nota di bibliografia: Includes bibliographical references at the end of each chapters.
• Nota di contenuto: Preface -- Biographical Summary of Ronald E. Mickens -- Deterministic and Stochastic SIR Epidemic Models with Power Function Transmission and Recovery Rates -- 1. Introduction -- 2. ODE Model -- 3. CTMC Model -- 4. SDE Model -- 5. Computational Results -- 6. Summary -- Acknowledgments -- References -- Evaluating the Cost-Effectiveness of Vaccination Programs -- 1. Introduction -- 2. Background and modeling framework -- 3. Model extensions and future research -- 4. Summary and concluding remarks -- References -- A Simple Two-Patch Epidemiological Model with Allee Effects and Disease-Modified Fitness -- 1. Introduction -- 2. A two-patch SI model -- 3. Endemic states -- 4. The effects of dispersal -- 5. Discussion -- 6. Proofs -- Acknowledgements -- References -- Designing NSFD Methods for Models of Population Interactions -- 1. Introduction -- 2. Definitions and Preliminaries -- 3. PESN methods for systems with hyperbolic equilibria -- 4. PAESN methods for systems with non-hyperbolic equilibria -- 5. Numerical Simulations -- 6. Discussion and Conclusions -- References -- Nonstandard Discretizations of the SIS Epidemiological Model with and without Diffusion -- 1. Introduction -- 2. Qualitative properties of the model ; -- 3. Nonstandard Runge-Kutta Method for the SIS Model -- 4. NSFD scheme for the SIS model -- 5. NSFD schemes for SIS-Diffusion Model -- 6. Conclusion -- Acknowledgements -- References -- Galerkin-Least Squares Approximations for Delay Differential Equations: Application to a Circadian Rhythm Model -- 1. Introduction -- 2. Galerkin-Least Squares Approximation -- 3. DDE Model for Circadian Rhythm -- 4. Equilibria and Linear Stability Analysis -- 5. Numerical Simulations -- Conclusions -- Acknowledgements -- References -- Exact Finite Difference Schemes -- 1. Introduction -- 2. Exact Finite Difference Schemes for ODEs -- 3. First-order linear system of two equations -- 4. Exact finite difference schemes for some PDEs -- 5. Discussion -- Acknowledgements -- References -- Design and Analysis of NSFD Methods for the Diffusion-Free Brusselator -- 1. Introduction -- 2. The diffusion-free Brusselator system -- 3. Design of NSFD methods -- 6. Conclusions and perspectives.