Modeling by nonlinear differential equations : dissipative and conservative processes /
This book aims to provide mathematical analyses of nonlinear differential equations, which have proved pivotal to understanding many phenomena in physics, chemistry and biology. Topics of focus are autocatalysis and dynamics of molecular evolution, relaxation oscillations, deterministic chaos, react...
| Основен автор: | Phillipson, Paul E. 1933- |
|---|---|
| Автор-организации: | World Scientific (Firm) |
| Други автори: | Schuster, P. 1941- |
| Формат: | Електронна книга |
| Език: | English |
| Публикувано: |
Singapore ; Hackensack, N.J. :
World Scientific Pub. Co.,
℗♭2009.
|
| Серия: |
World Scientific series on nonlinear science. Monographs and treatises ;
v. 69. |
| Предмети: | |
| Онлайн достъп: |
http://search.ebscohost.com/login.aspx?direct=true&scope=site&db=nlebk&AN=340581 |
Съдържание:
- 1. Theme and contents of this book
- 2. Processes in closed and open systems. 2.1. Introduction. 2.2. Thermodynamics of general systems. 2.3. Chemical reactions. 2.4. Autocatalysis in closed and open systems
- 3. Dynamics of molecular evolution. 3.1. Introduction. 3.2. Selection and evolution. 3.3. Template induced autocatalysis. 3.4. Replicator equations. 3.5. Unlimited growth and selection
- 4. Relaxation oscillations. 4.1. Introduction. 4.2. Self-exciting relaxation oscillations. 4.3. Current induced neuron oscillations. 4.4. Bistability and complex structure of harmonically forced relaxation oscillations
- 5. Order and chaos. 5.1. Introduction. 5.2. One dimensional maps. 5.3. Lorenz equations. 5.4. Low dimensional autocatalytic networks. 5.5. Chua equations
- 6. Reaction diffusion dynamics. 6.1. Introduction. 6.2. Pulse front solutions of Fisher and related equations. 6.3. Diffusion driven spatial inhomogeneities. 6.4. Turing mechanism of chemical pattern formation
- 7. Solitons. 7.1. Introduction. 7.2. One dimensional lattice dynamics. 7.3. Burgers equation
- 8. Neuron pulse propagation. 8.1. Introduction. 8.2. Properties of a neural pulse. 8.3. FitzHugh-Nagumo equations. 8.4. Hodgkin-Huxley equations. 8.5. An overview
- 9. Time reversal, dissipation and conservation. 9.1. Introduction. 9.2. Irreversibility and diffusion. 9.3. Reversibility and time recurrence. 9.4. Complex dynamics and chaos in Newtonian dynamics : Henon-Heiles equations.