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...

Descripción completa

Detalles Bibliográficos
Clasificación:Libro Electrónico
Formato: Electrónico eBook
Idioma:Inglés
Publicado: World Scientific 2009.
Colección:World Scientific Series on Nonlinear Science Series A.
Temas:
Differential equations, Nonlinear.
Differential equations, Partial.
Mathematical models.
Équations différentielles non linéaires.
Équations aux dérivées partielles.
Modèles mathématiques.
mathematical models.
Differential equations, Nonlinear
Differential equations, Partial
Mathematical models
Electronic resource.
Acceso en línea:Texto completo
Tabla de Contenidos:
  • Cover13;
  • Contents
  • Acknowledgments
  • 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
  • 2.4.1 Autocatalysis in closed systems
  • 2.4.2 Autocatalysis in the flow reactor
  • 3. Dynamics of Molecular Evolution
  • 3.1 Introduction
  • 3.2 Selection and evolution
  • 3.3 Template induced autocatalysis
  • 3.3.1 Autocatalytic oligomerization
  • 3.3.2 Biopolymer replication
  • 3.3.3 Replication and selection
  • 3.3.4 Replication and mutation
  • 3.3.5 Error thresholds
  • 3.4 Replicator equations
  • 3.4.1 Schlogl model
  • 3.4.2 Fisher's selection equation
  • 3.4.3 Symbioses and hypercycles
  • 3.5 Unlimited growth and selection
  • 4. Relaxation Oscillations
  • 4.1 Introduction
  • 4.2 Self-exciting relaxation oscillations
  • 4.2.1 van der Pol equation
  • 4.2.2 Stoker-Haag equation
  • 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
  • 5.2.1 Formation of a period window
  • 5.2.2 Stability of a period window
  • 5.2.3 Topology of 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
  • 7.2.1 Korteweg-de Vries equation
  • 7.2.2 sine-Gordon equation
  • 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 di usion
  • 9.2.1 Theory of random walk
  • 9.2.2 Langevin equation and equilibrium fluctuations
  • 9.2.3 Newtonian mechanics and asymptotic irreversibility
  • 9.3 Reversibility and time recurrence
  • 9.3.1 A linear synchronous system
  • 9.3.2 Recurrence in nonlinear Hamiltonian systems: Fermi-Pasta-Ulam Model
  • 9.4 Complex dynamics and chaos in Newtonian dynamics: H enon-Heiles equations
  • Bibliography
  • Index.

Ejemplares similares