Modeling by nonlinear differential equations : dissipative and conservative processes / Paul E. Phillipson, Peter Schuster.

Format:

Book

Author/Creator:

Phillipson, Paul E. (Paul Edgar), 1933-

Contributor:

Schuster, P. (Peter), 1941-

Series:

World Scientific Series on Nonlinear Science Series A

World Scientific series on nonlinear science. Series A ; vol. 69

Language:

English

Subjects (All):

Differential equations, Nonlinear.

Differential equations, Partial.

Mathematical models.

Physical Description:

1 online resource (238 p.)

Edition:

1st ed.

Place of Publication:

Singapore : World Scientific, c2009.

Language Note:

English

Summary:

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, reaction diffusion driven chemical pattern formation, solitons and neuron dynamics. Included is a discussion of processes from the viewpoints of reversibility, reflected by conservative classical mechanics, and irreversibility introduced by the dissipative role of diffusion. Each chapter presents the su

Contents:

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 equations5.4 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 diffusion; 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

Notes:

Description based upon print version of record.

Includes bibliographical references and index.

ISBN:

9786612757952

9781282757950

1282757954

9789814271608

9814271608

OCLC:

729020069