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Author Phillipson, Paul E
Title Modeling by Nonlinear Differential Equations : Dissipative and Conservative Processes
Imprint Singapore : World Scientific Publishing Co Pte Ltd, 2009
©2009
book jacket
Descript 1 online resource (238 pages)
text txt rdacontent
computer c rdamedia
online resource cr rdacarrier
Series Series In Soft Condensed Matter ; v.69
Series In Soft Condensed Matter
Note Intro -- 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
Key Features:Interested graduate students are offered an exposition of a given topic sufficient to encourage further explorationFor researchers familiar with a specific topic, the interconnections between chapters may stimulate interest in other subject matters
Description based on publisher supplied metadata and other sources
Electronic reproduction. Ann Arbor, Michigan : ProQuest Ebook Central, 2020. Available via World Wide Web. Access may be limited to ProQuest Ebook Central affiliated libraries
Link Print version: Phillipson, Paul E. Modeling by Nonlinear Differential Equations : Dissipative and Conservative Processes Singapore : World Scientific Publishing Co Pte Ltd,c2009 9789814271592
Subject Differential equations, Nonlinear.;Differential equations, Partial.;Mathematical models
Electronic books
Alt Author Schuster, Peter
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