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Modeling by nonlinear differential equations [[electronic resource] ] : dissipative and conservative processes / / Paul E. Phillipson, Peter Schuster
| Modeling by nonlinear differential equations [[electronic resource] ] : dissipative and conservative processes / / Paul E. Phillipson, Peter Schuster |
| Autore | Phillipson Paul E (Paul Edgar), <1933-> |
| Pubbl/distr/stampa | Singapore, : World Scientific, c2009 |
| Descrizione fisica | 1 online resource (238 p.) |
| Disciplina | 515.355 |
| Altri autori (Persone) | SchusterP <1941-> (Peter) |
| Collana | World Scientific series on nonlinear science. Series A |
| Soggetto topico |
Differential equations, Nonlinear
Differential equations, Partial Mathematical models |
| ISBN |
1-282-75795-4
9786612757952 981-4271-60-8 |
| Classificazione |
SK 520
WD 2100 |
| Formato | Materiale a stampa  |
| Livello bibliografico | Monografia |
| Lingua di pubblicazione | eng |
| Nota di contenuto |
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 |
| Record Nr. | UNINA-9910780731303321 |
Phillipson Paul E (Paul Edgar), <1933->
|
||
| Singapore, : World Scientific, c2009 | ||
| Materiale a stampa | ||
| Lo trovi qui: Univ. Federico II | ||
| ||
Modeling by nonlinear differential equations : dissipative and conservative processes / / Paul E. Phillipson, Peter Schuster
| Modeling by nonlinear differential equations : dissipative and conservative processes / / Paul E. Phillipson, Peter Schuster |
| Autore | Phillipson Paul E (Paul Edgar), <1933-> |
| Edizione | [1st ed.] |
| Pubbl/distr/stampa | Singapore, : World Scientific, c2009 |
| Descrizione fisica | 1 online resource (238 p.) |
| Disciplina | 515.355 |
| Altri autori (Persone) | SchusterP <1941-> (Peter) |
| Collana | World Scientific series on nonlinear science. Series A |
| Soggetto topico |
Differential equations, Nonlinear
Differential equations, Partial Mathematical models |
| ISBN |
1-282-75795-4
9786612757952 981-4271-60-8 |
| Classificazione |
SK 520
WD 2100 |
| Formato | Materiale a stampa |
| Livello bibliografico | Monografia |
| Lingua di pubblicazione | eng |
| Nota di contenuto |
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 |
| Record Nr. | UNINA-9910826385803321 |
|
Phillipson Paul E (Paul Edgar), <1933->
|
||
| Singapore, : World Scientific, c2009 | ||
| Materiale a stampa | ||
| Lo trovi qui: Univ. Federico II | ||
| ||