LEADER 05056nam 2200697Ia 450 001 9910780731303321 005 20230721024358.0 010 $a1-282-75795-4 010 $a9786612757952 010 $a981-4271-60-8 035 $a(CKB)2490000000001679 035 $a(EBL)1679740 035 $a(OCoLC)729020069 035 $a(SSID)ssj0000423328 035 $a(PQKBManifestationID)11293647 035 $a(PQKBTitleCode)TC0000423328 035 $a(PQKBWorkID)10440836 035 $a(PQKB)10599866 035 $a(MiAaPQ)EBC1679740 035 $a(WSP)00000548 035 $a(Au-PeEL)EBL1679740 035 $a(CaPaEBR)ebr10421988 035 $a(CaONFJC)MIL275795 035 $a(EXLCZ)992490000000001679 100 $a20090117d2009 uy 0 101 0 $aeng 135 $aurcuu|||uu||| 181 $ctxt 182 $cc 183 $acr 200 10$aModeling by nonlinear differential equations$b[electronic resource] $edissipative and conservative processes /$fPaul E. Phillipson, Peter Schuster 210 $aSingapore $cWorld Scientific$dc2009 215 $a1 online resource (238 p.) 225 0 $aWorld Scientific series on nonlinear science. Series A ;$vvol. 69 300 $aDescription based upon print version of record. 311 $a981-4271-59-4 320 $aIncludes bibliographical references and index. 327 $aContents; 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 327 $a3.4 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 327 $a5.3 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 327 $a8.5 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 330 $aThis book aims to provide mathematical analyses of nonlinear differential equations, which have proved pivotal to understanding many phenomena in physics, chemistry and biology. Topics of focus are autocatalysis and dynamics of molecular evolution, relaxation oscillations, deterministic chaos, reaction diffusion driven chemical pattern formation, solitons and neuron dynamics. Included is a discussion of processes from the viewpoints of reversibility, reflected by conservative classical mechanics, and irreversibility introduced by the dissipative role of diffusion. Each chapter presents the su 410 0$aWorld Scientific Series on Nonlinear Science Series A 606 $aDifferential equations, Nonlinear 606 $aDifferential equations, Partial 606 $aMathematical models 615 0$aDifferential equations, Nonlinear. 615 0$aDifferential equations, Partial. 615 0$aMathematical models. 676 $a515.355 686 $aSK 520$2rvk 686 $aWD 2100$2rvk 700 $aPhillipson$b Paul E$g(Paul Edgar),$f1933-$01484792 701 $aSchuster$b P$g(Peter),$f1941-$01484793 801 0$bMiAaPQ 801 1$bMiAaPQ 801 2$bMiAaPQ 906 $aBOOK 912 $a9910780731303321 996 $aModeling by nonlinear differential equations$93703587 997 $aUNINA