Chemical Oscillations, Waves, and Turbulence

Thishighlyrespected,frequentlycitedbookaddressestwoexcitingfields:patternformationandsynchronizationofoscillators.Itsystematicallydevelopsthedynamicsofmany-oscillatorsystemsofdissipativetype,withspecialemphasisonoscillatingreaction-diffusionsystems.Theauthorappliesthereductiveperturbationmethodandthephasede*ionmethodtotheonsetofcollectiverhythms,theformationofwavepatterns,anddiffusion-inducedchemicalturbulence.Thistwo-parttreatmentstartswithasectiononmethods,definingandexploringthereductiveperturbationmethod—oscillatorsversusfieldsofoscillators,theStuart-Landauequation,onsetofoscillationsindistributedsystems,andtheGinzburg-Landauequations.Itfurtherexaminesmethodsofphasede*ion,includingsystemsofweaklycoupledoscillators,one-oscillatorproblems,nonlinearphasediffusionequations,andrepresentationbytheFloqueteigenvectors.Additionalmethodsincludesystematicperturbationexpansion,generalizationofthenonlinearphasediffusionequation,andthedynamicsofbothslowlyvaryingwavefrontsandslowlyphase-modulatedperiodicwaves.Thesecondpartillustratesapplications,frommutualentrainmenttochemicalwavesandchemicalturbulence.Thetextconcludeswithapairofconvenientappendixes.