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Dynamical Systems - Columbia University

DynamicalSystemsJoshuaWilde,revisedbyIsa b elTecu,TakeshiSuzukiandMar aJos Bo ccardiAugust13,2013 DynamicalSystemsaresystems,describ edbyoneormoreequations, ,thegrowthofap opulationcanb edescrib eundersto o dtob eeitherdiscrete(day1,day2etc.)orcontinuo us( ).Ifwetaketimetob econtinuous,dynamicalsystemswillb edescrib edbydi erentialequations-equationsthatinvolveth ederivative(theinstantaneouschange) ediscrete,dynamicalsystemswillb edescrib edbydi erenceequations-equationsrelatingthevalu eofavariableattimet+ okatb othcasesb erentialEquationsAdi erentialequationisanequationwhichinvolve sanunknownfunctionf(t) (t).Thenwedenotef (t)asdfdt(t)oras y(t).

2 Dynamical Systems 3. Ordinary - An ordinary di erential equation is a di erential equation where the unknown function takes only one argument. orF example, the di erential equations mentioned thus far

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