▁of ▁state ▁variables . ▁ ▁Ex amples ▁Simple ▁p end ul um , ▁see ▁picture ▁( right ). ▁Simple ▁harm onic ▁oscill ator ▁where ▁the ▁phase ▁portrait ▁is ▁made ▁up ▁of ▁elli ps es ▁cent red ▁at ▁the ▁origin , ▁which ▁is ▁a ▁fixed ▁point . ▁Van ▁der ▁Pol ▁oscill ator ▁see ▁picture ▁( bottom ▁right ). ▁ ▁Parameter ▁plane ▁( c - plane ) ▁and ▁Mand el b rot ▁set ▁ ▁Ph ase ▁Port ra its ▁to ▁Visual ize ▁Be havior ▁of ▁Systems ▁of ▁Ord inary ▁D iffer ential ▁Equ ations ▁ ▁A ▁phase ▁portrait ▁represents ▁the ▁direction al ▁behavior ▁of ▁a ▁system ▁of ▁O DE s . ▁The ▁phase ▁portrait ▁can ▁indicate ▁the ▁stability ▁of ▁the ▁system . ▁▁ ▁The ▁phase ▁portrait ▁behavior ▁of ▁a ▁system ▁of ▁O DE s ▁can ▁be ▁determined ▁by ▁the ▁eigenvalues ▁or ▁the ▁trace ▁and ▁determin ant ▁( trace ▁= ▁ λ 1 ▁+ ▁ λ 2 , ▁determin ant ▁= ▁ λ 1 ▁x ▁ λ 2 ) ▁of ▁the ▁system . ▁ ▁See ▁also ▁ ▁Ph ase ▁space ▁Ph ase ▁plane ▁ ▁References ▁▁ ▁Chapter ▁ 1 . ▁ ▁External ▁links ▁ ▁Linear ▁Ph ase ▁Port ra its , ▁an ▁M IT ▁Math let . ▁Category : D ynam ical ▁systems ▁Category : Di agr ams <0x0A> </s> ▁G amb iss ara ▁Forest ▁Park ▁is ▁a ▁forest ▁park ▁in ▁the ▁G amb ia . ▁Est ab lished ▁on ▁January ▁ 1 , ▁ 1 9 5 4 , ▁it ▁covers ▁ 3 0 8