In　the　complex　space　environment,　the　antenna　of　the　running　satellite　may　cause　large　amplitude　nonlinear　vibrations.　In　scientific　experiments,　it　is　difficult　to　simulate　the　state　for　the　operation　of　the　antenna.　To　study　the　nonlinear　dynamic　behaviors　of　the　circular　mesh　antenna,　the　dynamic　models　and　dynamic　equations　are　established.　First,　the　circular　mesh　antenna　is　simplified　to　an　equivalent　cylindrical　shell　structure.　Then,　the　high-dimensional　nonlinear　dynamic　equation　is　derived.　The　dynamic　equations　of　the　circular　mesh　antenna　are　discrete　by　the　third-order　Galerkin　method.　The　breathing　vibration　nonlinear　equations　with　three-degree-of-freedom　are　obtained.　The　nonlinear　ordinary　equations　are　simplified　to　be　a　topological　equivalent　nonlinear　equation.　The　topological　equivalent　nonlinear　equation　under　the　conditions　of　the　unperturbed　and　perturbed　situations　is　analyzed,　respectively.　Based　on　the　energy　phase　method　of　Haller　and　Wiggins,　this　theory　for　the　six-dimensional　system　is　extended　and　improved.　The　multi-pulse　chaotic　motion　of　the　circular　mesh　antenna　system　is　verified　by　the　extended　energy　phase　method.　The　geometric　structure　of　the　three　jumping　pulses　in　the　six-dimensional　phase　space　is　described　in　the　first　time.　Finally,　numerical　simulation　is　used　to　verify　the　theoretical　analysis.