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Geometric Singular Perturbation TheoryHOPF BifurcationDynamical SystemDifferential EquationsPattern FormationCoupled OscillatorsPeriodic OrbitBifurcationOrdinary Differential EquationsDynamic Mode DecompositionExistence and StabilityParameterization MethodKoopman OperatorNumerical ContinuationMixed-mode OscillationsNormal FormHamiltonian SystemsSlow ManifoldBifurcation TheoryNumerical Computation