The　stability　of　the　ecosystem　is　essential　for　the　sustainable　development　of　the　earth.　Studying　the　population　model＇s　dynamic　behavior,　including　the　Allee　and　anxiety　effects,　can　better　represent　the　ecosystem＇s　working　mechanism,　which　is　crucial　for　preserving　ecological　balance.　In　light　of　this,　the　objective　of　this　paper　is　to　build　a　Leslie-Gower　model　that　incorporates　Allee　effect　on　the　birth　rate　and　the　saturated　fear　effect　on　the　predator,　then　analyze　its　dynamic　behavior　and　the　impact　of　the　saturated　fear　effect　on　population　density.　In　the　process　of　analysis,　the　existence　and　stability　of　boundary　and　positive　equilibria　are　established,　demonstrating　that　the　origin　is　an　attractor　using　the　blow-up　method.　By　varying　the　saturated　fear　effect　parameter,　the　corresponding　system　will　undergo　supercritical,　sub-critical,　and　even　degenerate　Hopf　bifurcations.　The　existence　of　Bogdanov-Takens　bifurcation　of　codimension-2　(or　codimension-3)　is　demonstrated　near　the　unique　positive　equilibrium.　In　light　of　these　bifurcation　phenomena,　the　validity　of　the　theoretical　results　is　confirmed　through　graphical　representations　via　numerical　simulations.　The　results　show　that　while　the　fear　effect　on　the　predator　favorably　contributes　to　the　ecological　stability,　high　levels　of　either　the　Allee　effect　or　the　saturated　fear　effect　pose　a　hazard　to　the　stability　of　the　ecosystem.