We　investigate　the　dynamical　blockade　in　a　nonlinear　cavity　and　demonstrate　the　connection　between　the　correlation　function　g　(2)　(t)　and　system　parameters　in　the　entire　nonlinear　region.　Utilizing　the　Liouville　exceptional　points　(LEP　s　)　and　quantum　dynamics,　a　near　-perfect　single　-photon　blockade　(1PB)　can　be　achieved.　By　fine-tuning　system　parameters　to　approach　the　second　-order　LEP　(LEP　2　),　we　improved　single　-photon　statistics　in　both　weak　and　strong　nonlinearity　regimes,　including　a　significant　reduction　of　g　(2)　(t)　and　a　pronounced　increase　in　the　single　-photon　occupation　number.　In　the　strong　nonlinearity　region,　the　maximum　photon　population　may　correspond　to　stronger　antibunching　effect.　Simultaneously,　the　time　window　and　period　of　blockade　can　be　controlled　by　selecting　detuning　based　on　the　LEP　2　.　Furthermore,　the　1PB　exhibits　robustness　against　parameter　fluctuations,　and　this　feature　can　be　generalized　to　systems　for　implementing　single　-photon　sources　with　nonharmonic　energy　levels.　(c)　2024　Optica　Publishing　Group