This paper investigates the dynamics and bifurcations of a three-dimensional quadratic map, focusing on both resonant and ergodic torus doubling bifurcations. It is shown that the map exhibits both types of bifurcations, with resonant torus doubling bifurcation involving mode-locked periodic orbits lying on a Möbius strip. The paper also analyzes ergodic torus doubling bifurcation using the second Poincaré section and Lyapunov bundles. The analysis involves constructing one-dimensional manifolds, continuing saddle periodic orbits, and using the multi-dimensional Newton-Raphson method to locate saddle periodic orbits. The paper addresses the question of whether a single three-dimensional discrete map can exhibit doubling bifurcations of both quasiperiodic invariant curves and resonant tori. It shows that such a phenomenon is possible in a three-dimensional quadratic map, which is the novelty of the paper. The paper also discusses the classification of doubling bifurcations of quasiperiodic orbits using two methods: the second Poincaré section and the Lyapunov bundle method. It also discusses the unfolding of quasiperiodic invariant curves and the analysis of possible local bifurcations of quasiperiodic orbits. The paper also discusses the doubling bifurcations of resonant tori, where mode-locked orbits are stable and saddle periodic orbits of the same periodicity lying on a closed invariant curve formed by the one-dimensional unstable manifolds of the saddle periodic points. Mode-locked orbits have rational rotation numbers and occupy shrimp-shaped regions in two-dimensional parameter space. The paper also tests the conjecture that resonant doubling bifurcations can be classified into two types based on the sign of the third eigenvalue. The main contributions of the paper are the prevalence of both ergodic and resonant torus doubling bifurcations, the examination of these bifurcations using the second Poincaré section and Lyapunov bundles method, and the testing of the conjecture on resonant torus doubling bifurcation. The paper is organized into sections introducing the three-dimensional discrete quadratic map, analyzing a two-parameter Lyapunov chart, discussing quasiperiodic torus doubling bifurcation, and discussing resonant torus doubling bifurcation using continuation algorithms.This paper investigates the dynamics and bifurcations of a three-dimensional quadratic map, focusing on both resonant and ergodic torus doubling bifurcations. It is shown that the map exhibits both types of bifurcations, with resonant torus doubling bifurcation involving mode-locked periodic orbits lying on a Möbius strip. The paper also analyzes ergodic torus doubling bifurcation using the second Poincaré section and Lyapunov bundles. The analysis involves constructing one-dimensional manifolds, continuing saddle periodic orbits, and using the multi-dimensional Newton-Raphson method to locate saddle periodic orbits. The paper addresses the question of whether a single three-dimensional discrete map can exhibit doubling bifurcations of both quasiperiodic invariant curves and resonant tori. It shows that such a phenomenon is possible in a three-dimensional quadratic map, which is the novelty of the paper. The paper also discusses the classification of doubling bifurcations of quasiperiodic orbits using two methods: the second Poincaré section and the Lyapunov bundle method. It also discusses the unfolding of quasiperiodic invariant curves and the analysis of possible local bifurcations of quasiperiodic orbits. The paper also discusses the doubling bifurcations of resonant tori, where mode-locked orbits are stable and saddle periodic orbits of the same periodicity lying on a closed invariant curve formed by the one-dimensional unstable manifolds of the saddle periodic points. Mode-locked orbits have rational rotation numbers and occupy shrimp-shaped regions in two-dimensional parameter space. The paper also tests the conjecture that resonant doubling bifurcations can be classified into two types based on the sign of the third eigenvalue. The main contributions of the paper are the prevalence of both ergodic and resonant torus doubling bifurcations, the examination of these bifurcations using the second Poincaré section and Lyapunov bundles method, and the testing of the conjecture on resonant torus doubling bifurcation. The paper is organized into sections introducing the three-dimensional discrete quadratic map, analyzing a two-parameter Lyapunov chart, discussing quasiperiodic torus doubling bifurcation, and discussing resonant torus doubling bifurcation using continuation algorithms.