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We have used the Darcy\u2013B\u00e9nard convection model for the momentum equation and a new local thermal nonequilibrium formulation for heat transport. Linear stability theory and nonlinear stability theory based on the double Fourier series representation are used to study the onset of stationary and chaotic convection in the hybrid nanofluid. The analytical expression of the stationary thermal Rayleigh\u2013Darcy number has been found as a function of dimensionless parameters and physicochemical properties of the hybrid nanoliquid. Tools such as bifurcation diagrams, Lyapunov exponent, phase spaces, and time histories were used to analyze the chaotic and regular behaviors of the resulting five\u2010dimensional system of nonlinear equations. 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