In this report, a modified Lorenz system is introduced for describing convective motion heated from below with a sinusoidal differential heating. The system includes two additional terms which intensifies the vorticity and stabilizes the temperature field. These two terms bring a new complex behavior. For a large horizontal temperature difference, the onset of chaotic convection is suppressed by the temperature difference and the marginal Rayleigh number is proportional to h2, where h is the horizontal difference in Rayleigh numbers. However, chaotic convection appears in a broad range of Rayleigh numbers.
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