A straightforward analytic method of stability in strong nonlinear autonomous system is introduced into the stability analysis of the themohaline double-diffusive system. The perturbation technique is used to obtain conditions of existence and stability for linear and nonlinear periodic solutions. For linear periodic solution in infinitesimal motion, the existence range of monotonic branch and oscillatory branch are outlined. The oscillatory branch of nonlinear periodic solution in finite-amplitude motion has unstable periodic solution when μis smaller than critical value μc in this case of 0 Rs-R121. The stability conclusions under different direction of vortex are drawn out.
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