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We report an open three-state perturbed system with quasi-statically varyingHamiltonian depending on the topological parameters. The effective system hoststwo second order exceptional points (EP2s). Here a third order exceptionalpoint (EP3) is explored with simultaneous encirclement of two EP2s by adiabaticvariation of topological parameters. We study the robust successivestate-exchange around the EP3. Applying adiabatic theorem, we estimate theevolution of total phase accumulated by each state during encirclement; whereinterestingly, the state-common to the pairs of coupled state picks up threetimes phase shift of 2{\pi}. Such an exclusively reported scheme can beexploited in potential applications of exceptional points, manipulating fewertopological parameters in various non-Hermitian systems.

Origin of third order exceptional singularities and its signature in successive state conversion