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An aspatial version for the famous Schelling's segregation model has recentlybeen proposed, which, called two-room model, is still in an agent-based formatlike the original Schelling model. In the present study, we propose a new,state equation version of the Schelling model. The new equation is based on thetwo-room model and is derived in terms of a set of discrete maps. Fixed pointsolutions for the new equation are found analytically and confirmednumerically. Especially, we show that the extremely simple state equations canreasonably reveal the essence of the Schelling dynamics: integration,segregation and tipping. In addition to the fixed point solutions, periodicsolutions are identified and conditions of the limit cycles are derivedanalytically.

A state equation for the Schelling's segregation model