A bifurcation sequence in the Waycross model is studied by means of Poincaré section techniques. The bifurcation parameter B is gradually reduced from 2.00 to 1.50. This parameter measures the inclination of one type of minority families (Lomanians) to move into the districts with many families of another type of minority population (Itrachians). Because of symmetry the attractors in this 4-dimensional migratory model occur in pairs with opposite directions of cyclic population movements. A pair of simple limit cycle attractors are found to remain stable under formation of a pair of period-2 attractors. In a certain parameter range, the model thus contains four entangled attractors. We follow how the period-2 attractor become chaotic through formation and subsequent destabilization of 2-dimensional tori. On the way, regular period-14, period-18 and period-4 attractors are produced through frequency-locking. We thereafter observe a case of type-III intermittency when the two period-1 orbits become unstable, and finally the two chaotic attractors merge with each other.

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• 1988

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• Document

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System Dynamic Society Records

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• This collection is part of the University Archives