TY - JOUR T1 - Exotic bifurcations in three connected populations with Allee effect JF - bioRxiv DO - 10.1101/2021.02.03.429609 SP - 2021.02.03.429609 AU - Gergely Röst AU - AmirHosein Sadeghimanesh Y1 - 2021/01/01 UR - http://biorxiv.org/content/early/2021/03/20/2021.02.03.429609.abstract N2 - We consider three connected populations with strong Allee effect, and give a complete classification of the steady state structure of the system with respect to the Allee threshold and the dispersal rate, describing the bifurcations at each critical point where the number of steady states change. One may expect that by increasing the dispersal rate between the patches, the system would become more well-mixed hence simpler. However, we show that it is not always the case, and the number of steady states may (temporarily) increase by increasing the dispersal rate. Besides sequences of pitchfork and saddle-node bifurcations, we find triple-transcritical bifurcations and also a sun-ray shaped bifurcation where twelve steady states meet at a single point then disappear. The major tool of our investigations is a novel algorithm that decomposes the parameter space with respect to the number of steady states and find the bifurcation values using cylindrical algebraic decomposition with respect to the discriminant variety of the polynomial system.Competing Interest StatementThe authors have declared no competing interest. ER -