Global Dynamics and Bifurcations in a Four-dimensional Replicator System


In this paper, the four-dimensional cyclic replicator system u̇i = ui[−(Bu)i + ∑4 j=1 uj(Bu)j ], 1 ≤ i ≤ 4, with b1 = b3 is considered, in which the first row of the matrix B is (0 b1 b2 b3) and the other rows of B are cyclic permutations of the first row. Our aim is to study the global dynamics and bifurcations in the system, and to show how and when all… (More)

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