Abstract
Several endomorphisms of the plane have been constructed by simple maps. We study the dynamics occuring in one of them, which is rich in global bifurcations. The invariants sets are stable manifolds of saddle type points or cycles, as well as closed curves issued from Hopf bifurcations. The present paper focuses some bifurcations related with attractors or basins which produce other attractors which coexist with invariant sets.
Highlights
Multistable systems, i.e. systems with a large number of coexisting stable systems, are very common in nature
We study the dynamics occuring in one of them, which is rich in global bifurcations
The present paper focuses some bifurcations related with attractors or basins which produce other attractors which coexist with invariant sets
Summary
Multistable systems, i.e. systems with a large number of coexisting stable systems, are very common in nature. In the following we shall write T ∗ instead of Ta∗,b∗,2 This new map T ∗ has two fixed points (0, 0) which corresponds to P for T and P ∗(1 + b∗ − a∗, 1 + b∗ − a∗) which corresponds to the trivial solution for T. O(0, 0)(a∗,b∗) related to parametric vector (a∗, b∗) = (a, 2a − b − 2) Both fixed point O and P can undergo identical sets of bifurcations in parameter space. The parametric line b − 2a + 3 = 0 is the symmetric of the line ∆ : b = 1 with respect to the line Λ(1)0 : b − a + 1 = 0 This line ∆ : b − 2a + 3 = 0 is associated with the fixed point P and plays a key role for global bifurcations.
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