International Journal of Bifurcation and Chaos · 1994 · 58 citations · 0 references
Natural SciencesMathematicsComplex SystemsDynamical SystemsTopologyBifurcation TheoryChaos TheoryComplex DynamicsFixed PointsNonlinear DynamicsTopological DynamicsAttractorsBifurcationChaotic AttractorsCritical CurvesGlobal Bifurcation Of Fixed PointsGlobal Bifurcation TheoryInvariant CurvesLogistic Map
Several endomorphisms of a plane have been constructed by coupling two logistic maps. Here we study the dynamics occurring in one of them, a twisted version due to J. Dorband, which (like the other models) is rich in global bifurcations. By use of critical curves, absorbing and invariant areas are determined, inside which global bifurcations of the attracting sets (fixed points, closed invariant curves, cycles or chaotic attractors) take place. The basins of attraction of the absorbing areas are determined together with their bifurcations.