Simultaneous border-collision and period-doubling bifurcations
Copyright policy )Simultaneous border-collision and period-doubling bifurcations
We unfold the codimension-two simultaneous occurrence of a border-collision bifurcation and a period-doubling bifurcation for a general piecewise-smooth, continuous map. We find that with sufficient nondegeneracy conditions, a locus of period-doubling bifurcations emanates nontangentially from a locus of border-collision bifurcations. The corresponding period-doubled solution undergoes a border-collision bifurcation along a curve emanating from the codimension-two point and tangent to the period-doubling locus here. In the case that the map is one-dimensional local dynamics is completely classified; in particular, we give conditions that ensure chaos.
- University of Colorado Boulder United States
- University of Colorado System United States
Bifurcation theory for ordinary differential equations, Models, Statistical, 37G15, Dynamical Systems (math.DS), Bifurcations and instability for nonlinear problems in mechanics, 37G10, Nonlinear Dynamics, Oscillometry, 37G10; 37G15, Bifurcations of limit cycles and periodic orbits in dynamical systems, FOS: Mathematics, Computer Simulation, Mathematics - Dynamical Systems, Algorithms
Bifurcation theory for ordinary differential equations, Models, Statistical, 37G15, Dynamical Systems (math.DS), Bifurcations and instability for nonlinear problems in mechanics, 37G10, Nonlinear Dynamics, Oscillometry, 37G10; 37G15, Bifurcations of limit cycles and periodic orbits in dynamical systems, FOS: Mathematics, Computer Simulation, Mathematics - Dynamical Systems, Algorithms
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