Knowledge about the behavior of discontinuous piecewise-linear maps is important for a
wide range of applications. An efficient way to investigate the bifurcation structure in
2D parameter spaces of such maps is to detect specific codimension-2 bifurcation points,
called organizing centers, and to describe the bifurcation structure in their
neighborhood. In this work, we present the organizing centers in the 1D discontinuous
piecewise-linear map...
This work contributes to classify the dynamic behaviors of piecewise smooth systems in
which characterize the qualitative changes
in the dynamics. A central point of our investigation is the intersection of two border
collision bifurcation curves in a parameter plane. This problem is also associated with
the continuity breaking in a fixed point of a piecewise smooth map. We will relax the
hypothesis needed in [4] where it was proved that in the case...
In this work we consider the discontinuous flat top tent map which represents an example
for discontinuous piecewise-smooth maps, whereby the system function is constant on some
interval. Such maps show several characteristics caused by this constant value which are
still insufficiently investigated. In this work we demonstrate that in the discontinuous
flat top tent map every unstable periodic orbit may become a Milnor attractor. Moreover,
it turns...
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