TY  - JOUR
AU  - Hosham, Hany A.
AU  - Alharthi, Thoraya N.
PY  - 2024
TI  - Bifurcation and chaos in simple discontinuous systems separated by a hypersurface
JO  - AIMS Mathematics
SP  - 17025
EP  - 17038
VL  - 9
IS  - 7
AB  - This research focuses on a mathematical examination of a path to sliding period doubling and chaotic behaviour for a novel limited discontinuous systems of dimension three separated by a nonlinear hypersurface. The switching system is composed of dissipative subsystems, one of which is a linear systems, and the other is not linked with equilibria. The non-linear sliding surface is designed to improve transient response for these subsystems. A Poincaré return map is created that accounts for the existence of the hypersurface, completely describing each individual sliding period-doubling orbits that route to the sliding chaotic attractor. Through a rigorous analysis, we show that the presence of a nonlinear sliding surface and a set of such hidden trajectories leads to novel bifurcation scenarios. The proposed system exhibits period-   m orbits as well as chaos, including partially hidden and sliding trajectories. The results are numerically verified through path-following techniques for discontinuous dynamical systems.
UR  - https://doi.org/10.3934/math.2024826
DO  - 10.3934/math.2024826