Local and global bifurcations in 3D piecewise smooth discontinuous maps. (English) Zbl 1467.37049
Summary: This paper approaches the problem of analyzing the bifurcation phenomena in three-dimensional discontinuous maps, using a piecewise linear approximation in the neighborhood of a border. The existence conditions of periodic orbits are analytically calculated and bifurcations of different periodic orbits are illustrated through numerical simulations. We have illustrated the peculiar features of discontinuous bifurcations involving a stable fixed point, a period-2 cycle, a saddle fixed point, etc. The occurrence of multiple attractor bifurcation and hyperchaos are also demonstrated.
©2021 American Institute of Physics
©2021 American Institute of Physics
MSC:
| 37G10 | Bifurcations of singular points in dynamical systems |
| 37G15 | Bifurcations of limit cycles and periodic orbits in dynamical systems |
| 37D45 | Strange attractors, chaotic dynamics of systems with hyperbolic behavior |
| 37C55 | Periodic and quasi-periodic flows and diffeomorphisms |
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