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Local and global bifurcations in 3D piecewise smooth discontinuous maps
Mahashweta Patra1, Sayan Gupta2, Soumitro Banerjee3
1Department of Earth and Atmospheric Sciences, Indiana University, Bloomington, Indiana 47405, USA.
Abstract:
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.
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