Torus destruction via global bifurcations in a piecewise-smooth, continuous map with square-root nonlinearity |
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Authors: | Partha Sharathi Dutta Soumitro Banerjee |
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Affiliation: | a Department of Mathematics and Centre for Theoretical Studies, Indian Institute of Technology, Kharagpur-721302, India b Department of Physics, Indian Institute of Science Education & Research, Mohanpur-741252, Nadia, West Bengal, India c Department of Mathematics, Indian Institute of Technology, Kharagpur-721302, India |
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Abstract: | It has been shown recently that torus formation in piecewise-smooth maps can occur through a special type of border collision bifurcation in which a pair of complex conjugate Floquet multipliers “jump” from the inside to the outside of the unit circle. It has also been shown that a large class of impacting mechanical systems yield piecewise-smooth maps with square-root singularity. In this Letter we investigate the dynamics of a two-dimensional piecewise-smooth map with square-root type nonlinearity, and describe two new routes to chaos through the destruction of two-frequency torus. In the first scenario, we identify the transition to chaos through the destruction of a loop torus via homoclinic bifurcation. In the other scenario, a change of structure in the torus occurs via heteroclinic saddle connections. Further parameter changes lead to a homoclinic bifurcation resulting in the creation of a chaotic attractor. However, this scenario is much more complex, with the appearance of a sequence of heteroclinic and homoclinic bifurcations. |
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Keywords: | 05.45.-a 05.45.Gg |
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