Torus destruction in a nonsmooth noninvertible map |
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Authors: | Soma DePartha Sharathi Dutta Soumitro Banerjee |
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Institution: | a Department of Mathematics and Centre for Theoretical Studies, Indian Institute of Technology, Kharagpur 721302, India b Theoretical Physics/Complex Systems, ICBM, Carl von Ossietzky Universität, PF 2503, 26111 Oldenburg, Germany c Department of Physics, Indian Institute of Science Education & Research, Mohanpur 741252, Nadia, West Bengal, India |
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Abstract: | We consider here a nonsmooth noninvertible map and report new route to chaos from a resonance loop torus which is not homeomorphic to circle but only endomorphic to it. We have found that cusp torus cannot develop before the onset of chaos, though the loop torus appears. The destruction of the loop torus occurs through homoclinic bifurcation in the presence of an infinite number of nonsmooth loops. We show that owing to the nonsmooth noninvertible nature of the map, the stable sets can bifurcate to form nonsmooth closed loops. However, that cannot be interpreted directly as basin bifurcation. |
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Keywords: | Piecewise-linear map Noninvertibility Homoclinic bifurcation Border collision bifurcation |
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