Abstract
Let Φ be a quasi-periodically forced quadratic map, where the rotation constant ω is a Diophantine irrational. A strange non-chaotic attractor (SNA) is an invariant (under Φ) attracting graph of a nowhere continuous measurable function ψ from the circle to .This paper investigates how a smooth attractor degenerates into a strange one, as a parameter approaches a critical value , and the asymptotics behind the bifurcation of the attractor from smooth to strange. In our model, the cause of the strange attractor is a so-called torus collision, whereby an attractor collides with a repeller.Our results show that the asymptotic minimum distance between the two colliding invariant curves decreases linearly in the parameter , as approaches the critical parameter value from below.Furthermore, we have been able to show that the asymptotic growth of the supremum of the derivative of the attracting graph is asymptotically bounded from both sides by a constant times the reciprocal of the square root of the minimum distance above.
Talk to us
Join us for a 30 min session where you can share your feedback and ask us any queries you have
Disclaimer: All third-party content on this website/platform is and will remain the property of their respective owners and is provided on "as is" basis without any warranties, express or implied. Use of third-party content does not indicate any affiliation, sponsorship with or endorsement by them. Any references to third-party content is to identify the corresponding services and shall be considered fair use under The CopyrightLaw.