Affiliation:
1. Department of Applied Mechanics, Technical University of Lublin, Nadbystrzycka 36, PL-20-618 Lublin, Poland
Abstract
We have applied the Melnikov criterion to examine a global homoclinic bifurcation and transition to chaos in a case of the Duffing system with nonlinear fractional damping and external excitation. Using perturbation methods we have found a critical forcing amplitude above which the system may behave chaotically. The results have been verified by numerical simulations using standard nonlinear tools as Poincare maps and a Lyapunov exponent. Above the critical Melnikov amplitude μ_c, which a sufficient condition of a global homoclinic bifurcation, we have observed the region with a transient chaotic motion.
Funder
Polish Ministry of Science and Informatization
Subject
Mechanical Engineering,Mechanics of Materials,Geotechnical Engineering and Engineering Geology,Condensed Matter Physics,Civil and Structural Engineering
Cited by
48 articles.
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