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Academic Paper
Yuu Miino, Tetsushi Ueta, Hiroshi Kawakami, Bending angles of a broken line causing bifurcations and chaos, Institute of Electronics, Information and Communication Engineers, Nonlinear Theory and Its Applications, IEICE, Vol.11, No.3, 359-371, July 2020.
Abstract: We replace the cubic characteristics in the Duffing equation by two line segments connected at a point and investigate how an angle of that broken line conducts bifurcations to periodic orbits. Firstly we discuss differences in periodic orbits between the Duffing equation and a forced planar system including the broken line. In the latter system, a grazing bifurcation split the parameter space into the linear and nonlinear response domains. Also, we show that bifurcations of non-resonant periodic orbits appeared in the former system are suppressed in the latter system. Secondly, we obtain bifurcation diagrams by changing a slant parameter of the broken line. We also nd the parameter set that a homoclinic bifurcation arises and the corresponding horseshoe map. It is clari ed that a grazing bifurcation and tangent bifurcations form boundaries between linear and nonlinear responses. Finally, we explore the piecewise linear functions that show the minimum bending angles exhibiting bifurcation and chaos.


Contact address: ueta @ tokushima-u.ac.jp
2020-10-01