A study of type I intermittency of a circular differential equation under a discontinuous right-hand side |
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Authors: | Chein-Shan Liu |
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Institution: | Department of Mechanical and Mechatronic Engineering, Taiwan Ocean University, Keelung, Taiwan |
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Abstract: | In this paper we study a circular differential equation under a discontinuous periodic input, developing a quadratic differential equations system on S1 and a linear differential equations system in the Minkowski space M3. The symmetry groups of these two systems are, respectively, PSOo(2,1) and SOo(2,1). The Poincaré circle map is constructed exactly, and a critical value αc of the parameter is identified. Depending on α of the input amplitude the equation may exhibit periodic, subharmonic or quasiperiodic motions. When α varies from α>αc to α<αc, there undergoes an inverse tangent bifurcation; consequently, the resultant Poincaré circle map offers one route to the quasiperiodicity via a type I intermittency. In the parameter range of α<αc the orbit generated by the Poincaré circle map is either m-periodic or quasiperiodic when n/m is a rational or an irrational number. |
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Keywords: | Circular differential equation Intermittency Quasiperiodicity Poincaré circle map Inverse tangent bifurcation Lorentz group |
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