کد مقاله | کد نشریه | سال انتشار | مقاله انگلیسی | نسخه تمام متن |
---|---|---|---|---|
1891733 | 1043919 | 2012 | 15 صفحه PDF | دانلود رایگان |
In this work we consider a simple system of piecewise linear discontinuous 1D map with two discontinuity points: X′ = aX if ∣X∣ < z, X′ = bX if ∣X∣ > z, where a and b can take any real value, and may have several applications. We show that its dynamic behaviors are those of a linear rotation: either periodic or quasiperiodic, and always structurally unstable. A generalization to piecewise monotone functions X′ = F(X) if ∣X∣ < z, X′ = G(X) if ∣X∣ > z is also given, proving the conditions leading to a homeomorphism of the circle.
► A discontinuous 1D map with two discontinuity points is considered.
► Dynamic behaviors are either periodic or quasiperiodic.
► Dynamics are always structurally unstable.
► Any small perturbation in one of the parameters leads to different dynamics.
Journal: Chaos, Solitons & Fractals - Volume 45, Issue 11, November 2012, Pages 1328–1342