کد مقاله | کد نشریه | سال انتشار | مقاله انگلیسی | نسخه تمام متن |
---|---|---|---|---|
1895309 | 1534007 | 2015 | 10 صفحه PDF | دانلود رایگان |

• Detailed bifurcation analysis for a relay control system with hysteresis.
• Demonstration of coexisting families of “hidden attractors”.
• Identification of typical bifurcations leading to the birth of “hidden attractors”.
For nonlinear dynamic systems with switching control, the concept of a “hidden attractor” naturally applies to a stable dynamic state that either (1) coexists with the stable switching cycle or (2), if the switching cycle is unstable, has a basin of attraction that does not intersect with the neighborhood of that cycle. We show how the equilibrium point of a relay system disappears in a boundary-equilibrium bifurcation as the system enters the region of autonomous switching dynamics and demonstrate experimentally how a relay system can exhibit large amplitude chaotic oscillations at high values of the supply voltage. By investigating a four-dimensional model of the experimental relay system we finally show how a variety of hidden periodic, quasiperiodic and chaotic attractors arise, transform and disappear through different bifurcations.
Journal: Physica D: Nonlinear Phenomena - Volume 306, 15 June 2015, Pages 6–15