The paper is devoted to investigation of the multistability in a multilevel pulse-modulated control system. The behavior of such systems is described by differential equations with discontinuous right-hand sides. As a specific example we consider a DC electric drive with a multilevel pulse modulated control.
We show that systems of this type can demonstrate a new type of multistability in which a several stable invariant tori coexist. Under such condition the action of external noise can induce a sadden transition from one dynamic state to another with different characteristics. These phenomena are extremely dangerous for the system.
We demonstrate that coexisting invariant tori can contain «heteroclinic loops» arising through a border-collision bifurcation. When the parameters are changed, the resonance torus with «heteroclinic loops» can transformed into a multilayered resonance torus through a global bifurcation.
Verghese G.C. Nonlinear Phenomena in Pow er Electronics // IEEE Press. New York. USA. 2001.
Mosekilde E. Bifurcations and Chaos in Piecewise-Smooth Dynamical Systems. World Scientific.
Di Bernardo M.,
Budd C.J., Champneys A.R., Kowalczyk P. Piecewise-Smooth Dynamical Systems:
Theory and Applications. London:
Nijmeijer H. Dynamics and Bifurcations of Non-Smooth Mechanical Systems. Berlin: Springer Verlag.
New York. 2004.
Mosekilde E. Border-Collision Bifurcations in a Dynamic Management Game //
Computers and Operations Research. 2006. V. 33. R. 464–478.
Yanochkina O.O., Mosekilde E. Coexisting Tori and Torus Bubbling in Non-Smooth
Systems // Physica D: Nonlinear Phenomena. 2011. V. 240. P. 397–405.