Abstract
In this paper we consider blinking systems, i.e. the systems randomly changing its structure in each sequential fixed period of time. Our goal is to find ghost attractors which arise in a blinking system being unexpectively different with respect to the attractors of composing systems. We study two blinking systems. One of them is a nonlinear rotator with switching torque and another is a blinking piecewise-linear Lorenz-type system. We prove the existence of ghost attractors in both cases for certain parameter ranges.
Highlights
The behaviour of a large number of living and technical systems can be represented as a process with instantaneous random changes in their structures
We show that there exist an interval of switching period 0 < τ < τ ∗ for which the blinking nonlinear rotator has oscillating ghost attractor
In this paper we presented blinking systems with instantaneous random switching between several autonomous systems in each fixed period of time
Summary
The behaviour of a large number of living and technical systems can be represented as a process with instantaneous random changes in their structures. The behaviour of pulse power converters can be modelled by a dynamical system, which parameters randomly and independently change their values in a piecewise-constant manner implying switching [Tse and Di Bernardo, 2002]. In literature such random and independent switching have been called blinking by analogy to blinking of an eye [Belykh et al, 2004], and systems with such o sort of switching got the name blinking systems. The attracting set corresponding to this behaviour has been called a ghost attractor In this talk we give examples of such systems in which we managed to find ghost attractors, and offer a way to find them in the general case
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