Ordinary differential systems describing hysteresis effects and numerical simulations. (English) Zbl 1022.34038

Minchev, Emil; Okazaki, Takanobu; Kenmochi, Nobuyuki

Abstr. Appl. Anal. 7, No. 11, 563-583 (2002).

The authors consider a class of ordinary differential systems which describe input-output relations of hysteresis type and include, for example, scalar stop and play operators. The systems with scalar-valued controls (inputs) and solutions (outputs) consist of a scalar ordinary differential equation and a scalar differential inclusion, generical both with nonlinear terms.
The main theoretical result is an existence-uniqueness theorem for the initial value problem. Furthermore, the authors present examples of numerical simulations for particular choices of the coefficients in the linear part of the system and particular choices of nonlinearities and observe various types of the behavior of orbits on the input-output plane. This includes clockwise and anti-clockwise behavior and a number of long-term scenarios like convergence of orbits to an equilibrium, to a periodic orbit as well as to some point at infinity.

Reviewer: D. Rachinskii (Moskva)

MSC:

34C55	Hysteresis for ordinary differential equations
34A34	Nonlinear ordinary differential equations and systems

Keywords:

hysteresis nonlinearity; initial value problem; orientation of hysteresis loop; long-term behavior of orbits; scalar differential inclusion