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Instruments and Systems: Monitoring, Control, and Diagnostics

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Region of asymptotic stability of the trivialequilibrium positions of the systems describedby difference equations quadratic
A.А. USKOV

Many mathematical models found quadratic differential equation (known in the literature as a quadratic map, logistic map, the map
Feigenbaum, display or display Verhulst Verhulst-Pearl) due to the following reasons:
1. Quadratic map if certain prerequisites is a model of the dynamics of population and is used in demography, population biology,
ecology and other fields.
2. Quadratic map is one of the fundamental equations of the theory of deterministic house showing how a relatively simple system
generates chaotic behavior.
3. Quadratic difference equation describes the dynamics of some of the technical facilities and systems, such as switched-capacitor
circuits, voltage converters with a jet with the actuator, closed control systems with local bilinear feedback, etc.
4. Autonomous dynamics of stationary nonlinear discrete systems of the first order under certain conditions described approximately
quadratic difference equation.
The paper first defined the exact boundaries of the initial conditions of the asymptotic stability of the trivial solution of quadratic
differential equations. In the approach to the determination of the stability region in the space of initial conditions of a dynamic system,
the essence of which is to define the original, though rather small, the region of stability, and then there are areas where the state
variables of the system are displayed in the previously defined area of sustainability. This approach titles “method related fields” and
can be used to study a variety of dynamic systems.
Keywords: asymptotic stability, quadratic differential equation, stability in the small region of stability

Contacts: E-mail: andrey@uskov.net

Pp. 13-20.

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